Multi-objective reinforcement learning (MORL) algorithms tackle sequential decision problems where agents may have different preferences over (possibly conflicting) reward functions. These algorithms often learn a set of policies, each optimized for a particular agent preference, that are later reused when optimizing policies for different preferences. We introduce a novel algorithm that builds upon Generalized Policy Improvement (GPI) to construct principled, formally-derived prioritization schemes that improve sample efficiency. These correspond to active-learning strategies by which the agent can identify (i) the most promising preferences/objectives to train on at each moment; and (ii) the most relevant previous experiences to learn policies for new agent preferences through a novel Dyna-style MORL method. We prove our algorithm is guaranteed to always converge to an optimal solution in a finite number of steps, or an $$\epsilon $$ -optimal solution (for a bounded $$\epsilon $$ ) if the agent can only identify sub-optimal policies. Our method monotonically improves the quality of its partial solutions while learning. We also introduce a bound that characterizes the maximum utility loss (with respect to the optimal solution) incurred by intermediate policies identified by our method during learning. Finally, we propose a novel epistemic uncertainty-aware extension of GPI that exploits high-confidence lower bounds to mitigate the impact of unreliable action-value estimates in GPI policies, and prove that it provides tighter performance bounds than the current state of the art. We empirically show that our method outperforms state-of-the-art MORL algorithms in challenging multi-objective tasks.

Multi-task reinforcement learning aims to quickly identify solutions for new tasks with minimal or no additional interaction with the environment. Generalized Policy Improvement (GPI) addresses this by combining a set of base policies to produce a new one that is at least as good—though not necessarily optimal—as any individual base policy. Optimality can be ensured, particularly in the linear-reward case, via techniques that compute a Convex Coverage Set (CCS). However, these are computationally expensive and do not scale to complex domains. The Option Keyboard (OK) improves upon GPI by producing policies that are at least as good—and often better. It achieves this through a learned meta-policy that dynamically combines base policies. However, its performance critically depends on the choice of base policies. This raises a key question: is there an optimal set of base policies—an optimal *behavior basis*—that enables zero-shot identification of optimal solutions for *any* linear tasks? We solve this open problem by introducing a novel method that efficiently constructs such an optimal behavior basis. We show that it significantly reduces the number of base policies needed to ensure optimality in new tasks. We also prove that it is strictly more expressive than a CCS, enabling particular classes of *non-linear* tasks to be solved optimally. We empirically evaluate our technique in challenging domains and show that it outperforms state-of-the-art approaches, increasingly so as task complexity increases.

Machine learning models are often designed to maximize a primary goal, such as accuracy. However, as these models are increasingly used to inform decisions that affect people's lives or well-being, it is often unclear what the real-world repercussions of their deployment might be—making it crucial to understand and manage such repercussions effectively. Models maximizing user engagement on social media platforms, e.g., may inadvertently contribute to the spread of misinformation and content that deepens political polarization. This issue is not limited to social media—it extends to other applications where machine learning-informed decisions can have real-world repercussions, such as education, employment, and lending. Existing methods addressing this issue require prior knowledge or estimates of analytical models describing the relationship between a classifier's predictions and their corresponding repercussions. We introduce Theia, a novel classification algorithm capable of optimizing a primary objective, such as accuracy, while providing high-confidence guarantees about its potential repercussions. Importantly, Theia solves the open problem of providing such guarantees based solely on existing data with observations of previous repercussions. We prove that it satisfies constraints on a model's repercussions with high confidence and that it is guaranteed to identify a solution, if one exists, given sufficient data. We empirically demonstrate, using real-life data, that Theia can identify models that achieve high accuracy while ensuring, with high confidence, that constraints on their repercussions are satisfied.

In this paper, we introduce a fresh perspective on the challenges of credit assignment and policy evaluation. First, we delve into the nuances of eligibility traces and explore instances where their updