Developing autonomous vehicles that can navigate complex environments with human-level safety and efficiency is a central goal in self-driving research. A common approach to achieving this is imitation learning, where agents are trained to mimic human expert demonstrations collected from real- world driving scenarios. However, discrepancies between human perception and the self-driving car's sensors can introduce an imitation gap, leading to imitation learning failures. In this work, we introduce IGDrivSim, a benchmark built on top of the Waymax simulator, designed to investigate the effects of the imitation gap in learning autonomous driving policy from human expert demonstrations. Our experiments show that this perception gap between human experts and selfdriving agents can hinder the learning of safe and effective driving behaviors. We further show that combining imitation with reinforcement learning, using a simple penalty reward for prohibited behaviors, effectively mitigates these failures. All code developed for this work is released as open source1.

Progress in offline reinforcement learning (RL) has been impeded by ambiguous problem definitions and entangled algorithmic designs, resulting in inconsistent implementations, insufficient ablations, and unfair evaluations. Although offline RL explicitly avoids environment interaction, prior methods frequently employ extensive, undocumented online evaluation for hyperparameter tuning, complicating method comparisons. Moreover, existing reference implementations differ significantly in boilerplate code, obscuring their core algorithmic contributions. We address these challenges by first introducing a rigorous taxonomy and a transparent evaluation protocol that explicitly quantifies online tuning budgets. To resolve opaque algorithmic design, we provide clean, minimalistic, single-file implementations of various model-free and model-based offline RL methods, significantly enhancing clarity and achieving substantial speed-ups. Leveraging these streamlined implementations, we propose Unifloral, a unified algorithm that encapsulates diverse prior approaches and enables development within a single, comprehensive hyperparameter space. Using Unifloral with our rigorous evaluation protocol, we develop two novel algorithms - TD3-AWR (model-free) and MoBRAC (model-based) - which substantially outperform established baselines. Our implementation is publicly available at https://github.com/EmptyJackson/unifloral.

Natural language can offer a concise and human-interpretable means of specifying reinforcement learning (RL) tasks. The ability to extract rewards from a language instruction can enable the development of robotic systems that can learn from human guidance; however, it remains a challenging problem, especially in visual environments. Existing approaches that employ large, pretrained language models either rely on non‑visual environment representations, require prohibitively large amounts of feedback, or generate noisy, ill‑shaped reward functions. In this paper, we propose a novel method, GoalLadder, that leverages vision-language models (VLMs) to train RL agents from a single language instruction in visual environments. GoalLadder works by incrementally discovering states that bring the agent closer to completing a task specified in natural language. To do so, it queries a VLM to identify states that represent an improvement in agent's task progress and to rank them using pairwise comparisons. Unlike prior work, GoalLadder does not trust VLM's feedback completely; instead, it uses it to rank potential goal states using an ELO-based rating system, thus reducing the detrimental effects of noisy VLM feedback. Over the course of training, the agent is tasked with minimising the distance to the top-ranked goal in a learned embedding space, which is trained on unlabelled visual data. This key feature allows us to bypass the need for abundant and accurate feedback typically required to train a well-shaped reward function. We demonstrate that GoalLadder outperforms existing related methods on classic control and robotic manipulation environments with the average final success rate of $\sim$95\% compared to only $\sim$45\% of the best competitor.

Recent advancements in meta-learning have enabled the automatic discovery of novel reinforcement learning algorithms parameterized by surrogate objective functions. To improve upon manually designed algorithms, the parameterization of this learned objective function must be expressive enough to represent novel principles of learning (instead of merely recovering already established ones) while still generalizing to a wide range of settings outside of its meta-training distribution. However, existing methods focus on discovering objective functions that, like many widely used objective functions in reinforcement learning, do not take into account the total number of steps allowed for training, or “training horizon”. In contrast, humans use a plethora of different learning objectives across the course of acquiring a new ability. For instance, students may alter their studying techniques based on the proximity to exam deadlines and their self-assessed capabilities. This paper contends that ignoring the optimization time horizon significantly restricts the expressive potential of discovered learning algorithms. We propose a simple augmentation to two existing objective discovery approaches that allows the discovered algorithm to dynamically update its objective function throughout the agent’s training procedure, resulting in expressive schedules and increased generalization across different training horizons. In the process, we find that commonly used meta-gradient approaches fail to discover such adaptive objective functions while evolution strategies discover highly dynamic learning rules. We demonstrate the effectiveness of our approach on a wide range of tasks and analyze the resulting learned algorithms, which we find effectively balance exploration and exploitation by modifying the structure of their learning rules throughout the agent’s lifetime.

Bayesian reinforcement learning (RL) offers a principled and elegant approach for sequential decision making under uncertainty. Most notably, Bayesian agents do not face an exploration/exploitation dilemma, a major pathology of frequentist methods. However theoretical understanding of model-free approaches is lacking. In this paper, we introduce a novel Bayesian model-free formulation and the first analysis showing that model-free approaches can yield Bayes-optimal policies. We show all existing model-free approaches make approximations that yield policies that can be arbitrarily Bayes-suboptimal. As a first step towards model-free Bayes optimality, we introduce the Bayesian exploration network (BEN) which uses normalising flows to model both the aleatoric uncertainty (via density estimation) and epistemic uncertainty (via variational inference) in the Bellman operator. In the limit of complete optimisation, BEN learns true Bayes-optimal policies, but like in variational expectation-maximisation, partial optimisation renders our approach tractable. Empirical results demonstrate that BEN can learn true Bayes-optimal policies in tasks where existing model-free approaches fail.

Learning a universal policy across different robot morphologies can significantly improve learning efficiency and enable zero-shot generalization to unseen morphologies. However, learning a highly performant universal policy requires sophisticated architectures like transformers (TF) that have larger memory and computational cost than simpler multi-layer perceptrons (MLP). To achieve both good performance like TF and high efficiency like MLP at inference time, we propose HyperDistill, which consists of: (1) A morphology-conditioned hypernetwork (HN) that generates robot-wise MLP policies, and (2) A policy distillation approach that is essential for successful training. We show that on UNIMAL, a benchmark with hundreds of diverse morphologies, HyperDistill performs as well as a universal TF teacher policy on both training and unseen test robots, but reduces model size by 6-14 times, and computational cost by 67-160 times in different environments. Our analysis attributes the efficiency advantage of HyperDistill at inference time to knowledge decoupling, i.e., the ability to decouple inter-task and intra-task knowledge, a general principle that could also be applied to improve inference efficiency in other domains. The code is publicly available at https://github.com/MasterXiong/Universal-Morphology-Control.

This paper introduces UniGen, a novel approach to generating new traffic scenarios for evaluating and improving autonomous driving software through simulation. Our approach models all driving scenario elements in a unified model: the position of new agents, their initial state, and their future motion trajectories. By predicting the distributions of all these variables from a shared global scenario embedding, we ensure that the final generated scenario is fully conditioned on all available context in the existing scene. Our unified modeling approach, combined with autoregressive agent injection, conditions the placement and motion trajectory of every new agent on all existing agents and their trajectories, leading to realistic scenarios with low collision rates. Our experimental results show that UniGen outperforms prior state of the art on the Waymo Open Motion Dataset.

In reinforcement learning (RL), it is common to apply techniques used broadly in machine learning such as neural network function approximators and momentum-based optimizers. However, such tools were largely developed for supervised learning rather than nonstationary RL, leading practitioners to adopt target networks, clipped policy updates, and other RL-specific implementation tricks to combat this mismatch, rather than directly adapting this toolchain for use in RL. In this paper, we take a different approach and instead address the effect of nonstationarity by adapting the widely used Adam optimiser. We first analyse the impact of nonstationary gradient magnitude --- such as that caused by a change in target network --- on Adam's update size, demonstrating that such a change can lead to large updates and hence sub-optimal performance. To address this, we introduce Adam-Rel. Rather than using the global timestep in the Adam update, Adam-Rel uses the *local* timestep within an epoch, essentially resetting Adam's timestep to 0 after target changes. We demonstrate that this avoids large updates and reduces to learning rate annealing in the absence of such increases in gradient magnitude. Evaluating Adam-Rel in both on-policy and off-policy RL, we demonstrate improved performance in both Atari and Craftax. We then show that increases in gradient norm occur in RL in practice, and examine the differences between our theoretical model and the observed data.

While reinforcement learning (RL) holds great potential for decision making in the real world, it suffers from a number of unique difficulties which often need specific consideration. In particular: it is highly non-stationary; suffers from high degrees of plasticity loss; and requires exploration to prevent premature convergence to local optima and maximize return. In this paper, we consider whether learned optimization can help overcome these problems. Our method, Learned **O**ptimization for **P**lasticity, **E**xploration and **N**on-stationarity (*OPEN*), meta-learns an update rule whose input features and output structure are informed by previously proposed solutions to these difficulties. We show that our parameterization is flexible enough to enable meta-learning in diverse learning contexts, including the ability to use stochasticity for exploration. Our experiments demonstrate that when meta-trained on single and small sets of environments, *OPEN* outperforms or equals traditionally used optimizers. Furthermore, *OPEN* shows strong generalization characteristics across a range of environments and agent architectures.

Benchmarks are crucial in the development of machine learning algorithms, significantly influencing reinforcement learning (RL) research through the available environments. Traditionally, RL environments run on the CPU, which limits their scalability with the computational resources typically available in academia. However, recent advancements in JAX have enabled the wider use of hardware acceleration, enabling massively parallel RL training pipelines and environments. While this has been successfully applied to single-agent RL, it has not yet been widely adopted for multi-agent scenarios. In this paper, we present JaxMARL, the first open-source, easy-to-use code base that combines GPU-enabled efficiency with support for a large number of commonly used MARL environments and popular baseline algorithms. Our experiments show that, in terms of wall clock time, our JAX-based training pipeline is up to 12,500 times faster than existing approaches. This enables efficient and thorough evaluations, potentially alleviating the evaluation crisis in the field. We also introduce and benchmark SMAX, a vectorised, simplified version of the popular StarCraft Multi-Agent Challenge, which removes the need to run the StarCraft II game engine. This not only enables GPU acceleration, but also provides a more flexible MARL environment, unlocking the potential for self-play, meta-learning, and other future applications in MARL. The code is available at https://github.com/flairox/jaxmarl.

Integral to recent successes in deep reinforcement learning has been a class of temporal difference methods that use infrequently updated target values for policy evaluation in a Markov Decision Process. Yet a complete theoretical explanation for the effectiveness of target networks remains elusive. In this work, we provide an analysis of this popular class of algorithms, to finally answer the question: “why do target networks stabilise TD learning”? To do so, we formalise the notion of a partially fitted policy evaluation method, which describes the use of target networks and bridges the gap between fitted methods and semigradient temporal difference algorithms. Using this framework we are able to uniquely characterise the so-called deadly triad–the use of TD updates with (nonlinear) function approximation and off-policy data–which often leads to nonconvergent algorithms.This insight leads us to conclude that the use of target networks can mitigate the effects of poor conditioning in the Jacobian of the TD update. Instead, we show that under mild regularity con- ditions and a well tuned target network update frequency, convergence can be guaranteed even in the extremely challenging off-policy sampling and nonlinear function approximation setting.

Learning a universal policy across different robot morphologies can significantly improve learning efficiency and generalization in continuous control. However, it poses a challenging multi-task reinforcement learning problem, as the optimal policy may be quite different across robots and critically depend on the morphology. Existing methods utilize graph neural networks or transformers to handle heterogeneous state and action spaces across different morphologies, but pay little attention to the dependency of a robot’s control policy on its morphology context. In this paper, we propose a hierarchical architecture to better model this dependency via contextual modulation, which includes two key submodules: (1) Instead of enforcing hard parameter sharing across robots, we use hypernetworks to generate morphology-dependent control parameters; (2) We propose a fixed attention mechanism that solely depends on the morphology to modulate the interactions between different limbs in a robot. Experimental results show that our method not only improves learning performance on a diverse set of training robots, but also generalizes better to unseen morphologies in a zero-shot fashion. The code is publicly available at https://github.com/MasterXiong/ModuMorph.

Many applications of imitation learning require the agent to generate the full distribution of behaviour observed in the training data. For example, to evaluate the safety of autonomous vehicles in simulation, accurate and diverse behaviour models of other road users are paramount. Existing methods that improve this distributional realism typically rely on hierarchical policies. These condition the policy on types such as goals or personas that give rise to multi-modal behaviour. However, such methods are often inappropriate for stochastic environments where the agent must also react to external factors: because agent types are inferred from the observed future trajectory during training, these environments require that the contributions of internal and external factors to the agent behaviour are disentangled and only internal factors, i.e., those under the agent's control, are encoded in the type. Encoding future information about external factors leads to inappropriate agent reactions during testing, when the future is unknown and types must be drawn independently from the actual future. We formalize this challenge as distribution shift in the conditional distribution of agent types under environmental stochasticity. We propose Robust Type Conditioning (RTC), which eliminates this shift with adversarial training under randomly sampled types. Experiments on two domains, including the large-scale Waymo Open Motion Dataset, show improved distributional realism while maintaining or improving task performance compared to state-of-the-art baselines.

Imitation learning (IL) is a simple and powerful way to use high-quality human driving data, which can be collected at scale, to produce human-like behavior. However, policies based on imitation learning alone often fail to sufficiently account for safety and reliability concerns. In this paper, we show how imitation learning combined with reinforcement learning using simple rewards can substan-tially improve the safety and reliability of driving policies over those learned from imitation alone. In particular, we train a policy on over lOOk miles of urban driving data, and measure its effectiveness in test scenarios grouped by different levels of collision likelihood. Our analysis shows that while imitation can perform well in low-difficulty scenarios that are well-covered by the demonstration data, our proposed approach significantly improves robustness on the most challenging scenarios (over 38 % reduction in failures). To our knowledge, this is the first application of a combined imitation and reinforcement learning approach in autonomous driving that utilizes large amounts of real- world human driving data.

Deep reinforcement learning (RL) is notoriously impractical to deploy due to sample inefficiency. Meta-RL directly addresses this sample inefficiency by learning to perform few-shot learning when a distribution of related tasks is available for meta-training. While many specialized meta-RL methods have been proposed, recent work suggests that end-to-end learning in conjunction with an off-the-shelf sequential model, such as a recurrent network, is a surprisingly strong baseline. However, such claims have been controversial due to limited supporting evidence, particularly in the face of prior work establishing precisely the opposite. In this paper, we conduct an empirical investigation. While we likewise find that a recurrent network can achieve strong performance, we demonstrate that the use of hypernetworks is crucial to maximizing their potential. Surprisingly, when combined with hypernetworks, the recurrent baselines that are far simpler than existing specialized methods actually achieve the strongest performance of all methods evaluated. We provide code at https://github.com/jacooba/hyper.

The availability of challenging benchmarks has played a key role in the recent progress of machine learning. In cooperative multi-agent reinforcement learning, the StarCraft Multi-Agent Challenge (SMAC) has become a popular testbed for centralised training with decentralised execution. However, after years of sustained improvement on SMAC, algorithms now achieve near-perfect performance. In this work, we conduct new analysis demonstrating that SMAC lacks the stochasticity and partial observability to require complex closed-loop policies. In particular, we show that an open-loop policy conditioned only on the timestep can achieve non-trivial win rates for many SMAC scenarios. To address this limitation, we introduce SMACv2, a new version of the benchmark where scenarios are procedurally generated and require agents to generalise to previously unseen settings (from the same distribution) during evaluation. We also introduce the extended partial observability challenge (EPO), which augments SMACv2 to ensure meaningful partial observability. We show that these changes ensure the benchmarkrequires the use of closed-loop policies. We evaluate state-of-the-art algorithms on SMACv2 and show that it presents significant challenges not present in the original benchmark. Our analysis illustrates that SMACv2 addresses the discovered deficiencies of SMAC and can help benchmark the next generation of MARL methods. Videos of training are available on our website.

The past decade has seen vast progress in deep reinforcement learning (RL) on the back of algorithms manually designed by human researchers. Recently, it has been shown that it is possible to meta-learn update rules, with the hope of discovering algorithms that can perform well on a wide range of RL tasks. Despite impressive initial results from algorithms such as Learned Policy Gradient (LPG), there remains a generalization gap when these algorithms are applied to unseen environments. In this work, we examine how characteristics of the meta-training distribution impact the generalization performance of these algorithms. Motivated by this analysis and building on ideas from Unsupervised Environment Design (UED), we propose a novel approach for automatically generating curricula to maximize the regret of a meta-learned optimizer, in addition to a novel approximation of regret, which we name algorithmic regret (AR). The result is our method, General RL Optimizers Obtained Via Environment Design (GROOVE). In a series of experiments, we show that GROOVE achieves superior generalization to LPG, and evaluate AR against baseline metrics from UED, identifying it as a critical component of environment design in this setting. We believe this approach is a step towards the discovery of truly general RL algorithms, capable of solving a wide range of real-world environments.

Simulation with realistic, interactive agents represents a key task for autonomous vehicle software development. In this work, we introduce the Waymo Open Sim Agents Challenge (WOSAC). WOSAC is the first public challenge to tackle this task and propose corresponding metrics. The goal of the challenge is to stimulate the design of realistic simulators that can be used to evaluate and train a behavior model for autonomous driving. We outline our evaluation methodology, present results for a number of different baseline simulation agent methods, and analyze several submissions to the 2023 competition which ran from March 16, 2023 to May 23, 2023. The WOSAC evaluation server remains open for submissions and we discuss open problems for the task.

Sample efficiency is crucial for imitation learning methods to be applicable in real-world applications. Many studies improve sample efficiency by extending adversarial imitation to be off-policy regardless of the fact that these off-policy extensions could either change the original objective or involve complicated optimization. We revisit the foundation of adversarial imitation and propose an off-policy sample efficient approach that requires no adversarial training or min-max optimization. Our formulation capitalizes on two key insights: (1) the similarity between the Bellman equation and the stationary state-action distribution equation allows us to derive a novel temporal difference (TD) learning approach; and (2) the use of a deterministic policy simplifies the TD learning. Combined, these insights yield a practical algorithm, Deterministic and Discriminative Imitation (D2-Imitation), which oper- ates by first partitioning samples into two replay buffers and then learning a deterministic policy via off-policy reinforcement learning. Our empirical results show that D2-Imitation is effective in achieving good sample efficiency, outperforming several off-policy extension approaches of adversarial imitation on many control tasks.

Self-play is a common method for constructing solutions in Markov games that can yield optimal policies in collaborative settings. However, these policies often adopt highly-specialized conventions that make playing with a novel partner difficult. To address this, recent approaches rely on encoding symmetry and convention-awareness into policy training, but these require strong environmental assumptions and can complicate policy training. To overcome this, we propose moving the learning of conventions to the belief space. Specifically, we propose a belief learning paradigm that can maintain beliefs over rollouts of policies not seen at training time, and can thus decode and adapt to novel conventions at test time. We show how to leverage this belief model for both search and training of a best response over a pool of policies to greatly improve zero-shot coordination. We also show how our paradigm promotes explainability and interpretability of nuanced agent conventions.

We consider the problem of communicating exogenous information by means of Markov decision process trajectories. This setting, which we call a Markov coding game (MCG), generalizes both source coding and a large class of referential games. MCGs also isolate a problem that is important in decentralized control settings in which cheap-talk is not available—namely, they require balancing communication with the associated cost of communicating. We contribute a theoretically grounded approach to MCGs based on maximum entropy reinforcement learning and minimum entropy coupling that we call MEME. Due to recent breakthroughs in approximation algorithms for minimum entropy coupling, MEME is not merely a theoretical algorithm, but can be applied to practical settings. Empirically, we show both that MEME is able to outperform a strong baseline on small MCGs and that MEME is able to achieve strong performance on extremely large MCGs. To the latter point, we demonstrate that MEME is able to losslessly communicate binary images via trajectories of Cartpole and Pong, while simultaneously achieving the maximal or near maximal expected returns, and that it is even capable of performing well in the presence of actuator noise.

Simulation is a crucial tool for accelerating the development of autonomous vehicles. Making simulation realistic requires models of the human road users who interact with such cars. Such models can be obtained by applying learning from demonstration (LfD) to trajectories observed by cars already on the road. However, existing LfD methods are typically insufficient, yielding policies that frequently collide or drive off the road. To address this problem, we propose Symphony, which greatly improves realism by combining conventional policies with a parallel beam search. The beam search refines these policies on the fly by pruning branches that are unfavourably evaluated by a discriminator. However, it can also harm diversity, i.e., how well the agents cover the entire distribution of realistic behaviour, as pruning can encourage mode collapse. Symphony addresses this issue with a hierarchical approach, factoring agent behaviour into goal generation and goal conditioning. The use of such goals ensures that agent diversity neither disappears during adversarial training nor is pruned away by the beam search. Experiments on both proprietary and open Waymo datasets confirm that Symphony agents learn more realistic and diverse behaviour than several baselines.

We demonstrate the first large-scale application of model-based generative adversarial imitation learning (MGAIL) to the task of dense urban self-driving. We augment standard MGAIL using a hierarchical model to enable generalization to arbitrary goal routes, and measure performance using a closed-loop evaluation framework with simulated interactive agents. We train policies from expert trajectories collected from real vehicles driving over 100,000 miles in San Francisco, and demonstrate a steerable policy that can navigate robustly even in a zero-shot setting, generalizing to synthetic scenarios with novel goals that never occurred in real-world driving. We also demonstrate the importance of mixing closed-loop MGAIL losses with open-loop behavior cloning losses, and show our best policy approaches the performance of the expert. We evaluate our imitative model in both average and challenging scenarios, and show how it can serve as a useful prior to plan successful trajectories.

Recent multi-task learning research argues against unitary scalarization, where training simply minimizes the sum of the task losses. Several ad-hoc multi-task optimization algorithms have instead been proposed, inspired by various hypotheses about what makes multi-task settings difficult. The majority of these optimizers require per-task gradients, and introduce significant memory, runtime, and implementation overhead. We show that unitary scalarization, coupled with standard regularization and stabilization techniques from single-task learning, matches or improves upon the performance of complex multi-task optimizers in popular supervised and reinforcement learning settings. We then present an analysis suggesting that many specialized multi-task optimizers can be partly interpreted as forms of regularization, potentially explaining our surprising results. We believe our results call for a critical reevaluation of recent research in the area.

Successful coordination in Dec-POMDPs requires agents to adopt robust strategies and interpretable styles of play for their partner. A common failure mode is symmetry breaking, when agents arbitrarily converge on one out of many equivalent but mutually incompatible policies. Commonly these examples include partial observability, e.g. waving your right hand vs. left hand to convey a covert message. In this paper, we present a novel equivariant network architecture for use in Dec-POMDPs that prevents the agent from learning policies which break symmetries, doing so more effectively than prior methods. Our method also acts as a "coordination-improvement operator" for generic, pre-trained policies, and thus may be applied at test-time in conjunction with any self-play algorithm. We provide theoretical guarantees of our work and test on the AI benchmark task of Hanabi, where we demonstrate our methods outperforming other symmetry-aware baselines in zero-shot coordination, as well as able to improve the coordination ability of a variety of pre-trained policies. In particular, we show our method can be used to improve on the state of the art for zero-shot coordination on the Hanabi benchmark.

Emphatic Temporal Difference (TD) methods are a class of off-policy Reinforcement Learning (RL) methods involving the use of followon traces. Despite the theoretical success of emphatic TD methods in addressing the notorious deadly triad of off-policy RL, there are still two open problems. First, followon traces typically suffer from large variance, making them hard to use in practice. Second, though Yu (2015) confirms the asymptotic convergence of some emphatic TD methods for prediction problems, there is still no finite sample analysis for any emphatic TD method for prediction, much less control. In this paper, we address those two open problems simultaneously via using truncated followon traces in emphatic TD methods. Unlike the original followon traces, which depend on all previous history, truncated followon traces depend on only finite history, reducing variance and enabling the finite sample analysis of our proposed emphatic TD methods for both prediction and control.

We present a mean-variance policy iteration (MVPI) framework for risk-averse control in a discounted infinite horizon MDP optimizing the variance of a per-step reward random variable. MVPI enjoys great flexibility in that any policy evaluation method and risk-neutral control method can be dropped in for risk-averse control off the shelf, in both on- and off-policy settings. This flexibility reduces the gap between risk-neutral control and risk-averse control and is achieved by working on a novel augmented MDP directly. We propose risk-averse TD3 as an example instantiating MVPI, which outperforms vanilla TD3 and many previous risk-averse control methods in challenging Mujoco robot simulation tasks under a risk-aware performance metric. This risk-averse TD3 is the first to introduce deterministic policies and off-policy learning into risk-averse reinforcement learning, both of which are key to the performance boost we show in Mujoco domains.

VDN and QMIX are two popular value-based algorithms for cooperative MARL that learn a centralized action value function as a monotonic mixing of per-agent utilities. While this enables easy decentralization of the learned policy, the restricted joint action value function can prevent them from solving tasks that require significant coordination between agents at a given timestep. We show that this problem can be overcome by improving the joint exploration of all agents during training. Specifically, we propose a novel MARL approach called Universal Value Exploration (UneVEn) that learns a set of related tasks simultaneously with a linear decomposition of universal successor features. With the policies of already solved related tasks, the joint exploration process of all agents can be improved to help them achieve better coordination. Empirical results on a set of exploration games, challenging cooperative predator-prey tasks requiring significant coordination among agents, and StarCraft II micromanagement benchmarks show that UneVEn can solve tasks where other state-of-the-art MARL methods fail.

Multi-agent settings in the real world often involve tasks with varying types and quantities of agents and non-agent entities; however, common patterns of behavior often emerge among these agents/entities. Our method aims to leverage these commonalities by asking the question: “What is the expected utility of each agent when only considering a randomly selected sub-group of its observed entities?” By posing this counterfactual question, we can recognize state-action trajectories within sub-groups of entities that we may have encountered in another task and use what we learned in that task to inform our prediction in the current one. We then reconstruct a prediction of the full returns as a combination of factors considering these disjoint groups of entities and train this “randomly factorized" value function as an auxiliary objective for value-based multi-agent reinforcement learning. By doing so, our model can recognize and leverage similarities across tasks to improve learning efficiency in a multi-task setting. Our approach, Randomized Entity-wise Factorization for Imagined Learning (REFIL), outperforms all strong baselines by a significant margin in challenging multi-task StarCraft micromanagement settings.

Reinforcement Learning in large action spaces is a challenging problem. This is especially true for cooperative multi-agent reinforcement learning (MARL), which often requires tractable learning while respecting various constraints like communication budget and information about other agents. In this work, we focus on the fundamental hurdle affecting both value-based and policy-gradient approaches: an exponential blowup of the action space with the number of agents. For value-based methods, it poses challenges in accurately representing the optimal value function for value-based methods, thus inducing suboptimality. For policy gradient methods, it renders the critic ineffective and exacerbates the problem of the lagging critic. We show that from a learning theory perspective, both problems can be addressed by accurately representing the associated action-value function with a low-complexity hypothesis class. This requires accurately modelling the agent interactions in a sample efficient way. To this end, we propose a novel tensorised formulation of the Bellman equation. This gives rise to our method Tesseract, which utilises the view of Q-function seen as a tensor where the modes correspond to action spaces of different agents. Algorithms derived from Tesseract decompose the Q-tensor across the agents and utilise low-rank tensor approximations to model the agent interactions relevant to the task. We provide PAC analysis for Tesseract based algorithms and highlight their relevance to the class of rich observation MDPs. Empirical results in different domains confirm the gains in sample efficiency using Tesseract as supported by the theory.

We consider off-policy policy evaluation with function approximation (FA) in average-reward MDPs, where the goal is to estimate both the reward rate and the differential value function. For this problem, bootstrapping is necessary and, along with off-policy learning and FA, results in the deadly triad (Sutton & Barto, 2018). To address the deadly triad, we propose two novel algorithms, reproducing the celebrated success of Gradient TD algorithms in the average-reward setting. In terms of estimating the differential value function, the algorithms are the first convergent off-policy linear function approximation algorithms. In terms of estimating the reward rate, the algorithms are the first convergent off-policy linear function approximation algorithms that do not require estimating the density ratio. We demonstrate empirically the advantage of the proposed algorithms, as well as their nonlinear variants, over a competitive density-ratio-based approach, in a simple domain as well as challenging robot simulation tasks.

The deadly triad refers to the instability of a reinforcement learning algorithm when it employs off-policy learning, function approximation, and bootstrapping simultaneously. In this paper, we investigate the target network as a tool for breaking the deadly triad, providing theoretical support for the conventional wisdom that a target network stabilizes training. We first propose and analyze a novel target network update rule which augments the commonly used Polyak-averaging style update with two projections. We then apply the target network and ridge regularization in several divergent algorithms and show their convergence to regularized TD fixed points. Those algorithms are off-policy with linear function approximation and bootstrapping, spanning both policy evaluation and control, as well as both discounted and average-reward settings. In particular, we provide the first convergent linear $Q$-learning algorithms under nonrestrictive and changing behavior policies without bi-level optimization.

To rapidly learn a new task, it is often essential for agents to explore efficiently - especially when performance matters from the first timestep. One way to learn such behaviour is via meta-learning. Many existing methods however rely on dense rewards for meta-training, and can fail catastrophically if the rewards are sparse. Without a suitable reward signal, the need for exploration during meta-training is exacerbated. To address this, we propose HyperX, which uses novel reward bonuses for meta-training to explore in approximate hyper-state space (where hyper-states represent the environment state and the agent’s task belief). We show empirically that HyperX meta-learns better task-exploration and adapts more successfully to new tasks than existing methods.

We revisit residual algorithms in both model-free and model-based reinforcement learning settings. We propose the bidirectional target network technique to stabilize residual algorithms, yielding a residual version of DDPG that significantly outperforms vanilla DDPG in commonly used benchmarks. Moreover, we find the residual algorithm an effective approach to the distribution mismatch problem in model-based planning. Compared with the existing TD(k) method, our residual-based method makes weaker assumptions about the model and yields a greater performance boost.

Recent research has shown that graph neural networks (GNNs) can learn policies for locomotion control that are as effective as a typical multi-layer perceptron (MLP), with superior transfer and multi-task performance. However, results have so far been limited to training on small agents, with the performance of GNNs deteriorating rapidly as the number of sensors and actuators grows. A key motivation for the use of GNNs in the supervised learning setting is their applicability to large graphs, but this benefit has not yet been realised for locomotion control. We show that poor scaling in GNNs is a result of increasingly unstable policy updates, caused by overfitting in parts of the network during training. To combat this, we introduce Snowflake, a GNN training method for high-dimensional continuous control that freezes parameters in selected parts of the network. Snowflake significantly boosts the performance of GNNs for locomotion control on large agents, now matching the performance of MLPs while offering superior transfer properties.

We introduce a novel perspective on Bayesian reinforcement learning (RL); whereas existing approaches infer a posterior over the transition distribution or Q-function, we characterise the uncertainty in the Bellman operator. Our Bayesian Bellman operator (BBO) framework is motivated by the insight that when bootstrapping is introduced, model-free approaches actually infer a posterior over Bellman operators, not value functions. In this paper, we use BBO to provide a rigorous theoretical analysis of model-free Bayesian RL to better understand its relationship to established frequentist RL methodologies. We prove that Bayesian solutions are consistent with frequentist RL solutions, even when approximate inference is used, and derive conditions for which convergence properties hold. Empirically, we demonstrate that algorithms derived from the BBO framework have sophisticated deep exploration properties that enable them to solve continuous control tasks at which state-of-the-art regularised actor-critic algorithms fail catastrophically.

Tackling overestimation in $Q$-learning is an important problem that has been extensively studied in single-agent reinforcement learning, but has received comparatively little attention in the multi-agent setting. In this work, we empirically demonstrate that QMIX, a popular $Q$-learning algorithm for cooperative multi-agent reinforcement learning (MARL), suffers from a more severe overestimation in practice than previously acknowledged, and is not mitigated by existing approaches. We rectify this with a novel regularization-based update scheme that penalizes large joint action-values that deviate from a baseline and demonstrate its effectiveness in stabilizing learning. Furthermore, we propose to employ a softmax operator, which we efficiently approximate in a novel way in the multi-agent setting, to further reduce the potential overestimation bias. Our approach, Regularized Softmax (RES) Deep Multi-Agent $Q$-Learning, is general and can be applied to any $Q$-learning based MARL algorithm. We demonstrate that, when applied to QMIX, RES avoids severe overestimation and significantly improves performance, yielding state-of-the-art results in a variety of cooperative multi-agent tasks, including the challenging StarCraft II micromanagement benchmarks.

We propose FACtored Multi-Agent Centralised policy gradients (FACMAC), a new method for cooperative multi-agent reinforcement learning in both discrete and continuous action spaces. Like MADDPG, a popular multi-agent actor-critic method, our approach uses deep deterministic policy gradients to learn policies. However, FACMAC learns a centralised but factored critic, which combines per-agent utilities into the joint action-value function via a non-linear monotonic function, as in QMIX, a popular multi-agent $Q$-learning algorithm. However, unlike QMIX, there are no inherent constraints on factoring the critic. We thus also employ a nonmonotonic factorisation and empirically demonstrate that its increased representational capacity allows it to solve some tasks that cannot be solved with monolithic, or monotonically factored critics. In addition, FACMAC uses a centralised policy gradient estimator that optimises over the entire joint action space, rather than optimising over each agent's action space separately as in MADDPG. This allows for more coordinated policy changes and fully reaps the benefits of a centralised critic. We evaluate FACMAC on variants of the multi-agent particle environments, a novel multi-agent MuJoCo benchmark, and a challenging set of StarCraft II micromanagement tasks. Empirical results demonstrate FACMAC's superior performance over MADDPG and other baselines on all three domains.

Recent years have seen the application of deep reinforcement learning techniques to cooperative multi-agent systems, with great empirical success. However, given the lack of theoretical insight, it remains unclear what the employed neural networks are learning, or how we should enhance their learning power to address the problems on which they fail. In this work, we empirically investigate the learning power of various network architectures on a series of one-shot games. Despite their simplicity, these games capture many of the crucial problems that arise in the multi-agent setting, such as an exponential number of joint actions or the lack of an explicit coordination mechanism. Our results extend those in Castellini et al. (Proceedings of the 18th International Conference on Autonomous Agents and MultiAgent Systems, AAMAS'19.International Foundation for Autonomous Agents and Multiagent Systems, pp 1862-1864, 2019) and quantify how well various approaches can represent the requisite value functions, and help us identify the reasons that can impede good performance, like sparsity of the values or too tight coordination requirements.

Trading off exploration and exploitation in an unknown environment is key to maximising expected online return during learning. A Bayes-optimal policy, which does so optimally, conditions its actions not only on the environment state but also on the agent's uncertainty about the environment. Computing a Bayes-optimal policy is however intractable for all but the smallest tasks. In this paper, we introduce variational Bayes-Adaptive Deep RL (variBAD), a way to meta-learn approximately Bayes-optimal policies for complex tasks. VariBAD simultaneously meta-learns a variational auto-encoder to perform approximate inference, and a policy that incorporates task uncertainty directly during action selection by conditioning on both the environment state and the approximate belief. In two toy domains, we illustrate how variBAD performs structured online exploration as a function of task uncertainty. We further evaluate variBAD on MuJoCo tasks widely used in meta-RL and show that it achieves higher online return than existing methods. On the recently proposed Meta-World ML1 benchmark, variBAD achieves state of the art results by a large margin, fully solving two out of the three ML1 tasks for the first time.

This paper introduces the deep coordination graph (DCG) for collaborative multi-agent reinforcement learning. DCG strikes a flexible trade-off between representational capacity and generalization by factoring the joint value function of all agents according to a coordination graph into payoffs between pairs of agents. The value can be maximized by local message passing along the graph, which allows training of the value function end-to-end with Q-learning. Payoff functions are approximated with deep neural networks that employ parameter sharing and low-rank approximations to significantly improve sample efficiency. We show that DCG can solve predator-prey tasks that highlight the relative overgeneralization pathology, as well as challenging StarCraft II micromanagement tasks.

In complex tasks, such as those with large combinatorial action spaces, random exploration may be too inefficient to achieve meaningful learning progress. In this work, we use a curriculum of progressively growing action spaces to accelerate learning. We assume the environment is out of our control, but that the agent may set an internal curriculum by initially restricting its action space. Our approach uses off-policy reinforcement learning to estimate optimal value functions for multiple action spaces simultaneously and efficiently transfers data, value estimates, and state representations from restricted action spaces to the full task. We show the efficacy of our approach in proof-of-concept control tasks and on challenging large-scale StarCraft micromanagement tasks with large, multi-agent action spaces.

We present GradientDICE for estimating the density ratio between the state distribution of the target policy and the sampling distribution in off-policy reinforcement learning. GradientDICE fixes several problems of GenDICE (Zhang et al., 2020), the current state-of-the-art for estimating such density ratios. Namely, the optimization problem in GenDICE is not a convex-concave saddle-point problem once nonlinearity in optimization variable parameterization is introduced to ensure positivity, so primal-dual algorithms are not guaranteed to find the desired solution. However, such nonlinearity is essential to ensure the consistency of GenDICE even with a tabular representation. This is a fundamental contradiction, resulting from GenDICE’s original formulation of the optimization problem. In GradientDICE, we optimize a different objective from GenDICE by using the Perron-Frobenius theorem and eliminating GenDICE’s use of divergence, such that nonlinearity in parameterization is not necessary for GradientDICE, which is provably convergent under linear function approximation.

We present the first provably convergent two-timescale off-policy actor-critic algorithm (COF-PAC) with function approximation. Key to COF-PAC is the introduction of a new critic, the emphasis critic, which is trained via Gradient Emphasis Learning (GEM), a novel combination of the key ideas of Gradient Temporal Difference Learning and Emphatic Temporal Difference Learning. With the help of the emphasis critic and the canonical value function critic, we show convergence for COF-PAC, where the critics are linear and the actor can be nonlinear.

We present Graph-Q-SAT, a branching heuristic for a Boolean SAT solver trained with value-based reinforcement learning (RL) using Graph Neural Networks for function approximation. Solvers using Graph-Q-SAT are complete SAT solvers that either provide a satisfying assignment or proof of unsatisfiability, which is required for many SAT applications. The branching heuristics commonly used in SAT solvers make poor decisions during their warm-up period, whereas Graph-Q-SAT is trained to examine the structure of the particular problem instance to make better decisions early in the search. Training Graph-Q-SAT is data efficient and does not require elaborate dataset preparation or feature engineering. We train Graph-Q-SAT using RL interfacing with MiniSat solver and show that Graph-Q-SAT can reduce the number of iterations required to solve SAT problems by 2-3X. Furthermore, it generalizes to unsatisfiable SAT instances, as well as to problems with 5X more variables than it was trained on. We show that for larger problems, reductions in the number of iterations lead to wall clock time reductions, the ultimate goal when designing heuristics. We also show positive zero-shot transfer behavior when testing Graph-Q-SAT on a task family different from that used for training. While more work is needed to apply Graph-Q-SAT to reduce wall clock time in modern SAT solving settings, it is a compelling proof-of-concept showing that RL equipped with Graph Neural Networks can learn a generalizable branching heuristic for SAT search.

QMIX is a popular $Q$-learning algorithm for cooperative MARL in the centralised training and decentralised execution paradigm. In order to enable easy decentralisation, QMIX restricts the joint action $Q$-values it can represent to be a monotonic mixing of each agent's utilities. However, this restriction prevents it from representing value functions in which an agent's ordering over its actions can depend on other agents' actions. To analyse this representational limitation, we first formalise the objective QMIX optimises, which allows us to view QMIX as an operator that first computes the $Q$-learning targets and then projects them into the space representable by QMIX. This projection returns a representable $Q$-value that minimises the unweighted squared error across all joint actions. We show in particular that this projection can fail to recover the optimal policy even with access to $Q^*$, which primarily stems from the equal weighting placed on each joint action. We rectify this by introducing a weighting into the projection, in order to place more importance on the better joint actions. We propose two weighting schemes and prove that they recover the correct maximal action for any joint action $Q$-values, and therefore for $Q^*$ as well. Based on our analysis and results in the tabular setting we introduce two scalable versions of our algorithm, Centrally-Weighted (CW) QMIX and Optimistically-Weighted (OW) QMIX and demonstrate improved performance on both predator-prey and challenging multi-agent StarCraft benchmark tasks (Samvelyan et al., 2019).

We present a Reverse Reinforcement Learning (Reverse RL) approach for representing retrospective knowledge. General Value Functions (GVFs) have enjoyed great success in representing predictive knowledge, i.e., answering questions about possible future outcomes such as “how much fuel will be consumed in expectation if we drive from A to B?”. GVFs, however, cannot answer questions like “how much fuel do we expect a car to have given it is at B at time t?”. To answer this question, we need to know when that car had a full tank and how that car came to B. Since such questions emphasize the influence of possible past events on the present, we refer to their answers as retrospective knowledge. In this paper, we show how to represent retrospective knowledge with Reverse GVFs, which are trained via Reverse RL. We demonstrate empirically the utility of Reverse GVFs in both representation learning and anomaly detection.

We present Multitask Soft Option Learning (MSOL), a hierarchical multitask framework based on Planning as Inference. MSOL extends the concept of options, using separate variational posteriors for each task, regularized by a shared prior. This “soft” version of options avoids several instabilities during training in a multitask setting, and provides a natural way to learn both intra-option policies and their terminations. Furthermore, it allows fine-tuning of options for new tasks without forgetting their learned policies, leading to faster training without reducing the expressiveness of the hierarchical policy. We demonstrate empirically that MSOL significantly outperforms both hierarchical and flat transfer-learning baselines.

Abstract Interactive reinforcement learning provides a way for agents to learn to solve tasks from evaluative feedback provided by a human user. Previous research showed that humans give copious feedback early in training but very sparsely thereafter. In this article, we investigate the potential of agent learning from trainers’ facial expressions via interpreting them as evaluative feedback. To do so, we implemented TAMER which is a popular interactive reinforcement learning method in a reinforcement-learning benchmark problem—Infinite Mario, and conducted the first large-scale study of TAMER involving 561 participants. With designed CNN–RNN model, our analysis shows that telling trainers to use facial expressions and competition can improve the accuracies for estimating positive and negative feedback using facial expressions. In addition, our results with a simulation experiment show that learning solely from predicted feedback based on facial expressions is possible and using strong/effective prediction models or a regression method, facial responses would significantly improve the performance of agents. Furthermore, our experiment supports previous studies demonstrating the importance of bi-directional feedback and competitive elements in the training interface.

We propose expected policy gradients (EPG), which unify stochastic policy gradients (SPG) and deterministic policy gradients (DPG) for reinforcement learning. Inspired by expected sarsa, EPG integrates (or sums) across actions when estimating the gradient, instead of relying only on the action in the sampled trajectory. For continuous action spaces, we first derive a practical result for Gaussian policies and quadratic critics and then extend it to a universal analytical method, covering a broad class of actors and critics, including Gaussian, exponential families, and policies with bounded support. For Gaussian policies, we introduce an exploration method that uses covariance proportional to the matrix exponential of the scaled Hessian of the critic with respect to the actions. For discrete action spaces, we derive a variant of EPG based on softmax policies. We also establish a new general policy gradient theorem, of which the stochastic and deterministic policy gradient theorems are special cases. Furthermore, we prove that EPG reduces the variance of the gradient estimates without requiring deterministic policies and with little computational overhead. Finally, we provide an extensive experimental evaluation of EPG and show that it outperforms existing approaches on multiple challenging control domains.

Bayesian optimisation has been successfully applied to a variety of reinforcement learning problems. However, the traditional approach for learning optimal policies in simulators does not utilise the opportunity to improve learning by adjusting certain environment variables: state features that are unobservable and randomly determined by the environment in a physical setting but are controllable in a simulator. This article considers the problem of finding a robust policy while taking into account the impact of environment variables. We present Alternating Optimisation and Quadrature (ALOQ), which uses Bayesian optimisation and Bayesian quadrature to address such settings. We also present Transferable ALOQ (TALOQ), for settings where simulator inaccuracies lead to difficulty in transferring the learnt policy to the physical system. We show that our algorithms are robust to the presence of significant rare events, which may not be observable under random sampling but play a substantial role in determining the optimal policy. Experimental results across different domains show that our algorithms learn robust policies efficiently.

In many real-world settings, a team of agents must coordinate its behaviour while acting in a decentralised fashion. At the same time, it is often possible to train the agents in a centralised fashion where global state information is available and communication constraints are lifted. Learning joint action-values conditioned on extra state information is an attractive way to exploit centralised learning, but the best strategy for then extracting decentralised policies is unclear. Our solution is QMIX, a novel value-based method that can train decentralised policies in a centralised end-to-end fashion. QMIX employs a mixing network that estimates joint action-values as a monotonic combination of per-agent values. We structurally enforce that the joint-action value is monotonic in the per-agent values, through the use of non-negative weights in the mixing network, which guarantees consistency between the centralised and decentralised policies. To evaluate the performance of QMIX, we propose the StarCraft Multi-Agent Challenge (SMAC) as a new benchmark for deep multi-agent reinforcement learning. We evaluate QMIX on a challenging set of SMAC scenarios and show that it significantly outperforms existing multi-agent reinforcement learning methods.

When observing the actions of others, humans make inferences about why they acted as they did, and what this implies about the world; humans also use the fact that their actions will be interpreted in this manner, allowing them to act informatively and thereby communicate efficiently with others. Although learning algorithms have recently achieved superhuman performance in a number of two-player, zero-sum games, scalable multi-agent reinforcement learning algorithms that can discover effective strategies and conventions in complex, partially observable settings have proven elusive. We present the Bayesian action decoder (BAD), a new multi-agent learning method that uses an approximate Bayesian update to obtain a public belief that conditions on the actions taken by all agents in the environment. BAD introduces a new Markov decision process, the public belief MDP, in which the action space consists of all deterministic partial policies, and exploits the fact that an agent acting only on this public belief state can still learn to use its private information if the action space is augmented to be over all partial policies mapping private information into environment actions. The Bayesian update is closely related to the theory of mind reasoning that humans carry out when observing others’ actions. We first validate BAD on a proof-of-principle two-step matrix game, where it outperforms policy gradient methods; we then evaluate BAD on the challenging, cooperative partial-information card game Hanabi, where, in the two-player setting, it surpasses all previously published learning and hand-coded approaches, establishing a new state of the art.

By enabling correct differentiation in Stochastic Computation Graphs (SCGs), the infinitely differentiable Monte-Carlo estimator (DiCE) can generate correct estimates for the higher order gradients that arise in, e.g., multi-agent reinforcement learning and meta-learning. However, the baseline term in DiCE that serves as a control variate for reducing variance applies only to first order gradient estimation, limiting the utility of higher-order gradient estimates. To improve the sample efficiency of DiCE, we propose a new baseline term for higher order gradient estimation. This term may be easily included in the objective, and produces unbiased variance-reduced estimators under (automatic) differentiation, without affecting the estimate of the objective itself or of the first order gradient estimate. It reuses the same baseline function (e.g., the state-value function in reinforcement learning) already used for the first order baseline. We provide theoretical analysis and numerical evaluations of this new baseline, which demonstrate that it can dramatically reduce the variance of DiCE’s second order gradient estimators and also show empirically that it reduces the variance of third and fourth order gradients. This computational tool can be easily used to estimate higher order gradients with unprecedented efficiency and simplicity wherever automatic differentiation is utilised, and it has the potential to unlock applications of higher order gradients in reinforcement learning and meta-learning.

Policy gradient methods ignore the potential value of adjusting environment variables: unobservable state features that are randomly determined by the environment in a physical setting, but are controllable in a simulator. This can lead to slow learning, or convergence to suboptimal policies, if the environment variable has a large impact on the transition dynamics. In this paper, we present fingerprint policy optimisation (FPO), which finds a policy that is optimal in expectation across the distribution of environment variables. The central idea is to use Bayesian optimisation (BO) to actively select the distribution of the environment variable that maximises the improvement generated by each iteration of the policy gradient method. To make this BO practical, we contribute two easy-to-compute low-dimensional fingerprints of the current policy. Our experiments show that FPO can efficiently learn policies that are robust to significant rare events, which are unlikely to be observable under random sampling, but are key to learning good policies.

We propose CAVIA for meta-learning, a simple extension to MAML that is less prone to meta-overfitting, easier to parallelise, and more interpretable. CAVIA partitions the model parameters into two parts: context parameters that serve as additional input to the model and are adapted on individual tasks, and shared parameters that are meta-trained and shared across tasks. At test time, only the context parameters are updated, leading to a low-dimensional task representation. We show empirically that CAVIA outperforms MAML for regression, classification, and reinforcement learning. Our experiments also highlight weaknesses in current benchmarks, in that the amount of adaptation needed in some cases is small.

Learning from demonstration (LfD) is useful in settings where hand-coding behaviour or a reward function is impractical. It has succeeded in a wide range of problems but typically relies on manually generated demonstrations or specially deployed sensors and has not generally been able to leverage the copious demonstrations available in the wild: those that capture behaviours that were occurring anyway using sensors that were already deployed for another purpose, e.g., traffic camera footage capturing demonstrations of natural behaviour of vehicles, cyclists, and pedestrians. We propose video to behaviour (ViBe), a new approach to learn models of behaviour from unlabelled raw video data of a traffic scene collected from a single, monocular, initially uncalibrated camera with ordinary resolution. Our approach calibrates the camera, detects relevant objects, tracks them through time, and uses the resulting trajectories to perform LfD, yielding models of naturalistic behaviour. We apply ViBe to raw videos of a traffic intersection and show that it can learn purely from videos, without additional expert knowledge.

To be successful in real-world tasks, Reinforcement Learning (RL) needs to exploit the compositional, relational, and hierarchical structure of the world, and learn to transfer it to the task at hand. Recent advances in representation learning for language make it possible to build models that acquire world knowledge from text corpora and integrate this knowledge into downstream decision making problems. We thus argue that the time is right to investigate a tight integration of natural language understanding into RL in particular. We survey the state of the field, including work on instruction following, text games, and learning from textual domain knowledge. Finally, we call for the development of new environments as well as further investigation into the potential uses of recent Natural Language Processing (NLP) techniques for such tasks.

Gradient-based methods for optimisation of objectives in stochastic settings with unknown or intractable dynamics require estimators of derivatives. We derive an objective that, under automatic differentiation, produces low-variance unbiased estimators of derivatives at any order. Our objective is compatible with arbitrary advantage estimators, which allows the control of the bias and variance of any-order derivatives when using function approximation. Furthermore, we propose a method to trade off bias and variance of higher order derivatives by discounting the impact of more distant causal dependencies. We demonstrate the correctness and utility of our estimator in analytically tractable MDPs and in meta-reinforcement-learning for continuous control.

Applying probabilistic models to reinforcement learning (RL) enables the uses of powerful optimisation tools such as variational inference in RL. However, existing inference frameworks and their algorithms pose significant challenges for learning optimal policies, e.g., the lack of mode capturing behaviour in pseudo-likelihood methods, difficulties learning deterministic policies in maximum entropy RL based approaches, and a lack of analysis when function approximators are used. We propose VIREL, a theoretically grounded probabilistic inference framework for RL that utilises a parametrised action-value function to summarise future dynamics of the underlying MDP, generalising existing approaches. VIREL also benefits from a mode-seeking form of KL divergence, the ability to learn deterministic optimal polices naturally from inference, and the ability to optimise value functions and policies in separate, iterative steps. In applying variational expectation-maximisation to VIREL, we thus show that the actor-critic algorithm can be reduced to expectation-maximisation, with policy improvement equivalent to an E-step and policy evaluation to an M-step. We then derive a family of actor-critic methods fromVIREL, including a scheme for adaptive exploration. Finally, we demonstrate that actor-critic algorithms from this family outperform state-of-the-art methods based on soft value functions in several domains.

Centralised training with decentralised execution is an important setting for cooperative deep multi-agent reinforcement learning due to communication constraints during execution and computational tractability in training. In this paper, we analyse value-based methods that are known to have superior performance in complex environments. We specifically focus on QMIX, the current state-of-the-art in this domain. We show that the representation constraints on the joint action-values introduced by QMIX and similar methods lead to provably poor exploration and suboptimality. Furthermore, we propose a novel approach called MAVEN that hybridises value and policy-based methods by introducing a latent space for hierarchical control. The value-based agents condition their behaviour on the shared latent variable controlled by a hierarchical policy. This allows MAVEN to achieve committed, temporally extended exploration, which is key to solving complex multi-agent tasks. Our experimental results show that MAVEN achieves significant performance improvements on the challenging SMAC domain.

The performance of policy gradient methods is sensitive to hyperparameter settings that must be tuned for any new application. Widely used grid search methods for tuning hyperparameters are sample inefficient and computationally expensive. More advanced methods like Population Based Training that learn optimal schedules for hyperparameters instead of fixed settings can yield better results, but are also sample inefficient and computationally expensive. In this paper, we propose Hyperparameter Optimisation on the Fly (HOOF), a gradient-free algorithm that requires no more than one training run to automatically adapt the hyperparameter that affect the policy update directly through the gradient. The main idea is to use existing trajectories sampled by the policy gradient method to optimise a one-step improvement objective, yielding a sample and computationally efficient algorithm that is easy to implement. Our experimental results across multiple domains and algorithms show that using HOOF to learn these hyperparameter schedules leads to faster learning with improved performance.

Cooperative multi-agent reinforcement learning often requires decentralised policies, which severely limit the agents' ability to coordinate their behaviour. In this paper, we show that common knowledge between agents allows for complex decentralised coordination. Common knowledge arises naturally in a large number of decentralised cooperative multi-agent tasks, for example, when agents can reconstruct parts of each others' observations. Since agents can independently agree on their common knowledge, they can execute complex coordinated policies that condition on this knowledge in a fully decentralised fashion. We propose multi-agent common knowledge reinforcement learning (MACKRL), a novel stochastic actor-critic algorithm that learns a hierarchical policy tree. Higher levels in the hierarchy coordinate groups of agents by conditioning on their common knowledge, or delegate to lower levels with smaller subgroups but potentially richer common knowledge. The entire policy tree can be executed in a fully decentralised fashion. As the lowest policy tree level consists of independent policies for each agent, MACKRL reduces to independently learnt decentralised policies as a special case. We demonstrate that our method can exploit common knowledge for superior performance on complex decentralised coordination tasks, including a stochastic matrix game and challenging problems in StarCraft II unit micromanagement.

We propose a new objective, the counterfactual objective, unifying existing objectives for off-policy policy gradient algorithms in the continuing reinforcement learning (RL) setting. Compared to the commonly used excursion objective, which can be misleading about the performance of the target policy when deployed, our new objective better predicts such performance. We prove the Generalized Off-Policy Policy Gradient Theorem to compute the policy gradient of the counterfactual objective and use an emphatic approach to get an unbiased sample from this policy gradient, yielding the Generalized Off-Policy Actor-Critic (Geoff-PAC) algorithm. We demonstrate the merits of Geoff-PAC over existing algorithms in Mujoco robot simulation tasks, the first empirical success of emphatic algorithms in prevailing deep RL benchmarks.

We reformulate the option framework as two parallel augmented MDPs. Under this novel formulation, all policy optimization algorithms can be used off the shelf to learn intra-option policies, option termination conditions, and a master policy over options. We apply an actor-critic algorithm on each augmented MDP, yielding the Double Actor-Critic (DAC) architecture. Furthermore, we show that, when state-value functions are used as critics, one critic can be expressed in terms of the other, and hence only one critic is necessary. We conduct an empirical study on challenging robot simulation tasks. In a transfer learning setting, DAC outperforms both its hierarchy-free counterpart and previous gradient-based option learning algorithms.

We propose expected policy gradients (EPG), which unify stochastic policy gradients (SPG) and deterministic policy gradients (DPG) for reinforcement learning. Inspired by expected sarsa, EPG integrates across the action when estimating the gradient, instead of relying only on the action in the sampled trajectory. We establish a new general policy gradient theorem, of which the stochastic and deterministic policy gradient theorems are special cases. We also prove that EPG reduces the variance of the gradient estimates without requiring deterministic policies and, for the Gaussian case, with no computational overhead. Finally, we show that it is optimal in a certain sense to explore with a Gaussian policy such that the covariance is proportional to the exponential of the scaled Hessian of the critic with respect to the actions. We present empirical results confirming that this new form of exploration substantially outperforms DPG with the Ornstein-Uhlenbeck heuristic in four challenging MuJoCo domains.

Many real-world problems, such as network packet routing and the coordination of autonomous vehicles, are naturally modelled as cooperative multi-agent systems. There is a great need for new reinforcement learning methods that can efficiently learn decentralised policies for such systems. To this end, we propose a new multi-agent actor-critic method called counterfactual multi-agent (COMA) policy gradients. COMA uses a centralised critic to estimate the Q-function and decentralised actors to optimise the agents' policies. In addition, to address the challenges of multi-agent credit assignment, it uses a counterfactual baseline that marginalises out a single agent's action, while keeping the other agents' actions fixed. COMA also uses a critic representation that allows the counterfactual baseline to be computed efficiently in a single forward pass. We evaluate COMA in the testbed of StarCraft unit micromanagement, using a decentralised variant with significant partial observability. COMA significantly improves average performance over other multi-agent actor-critic methods in this setting, and the best performing agents are competitive with state-of-the-art centralised controllers that get access to the full state.

Bayesian optimisation has been successfully applied to a variety of reinforcement learning problems. However, the traditional approach for learning optimal policies in simulators does not utilise the opportunity to improve learning by adjusting certain environment variables: state features that are unobservable and randomly determined by the environment in a physical setting but are controllable in a simulator. This paper considers the problem of finding a robust policy while taking into account the impact of environment variables. We present Alternating Optimisation and Quadrature (ALOQ), which uses Bayesian optimisation and Bayesian quadrature to address such settings. ALOQ is robust to the presence of significant rare events, which may not be observable under random sampling, but play a substantial role in determining the optimal policy. Experimental results across different domains show that ALOQ can learn more efficiently and robustly than existing methods.

We propose a new way of deriving policy gradient updates for reinforcement learning. Our technique, based on Fourier analysis, recasts integrals that arise with expected policy gradients as convolutions and turns them into multiplications. The obtained analytical solutions allow us to capture the low variance benefits of EPG in a broad range of settings. For the critic, we treat trigonometric and radial basis functions, two function families with the universal approximation property. The choice of policy can be almost arbitrary, including mixtures or hybrid continuous-discrete probability distributions. Moreover, we derive a general family of sample-based estimators for stochastic policy gradients, which unifies existing results on sample-based approximation. We believe that this technique has the potential to shape the next generation of policy gradient approaches, powered by analytical results.

The score function estimator is widely used for estimating gradients of stochastic objectives in stochastic computation graphs (SCG), eg., in reinforcement learning and meta-learning. While deriving the first-order gradient estimators by differentiating a surrogate loss (SL) objective is computationally and conceptually simple, using the same approach for higher-order derivatives is more challenging. Firstly, analytically deriving and implementing such estimators is laborious and not compliant with automatic differentiation. Secondly, repeatedly applying SL to construct new objectives for each order derivative involves increasingly cumbersome graph manipulations. Lastly, to match the first-order gradient under differentiation, SL treats part of the cost as a fixed sample, which we show leads to missing and wrong terms for estimators of higher-order derivatives. To address all these shortcomings in a unified way, we introduce DiCE, which provides a single objective that can be differentiated repeatedly, generating correct estimators of derivatives of any order in SCGs. Unlike SL, DiCE relies on automatic differentiation for performing the requisite graph manipulations. We verify the correctness of DiCE both through a proof and numerical evaluation of the DiCE derivative estimates. We also use DiCE to propose and evaluate a novel approach for multi-agent learning. Our code is available at https://github.com/alshedivat/lola.

Many real-world sequential decision making problems are partially observable by nature, and the environment model is typically unknown. Consequently, there is great need for reinforcement learning methods that can tackle such problems given only a stream of rewards and incomplete and noisy observations. In this paper, we propose deep variational reinforcement learning (DVRL), which introduces an inductive bias that allows an agent to learn a generative model of the environment and perform inference in that model to effectively aggregate the available information. We develop an n-step approximation to the evidence lower bound (ELBO), allowing the model to be trained jointly with the policy. This ensures that the latent state representation is suitable for the control task. In experiments on Mountain Hike and flickering Atari we show that our method outperforms previous approaches relying on recurrent neural networks to encode the past.

In many real-world settings, a team of agents must coordinate their behaviour while acting in a decentralised way. At the same time, it is often possible to train the agents in a centralised fashion in a simulated or laboratory setting, where global state information is available and communication constraints are lifted. Learning joint action-values conditioned on extra state information is an attractive way to exploit centralised learning, but the best strategy for then extracting decentralised policies is unclear. Our solution is QMIX, a novel value-based method that can train decentralised policies in a centralised end-to-end fashion. QMIX employs a network that estimates joint action-values as a complex non-linear combination of per-agent values that condition only on local observations. We structurally enforce that the joint-action value is monotonic in the per-agent values, which allows tractable maximisation of the joint action-value in off-policy learning, and guarantees consistency between the centralised and decentralised policies. We evaluate QMIX on a challenging set of StarCraft II micromanagement tasks, and show that QMIX significantly outperforms existing value-based multi-agent reinforcement learning methods.

Many advanced Learning from Demonstration (LfD) methods consider the decomposition of complex, real-world tasks into simpler sub-tasks. By reusing the corresponding sub-policies within and between tasks, we can provide training data for each policy from different high-level tasks and compose them to perform novel ones. Existing approaches to modular LfD focus either on learning a single high-level task or depend on domain knowledge and temporal segmentation. In contrast, we propose a weakly supervised, domain-agnostic approach based on task sketches, which include only the sequence of sub-tasks performed in each demonstration. Our approach simultaneously aligns the sketches with the observed demonstrations and learns the required sub-policies. This improves generalisation in comparison to separate optimisation procedures. We evaluate the approach on multiple domains, including a simulated 3D robot arm control task using purely image-based observations. The results show that our approach performs commensurately with fully supervised approaches, while requiring significantly less annotation effort.

Learning from rewards generated by a human trainer observing an agent in action has been proven to be a powerful method for teaching autonomous agents to perform challenging tasks, especially for those non-technical users. Since the efficacy of this approach depends critically on the reward the trainer provides, we consider how the interaction between the trainer and the agent should be designed so as to increase the efficiency of the training process. This article investigates the influence of the agent’s socio-competitive feedback on the human trainer’s training behavior and the agent’s learning. The results of our user study with 85 participants suggest that the agent’s passive socio-competitive feedback—showing performance and score of agents trained by trainers in a leaderboard—substantially increases the engagement of the participants in the game task and improves the agents’ performance, even though the participants do not directly play the game but instead train the agent to do so. Moreover, making this feedback active—sending the trainer her agent’s performance relative to others—further induces more participants to train agents longer and improves the agent’s learning. Our further analysis shows that agents trained by trainers affected by both the passive and active social feedback could obtain a higher performance under a score mechanism that could be optimized from the trainer’s perspective and the agent’s additional active social feedback can keep participants to further train agents to learn policies that can obtain a higher performance under such a score mechanism.

Policy gradient methods have been widely applied in reinforcement learning. For reasons of safety and cost, learning is often conducted using a simulator. However, learning in simulation does not traditionally utilise the opportunity to improve learning by adjusting certain environment variables - state features that are randomly determined by the environment in a physical setting but controllable in a simulator. Exploiting environment variables is crucial in domains containing significant rare events (SREs), e.g., unusual wind conditions that can crash a helicopter, which are rarely observed under random sampling but have a considerable impact on expected return. We propose off environment reinforcement learning (OFFER), which addresses such cases by simultaneously optimising the policy and a proposal distribution over environment variables. We prove that OFFER converges to a locally optimal policy and show experimentally that it learns better and faster than a policy gradient baseline.

Many real-world problems, such as network packet routing and urban traffic control, are naturally modeled as multi-agent reinforcement learning (RL) problems. However, existing multi-agent RL methods typically scale poorly in the problem size. Therefore, a key challenge is to translate the success of deep learning on single-agent RL to the multi-agent setting. A major stumbling block is that independent Q-learning, the most popular multi-agent RL method, introduces nonstationarity that makes it incompatible with the experience replay memory on which deep Q-learning relies. This paper proposes two methods that address this problem: 1) using a multi-agent variant of importance sampling to naturally decay obsolete data and 2) conditioning each agent’s value function on a fingerprint that disambiguates the age of the data sampled from the replay memory. Results on a challenging decentralised variant of StarCraft unit micromanagement confirm that these methods enable the successful combination of experience replay with multi-agent RL.

Inverse Reinforcement Learning (IRL) for path planning enables robots to learn cost functions for difficult tasks from demonstration, instead of hard-coding them. However, IRL methods face practical limitations that stem from the need to repeat costly planning procedures. In this paper, we propose Rapidly Exploring Learning Trees (RLT*), which learns the cost functions of Optimal Rapidly Exploring Random Trees (RRT*) from demonstration, thereby making inverse learning methods applicable to more complex tasks. Our approach extends Maximum Margin Planning to work with RRT* cost functions. Furthermore, we propose a caching scheme that greatly reduces the computational cost of this approach. Experimental results on simulated and real-robot data from a social navigation scenario show that RLT* achieves better performance at lower computational cost than existing methods. We also successfully deploy control policies learned with RLT* on a real telepresence robot.

As robots begin to inhabit public and social spaces, it is increasingly important to ensure that they behave in a socially appropriate way. However, manually coding social behaviours is prohibitively difficult since social norms are hard to quantify. Therefore, learning from demonstration (LfD), wherein control policies are inferred from demonstrations of correct behaviour, is a powerful tool for helping robots acquire social intelligence. In this paper, we propose a deep learning approach to learning social behaviours from demonstration. We apply this method to two challenging social tasks for a semi-autonomous telepresence robot. Our results show that our approach outperforms gradient boosting regression and performs well against a hard-coded controller. Furthermore, ablation experiments confirm that each element of our method is essential to its success.

Reinforcement learning (RL) in partially observable settings is challenging because the agent’s observations are not Markov. Recently proposed methods can learn variable-order Markov models of the underlying process but have steep memory requirements and are sensitive to aliasing between observation histories due to sensor noise. This paper proposes dynamic-depth context tree weighting (D2-CTW), a model-learning method that addresses these limitations. D2-CTW dynamically expands a suffix tree while ensuring that the size of the model, but not its depth, remains bounded. We show that D2-CTW approximately matches the performance of state-of-the-art alternatives at stochastic time-series prediction while using at least an order of magnitude less memory. We also apply D2-CTW to model-based RL, showing that, on tasks that require memory of past observations, D2-CTW can learn without prior knowledge of a good state representation, or even the length of history upon which such a representation should depend.

We consider the problem of multiple agents sensing and acting in environments with the goal of maximising their shared utility. In these environments, agents must learn communication protocols in order to share information that is needed to solve the tasks. By embracing deep neural networks, we are able to demonstrate end-to-end learning of protocols in complex environments inspired by communication riddles and multi-agent computer vision problems with partial observability. We propose two approaches for learning in these domains: Reinforced Inter-Agent Learning (RIAL) and Differentiable Inter-Agent Learning (DIAL). The former uses deep Q-learning, while the latter exploits the fact that, during learning, agents can backpropagate error derivatives through (noisy) communication channels. Hence, this approach uses centralised learning but decentralised execution. Our experiments introduce new environments for studying the learning of communication protocols and present a set of engineering innovations that are essential for success in these domains.

Modern search systems are based on dozens or even hundreds of ranking features. The dueling bandit gradient descent (DBGD) algorithm has been shown to effectively learn combinations of these features solely from user interactions. DBGD explores the search space by comparing a possibly improved ranker to the current production ranker. To this end, it uses interleaved comparison methods, which can infer with high sensitivity a preference between two rankings based only on interaction data. A limiting factor is that it can compare only to a single exploratory ranker. We propose an online learning to rank algorithm called multileave gradient descent (MGD) that extends DBGD to learn from so-called multileaved comparison methods that can compare a set of rankings instead of merely a pair. We show experimentally that MGD allows for better selection of candidates than DBGD without the need for more comparisons involving users. An important implication of our results is that orders of magnitude less user interaction data is required to find good rankers when multileaved comparisons are used within online learning to rank. Hence, fewer users need to be exposed to possibly inferior rankers and our method allows search engines to adapt more quickly to changes in user preferences.

In this work, we address a relatively unexplored aspect of designing agents that learn from human reward. We investigate how an agent’s non-task behavior can affect a human trainer’s training and agent learning. We use the TAMER framework, which facilitates the training of agents by human-generated reward signals, i.e., judgements of the quality of the agent’s actions, as the foundation for our investigation. Then, starting from the premise that the interaction between the agent and the trainer should be bi-directional, we propose two new training interfaces to increase a human trainer’s active involvement in the training process and thereby improve the agent’s task performance. One provides information on the agent’s uncertainty which is a metric calculated as data coverage, the other on its performance. Our results from a 51-subject user study show that these interfaces can induce the trainers to train longer and give more feedback. The agent’s performance, however, increases only in response to the addition of performance-oriented information, not by sharing uncertainty levels. These results suggest that the organizational maxim about human behavior, “you get what you measure”—i.e., sharing metrics with people causes them to focus on optimizing those metrics while de-emphasizing other objectives—also applies to the training of agents. Using principle component analysis, we show how trainers in the two conditions train agents differently. In addition, by simulating the influence of the agent’s uncertainty–informative behavior on a human’s training behavior, we show that trainers could be distracted by the agent sharing its uncertainty levels about its actions, giving poor feedback for the sake of reducing the agent’s uncertainty without improving the agent’s performance.

A key challenge in the design of multi-sensor systems is the efficient allocation of scarce resources such as bandwidth, CPU cycles, and energy, leading to the dynamic sensor selection problem in which a subset of the available sensors must be selected at each timestep. While partially observable Markov decision processes (POMDPs) provide a natural decision-theoretic model for this problem, the computational cost of POMDP planning grows exponentially in the number of sensors, making it feasible only for small problems. We propose a new POMDP planning method that uses greedy maximization to greatly improve scalability in the number of sensors. We show that, under certain conditions, the value function of a dynamic sensor selection POMDP is submodular and use this result to bound the error introduced by performing greedy maximization. Experimental results on a real-world dataset from a multi-camera tracking system in a shopping mall show it achieves similar performance to existing methods but incurs only a fraction of the computational cost, leading to much better scalability in the number of cameras.

A version of the dueling bandit problem is addressed in which a Condorcet winner may not exist. Two algorithms are proposed that instead seek to minimize regret with respect to the Copeland winner, which, unlike the Condorcet winner, is guaranteed to exist. The first, Copeland Confidence Bound (CCB), is designed for small numbers of arms, while the second, Scalable Copeland Bandits (SCB), works better for large-scale problems. We provide theoretical results bounding the regret accumulated by CCB and SCB, both substantially improving existing results. Such existing results either offer bounds of the form O(K log T) but require restrictive assumptions, or offer bounds of the form O(K^2 log T) without requiring such assumptions. Our results offer the best of both worlds: O(K log T) bounds without restrictive assumptions.

We address the problem of how to safely compare rankers for information retrieval. In particular, we consider how to control the risks associated with switching from an existing production ranker to a new candidate ranker. Whereas existing online comparison methods require showing potentially suboptimal result lists to users during the comparison process, which can lead to user frustration and abandonment, our approach only requires user interaction data generated through the natural use of the production ranker. Specifically, we propose a Bayesian approach for (1) comparing the production ranker to candidate rankers and (2) estimating the confidence of this comparison. The comparison of rankers is performed using click model-based information retrieval metrics, while the confidence of the comparison is derived from Bayesian estimates of uncertainty in the underlying click model. These confidence estimates are then used to determine whether a risk-averse decision criterion for switching to the candidate ranker has been satisfied. Experimental results on several learning to rank datasets and on a click log show that the proposed approach outperforms an existing ranker comparison method that does not take uncertainty into account.

A key challenge in information retrieval is that of on-line ranker evaluation: determining which one of a finite set of rankers performs the best in expectation on the basis of user clicks on presented document lists. When the presented lists are constructed using interleaved comparison methods, which interleave lists proposed by two different candidate rankers, then the problem of minimizing the total regret accumulated while evaluating the rankers can be formalized as a K-armed dueling bandit problem. In the setting of web search, the number of rankers under consideration may be large. Scaling effectively in the presence of so many rankers is a key challenge not adequately addressed by existing algorithms.

In this article, we propose new algorithms for multi-objective coordination graphs (MO-CoGs). Key to the efficiency of these algorithms is that they compute a convex coverage set (CCS) instead of a Pareto coverage set (PCS). Not only is a CCS a sufficient solution set for a large class of problems, it also has important characteristics that facilitate more efficient solutions. We propose two main algorithms for computing a CCS in MO-CoGs. Convex multi-objective variable elimination (CMOVE) computes a CCS by performing a series of agent eliminations, which can be seen as solving a series of local multi-objective subproblems. Variable elimination linear support (VELS) iteratively identifies the single weight vector, w, that can lead to the maximal possible improvement on a partial CCS and calls variable elimination to solve a scalarized instance of the problem for w. VELS is faster than CMOVE for small and medium numbers of objectives and can compute an ε-approximate CCS in a fraction of the runtime. In addition, we propose variants of these methods that employ AND/OR tree search instead of variable elimination to achieve memory efficiency. We analyze the runtime and space complexities of these methods, prove their correctness, and compare them empirically against a naive baseline and an existing PCS method, both in terms of memory-usage and runtime. Our results show that, by focusing on the CCS, these methods achieve much better scalability in the number of agents than the current state of the art.

Evaluation methods for information retrieval systems come in three types: offline evaluation, using static data sets annotated for relevance by human judges; user studies, usually conducted in a lab-based setting; and online evaluation, using implicit signals such as clicks from actual users. For the latter, preferences between rankers are typically inferred from implicit signals via interleaved comparison methods, which combine a pair of rankings and display the result to the user. We propose a new approach to online evaluation called multileaved comparisons that is useful in the prevalent case where designers are interested in the relative performance of more than two rankers. Rather than combining only a pair of rankings, multileaved comparisons combine an arbitrary number of rankings. The resulting user clicks then give feedback about how all these rankings compare to each other. We propose two specific multileaved comparison methods. The first, called team draft multileave, is an extension of team draft interleave. The second, called optimized multileave, is an extension of optimized interleave and is designed to handle cases where a large number of rankers must be multileaved. We present experimental results that demonstrate that both team draft multileave and optimized multileave can accurately determine all pairwise preferences among a set of rankers using far less data than the interleaving methods that they extend.

This paper proposes a new method for the K-armed dueling bandit problem, a variation on the regular K-armed bandit problem that offers only relative feedback about pairs of arms. Our approach extends the Upper Confidence Bound algorithm to the relative setting by using estimates of the pairwise probabilities to select a promising arm and applying Upper Confidence Bound with the winner as a benchmark. We prove a sharp finite-time regret bound of order O(K log t) on a very general class of dueling bandit problems that matches a lower bound proven in (Yue et al., 2012). In addition, our empirical results using real data from an information retrieval application show that it greatly outperforms the state of the art.

A key challenge in information retrieval is that of on-line ranker evaluation: determining which one of a finite set of rankers performs the best in expectation on the basis of user clicks on presented document lists. When the presented lists are constructed using interleaved comparison methods, which interleave lists proposed by two different candidate rankers, then the problem of minimizing the total regret accumulated while evaluating the rankers can be formalized as a K-armed dueling bandits problem. In this paper, we propose a new method called relative confidence sampling (RCS) that aims to reduce cumulative regret by being less conservative than existing methods in eliminating rankers from contention. In addition, we present an empirical comparison between RCS and two state-of-the-art methods, relative upper confidence bound and SAVAGE. The results demonstrate that RCS can substantially outperform these alternatives on several large learning to rank datasets.

This article addresses reinforcement learning problems based on factored Markov decision processes (MDPs) in which the agent must choose among a set of candidate abstractions, each build up from a different combination of state components. We present and evaluate a new approach that can perform effective abstraction selection that is more resource‐efficient and/or more general than existing approaches. The core of the approach is to make selection of an abstraction part of the learning agent's decision‐making process by augmenting the agent's action space with internal actions that select the abstraction it uses. We prove that under certain conditions this approach results in a derived MDP whose solution yields both the optimal abstraction for the original MDP and the optimal policy under that abstraction. We examine our approach in three domains of increasing complexity: contextual bandit problems, episodic MDPs, and general MDPs with context‐specific structure. © 2013 Wiley Periodicals, Inc.

HyperNEAT is a popular indirect encoding method for evolutionary computation that has performed well on a number of benchmark tasks. This paper presents a series of experiments designed to examine the critical factors for its success. First, we determine the fewest hidden nodes a genotypic network needs to solve several of these tasks. Our results show that all of these tasks are easy: they can be solved with at most one hidden node and require generating only trivial regular patterns. Then, we examine how HyperNEAT performs when the tasks are made harder. Our results show that HyperNEAT's performance decays quickly: it fails to solve all variants of these tasks that require more complex solutions. Next, we examine the hypothesis that fracture in the problem space, known to be challenging for regular NEAT, is even more so for HyperNEAT. Our results suggest that quite complex networks are needed to cope with fracture and HyperNEAT can have difficulty discovering them. Finally, we connect these results to previous experiments showing that HyperNEAT's performance decreases on irregular tasks. Our results suggest irregularity is an extreme form of fracture and that HyperNEAT's limitations are thus more severe than those experiments suggested.

Online learning to rank for information retrieval (IR) holds promise for allowing the development of "self-learning" search engines that can automatically adjust to their users. With the large amount of e.g., click data that can be collected in web search settings, such techniques could enable highly scalable ranking optimization. However, feedback obtained from user interactions is noisy, and developing approaches that can learn from this feedback quickly and reliably is a major challenge.

As retrieval systems become more complex, learning to rank approaches are being developed to automatically tune their parameters. Using online learning to rank, retrieval systems can learn directly from implicit feedback inferred from user interactions. In such an online setting, algorithms must obtain feedback for effective learning while simultaneously utilizing what has already been learned to produce high quality results. We formulate this challenge as an exploration–exploitation dilemma and propose two methods for addressing it. By adding mechanisms for balancing exploration and exploitation during learning, each method extends a state-of-the-art learning to rank method, one based on listwise learning and the other on pairwise learning. Using a recently developed simulation framework that allows assessment of online performance, we empirically evaluate both methods. Our results show that balancing exploration and exploitation can substantially and significantly improve the online retrieval performance of both listwise and pairwise approaches. In addition, the results demonstrate that such a balance affects the two approaches in different ways, especially when user feedback is noisy, yielding new insights relevant to making online learning to rank effective in practice.

This article presents the state-of-the-art in optimal solution methods for decentralized partially observable Markov decision processes (Dec-POMDPs), which are general models for collaborative multiagent planning under uncertainty. Building off the generalized multiagent A* (GMAA*) algorithm, which reduces the problem to a tree of one-shot collaborative Bayesian games (CBGs), we describe several advances that greatly expand the range of Dec-POMDPs that can be solved optimally. First, we introduce lossless incremental clustering of the CBGs solved by GMAA*, which achieves exponential speedups without sacrificing optimality. Second, we introduce incremental expansion of nodes in the GMAA* search tree, which avoids the need to expand all children, the number of which is in the worst case doubly exponential in the node's depth. This is particularly beneficial when little clustering is possible. In addition, we introduce new hybrid heuristic representations that are more compact and thereby enable the solution of larger Dec-POMDPs. We provide theoretical guarantees that, when a suitable heuristic is used, both incremental clustering and incremental expansion yield algorithms that are both complete and search equivalent. Finally, we present extensive empirical results demonstrating that GMAA*-ICE, an algorithm that synthesizes these advances, can optimally solve Dec-POMDPs of unprecedented size.

Sequential decision-making problems with multiple objectives arise naturally in practice and pose unique challenges for research in decision-theoretic planning and learning, which has largely focused on single-objective settings. This article surveys algorithms designed for sequential decision-making problems with multiple objectives. Though there is a growing body of literature on this subject, little of it makes explicit under what circumstances special methods are needed to solve multi-objective problems. Therefore, we identify three distinct scenarios in which converting such a problem to a single-objective one is impossible, infeasible, or undesirable. Furthermore, we propose a taxonomy that classifies multi-objective methods according to the applicable scenario, the nature of the scalarization function (which projects multi-objective values to scalar ones), and the type of policies considered. We show how these factors determine the nature of an optimal solution, which can be a single policy, a convex hull, or a Pareto front. Using this taxonomy, we survey the literature on multi-objective methods for planning and learning. Finally, we discuss key applications of such methods and outline opportunities for future work.

Ranker evaluation is central to the research into search engines, be it to compare rankers or to provide feedback for learning to rank. Traditional evaluation approaches do not scale well because they require explicit relevance judgments of document-query pairs, which are expensive to obtain. A promising alternative is the use of interleaved comparison methods, which compare rankers using click data obtained when interleaving their rankings. In this article, we propose a framework for analyzing interleaved comparison methods. An interleaved comparison method has fidelity if the expected outcome of ranker comparisons properly corresponds to the true relevance of the ranked documents. It is sound if its estimates of that expected outcome are unbiased and consistent. It is efficient if those estimates are accurate with only little data. We analyze existing interleaved comparison methods and find that, while sound, none meet our criteria for fidelity. We propose a probabilistic interleave method, which is sound and has fidelity. We show empirically that, by marginalizing out variables that are known, it is more efficient than existing interleaved comparison methods. Using importance sampling we derive a sound extension that is able to reuse historical data collected in previous comparisons of other ranker pairs.

Interleaved comparison methods, which compare rankers using click data, are a promising alternative to traditional information retrieval evaluation methods that require expensive explicit judgments. A major limitation of these methods is that they assume access to live data, meaning that new data must be collected for every pair of rankers compared. We investigate the use of previously collected click data (i.e., historical data) for interleaved comparisons. We start by analyzing to what degree existing interleaved comparison methods can be applied and find that a recent probabilistic method allows such data reuse, even though it is biased when applied to historical data. We then propose an interleaved comparison method that is based on the probabilistic approach but uses importance sampling to compensate for bias. We experimentally confirm that probabilistic methods make the use of historical data for interleaved comparisons possible and effective.

Empirical evaluations play an important role in machine learning. However, the usefulness of any evaluation depends on the empirical methodology employed. Designing good empirical methodologies is difficult in part because agents can overfit test evaluations and thereby obtain misleadingly high scores. We argue that reinforcement learning is particularly vulnerable to environment overfitting and propose as a remedy generalized methodologies, in which evaluations are based on multiple environments sampled from a distribution. In addition, we consider how to summarize performance when scores from different environments may not have commensurate values. Finally, we present proof-of-concept results demonstrating how these methodologies can validate an intuitively useful range-adaptive tile coding method.

Evaluating rankers using implicit feedback, such as clicks on documents in a result list, is an increasingly popular alternative to traditional evaluation methods based on explicit relevance judgments. Previous work has shown that so-called interleaved comparison methods can utilize click data to detect small differences between rankers and can be applied to learn ranking functions online. In this paper, we analyze three existing interleaved comparison methods and find that they are all either biased or insensitive to some differences between rankers. To address these problems, we present a new method based on a probabilistic interleaving process. We derive an unbiased estimator of comparison outcomes and show how marginalizing over possible comparison outcomes given the observed click data can make this estimator even more effective.

Novelty search is a recently proposed method for evolutionary computation designed to avoid the problem of deception, in which the fitness function guides the search process away from global optima. Novelty search replaces fitness-based selection with novelty-based selection, where novelty is measured by comparing an individual's behavior to that of the current population and an archive of past novel individuals. Though there is substantial evidence that novelty search can overcome the problem of deception, the critical factors in its performance remain poorly understood. This paper helps to bridge this gap by analyzing how the behavior function, which maps each genotype to a behavior, affects performance. We propose the notion of descendant fitness probability (DFP), which describes how likely a genotype's descendants are to have a certain fitness, and formulate two hypotheses about when changes to the behavior function will improve novelty search's performance, based on the effect of those changes on behavior and DFP. Experiments in both artificial and deceptive maze domains provide substantial empirical support for these hypotheses.

The field of reinforcement learning aims to develop algorithms that use experience to optimize behavior in sequential decision problems such as (partially observable) Markov decision processes ((PO)MDPs).In such problems, an autonomous agent interacts with an external environment by selecting actions and seeks the sequence of actions that maximizes its long-term performance.In reinforcement learning, the environment is typically initially unknown and learning takes place online, that is, the agent's performance is assessed throughout learning instead of only afterwards.Since many challenging and realistic tasks are well described as sequential decision problems, the development of effective reinforcement-learning algorithms plays an important role in artificial intelligence research.Recent years have seen enormous progress, both in the development of new methods and the theoretical understanding of existing methods.In particular, great strides have been made in approximating value functions, exploring efficiently, learning in the presence of multiple agents, coping with partial observability, inducing models, and reasoning hierarchically.The focus of this special issue is not the development of new algorithms but the empirical evaluation of existing ones.Like other machine-learning methods, reinforcement-learning approaches are typically evaluated in one or more of the following three ways: (1) subjectively, (2) theoretically, and (3) empirically.Subjective evaluations, in which researchers assess the significance and potential of new ideas, are important because they leverage the powerful intuition of experts to guide the research process.However, they are also limited because they cannot validate ideas that go against such intuition; for example, they cannot expose fallacious assumptions.Theoretical evaluations are also important, as they are

Shaping functions can be used in multi-task reinforcement learning (RL) to incorporate knowledge from previously experienced tasks to speed up learning on a new task. So far, researchers have pre-specified a separate representation for shaping and value functions in multi-task settings. However, no work has made precise what distinguishes these representations, or what makes a good representation for either function. This paper shows two alternative methods by which an evolutionary algorithm can find a shaping function in multi-task RL without pre-specifying a separate representation. The second method, which uses an indirect fitness measure, is demonstrated to achieve similar performance to the first against a significantly lower computational cost. In addition, we define a formal categorisation of representations that makes precise what makes a good representation for shaping and value functions. We validate the categorisation with an evolutionary feature selection method and show that this method chooses the representations that our definitions predict are suitable.

Temporal difference and evolutionary methods are two of the most common approaches to solving reinforcement learning problems. However, there is little consensus on their relative merits and there have been few empirical studies that directly compare their performance. This article aims to address this shortcoming by presenting results of empirical comparisons between Sarsa and NEAT, two representative methods, in mountain car and keepaway, two benchmark reinforcement learning tasks. In each task, the methods are evaluated in combination with both linear and nonlinear representations to determine their best configurations. In addition, this article tests two specific hypotheses about the critical factors contributing to these methods’ relative performance: (1) that sensor noise reduces the final performance of Sarsa more than that of NEAT, because Sarsa’s learning updates are not reliable in the absence of the Markov property and (2) that stochasticity, by introducing noise in fitness estimates, reduces the learning speed of NEAT more than that of Sarsa. Experiments in variations of mountain car and keepaway designed to isolate these factors confirm both these hypotheses.

This paper presents a theoretical and empirical analysis of Expected Sarsa, a variation on Sarsa, the classic on-policy temporal-difference method for model-free reinforcement learning. Expected Sarsa exploits knowledge about stochasticity in the behavior policy to perform updates with lower variance. Doing so allows for higher learning rates and thus faster learning. In deterministic environments, Expected Sarsas updates have zero variance, enabling a learning rate of 1. We prove that Expected Sarsa converges under the same conditions as Sarsa and formulate specific hypotheses about when Expected Sarsa will outperform Sarsa and Q-learning. Experiments in multiple domains confirm these hypotheses and demonstrate that Expected Sarsa has significant advantages over these more commonly used methods.

Helicopter hovering is an important challenge problem in the field of reinforcement learning. This paper considers several neuroevolutionary approaches to discovering robust controllers for a generalized version of the problem used in the 2008 Reinforcement Learning Competition, in which wind in the helicopter's environment varies from run to run. We present the simple model-free strategy that won first place in the competition and also describe several more complex model-based approaches. Our empirical results demonstrate that neuroevolution is effective at optimizing the weights of multi-layer perceptrons, that linear regression is faster and more effective than evolution for learning models, and that model-based approaches can outperform the simple model-free strategy, especially if prior knowledge is used to aid model learning.

Feature selection is an important challenge in machine learning. Unfortunately, most methods for automating feature selection are designed for supervised learning tasks and are thus either inapplicable or impractical for reinforcement learning. This paper presents a new approach to feature selection specifically designed for the challenges of reinforcement learning. In our method, the agent learns a model, represented as a dynamic Bayesian network, of a factored Markov decision process, deduces a minimal feature set from this network, and efficiently computes a policy on this feature set using dynamic programming methods. Experiments in a stock-trading benchmark task demonstrate that this approach can reliably deduce minimal feature sets and that doing so can substantially improve performance and reduce the computational expense of planning.

This paper presents postponed updates, a new strategy for TD methods that can improve sample efficiency without incurring the computational and space requirements of model-based RL. By recording the agent's last-visit experience, the agent can delay its update until the given state is revisited, thereby improving the quality of the update. Experimental results demonstrate that postponed updates outperforms several competitors, most notably eligibility traces, a traditional way to improve the sample efficiency of TD methods. It achieves this without the need to tune an extra parameter as is needed for eligibility traces.

Both genetic algorithms (GAs) and temporal difference (TD) methods have proven effective at solving reinforcement learning (RL) problems. However, since few rigorous empirical comparisons have been conducted, there are no general guidelines describing the methods' relative strengths and weaknesses. This paper presents the results of a detailed empirical comparison between a GA and a TD method in Keepaway, a standard RL benchmark domain based on robot soccer. In particular, we compare the performance of NEAT [19], a GA that evolves neural networks, with Sarsa [16, 17], a popular TD method. The results demonstrate that NEAT can learn better policies in this task, though it requires more evaluations to do so. Additional experiments in two variations of Keepaway demonstrate that Sarsa learns better policies when the task is fully observable and NEAT learns faster when the task is deterministic. Together, these results help isolate the factors critical to the performance of each method and yield insights into their general strengths and weaknesses.

In reinforcement learning, an agent interacting with its environment strives to learn a policy that specifies, for each state it may encounter, what action to take. Evolutionary computation is one of the most promising approaches to reinforcement learning but its success is largely restricted to off-line scenarios. In on-line scenarios, an agent must strive to maximize the reward it accrues while it is learning. Temporal difference (TD) methods, another approach to reinforcement learning, naturally excel in on-line scenarios because they have selection mechanisms for balancing the need to search for better policies exploration) with the need to accrue maximal reward (exploitation). This paper presents a novel way to strike this balance in evolutionary methods by borrowing the selection mechanisms used by TD methods to choose individual actions and using them in evolution to choose policies for evaluation. Empirical results in the mountain car and server job scheduling domains demonstrate that these techniques can substantially improve evolution's on-line performance in stochastic domains.

Temporal difference methods are theoretically grounded and empirically effective methods for addressing reinforcement learning problems. In most real-world reinforcement learning tasks, TD methods require a function approximator to represent the value function. However, using function approximators requires manually making crucial representational decisions. This paper investigates evolutionary function approximation, a novel approach to automatically selecting function approximator representations that enable efficient individual learning. This method evolves individuals that are better able to learn. We present a fully implemented instantiation of evolutionary function approximation which combines NEAT, a neuroevolutionary optimization technique, with Q-learning, a popular TD method. The resulting NEAT+Q algorithm automatically discovers effective representations for neural network function approximators. This paper also presents on-line evolutionary computation, which improves the on-line performance of evolutionary computation by borrowing selection mechanisms used in TD methods to choose individual actions and using them in evolutionary computation to select policies for evaluation. We evaluate these contributions with extended empirical studies in two domains: 1) the mountain car task, a standard reinforcement learning benchmark on which neural network function approximators have previously performed poorly and 2) server job scheduling, a large probabilistic domain drawn from the field of autonomic computing. The results demonstrate that evolutionary function approximation can significantly improve the performance of TD methods and on-line evolutionary computation can significantly improve evolutionary methods. This paper also presents additional tests that offer insight into what factors can make neural network function approximation difficult in practice.

Feature selection is the process of finding the set of inputs to a machine learning algorithm that will yield the best performance. Developing a way to solve this problem automatically would make current machine learning methods much more useful. Previous efforts to automate feature selection rely on expensive meta-learning or are applicable only when labeled training data is available. This paper presents a novel method called FS-NEAT which extends the NEAT neuroevolution method to automatically determine an appropriate set of inputs for the networks it evolves. By learning the network's inputs, topology, and weights simultaneously, FS-NEAT addresses the feature selection problem without relying on meta-learning or labeled data. Initial experiments in an autonomous car racing simulation demonstrate that FS-NEAT can learn better and faster than regular NEAT. In addition, the networks it evolves are smaller and require fewer inputs. Furthermore, FS-NEAT's performance remains robust even as the feature selection task it faces is made increasingly difficult.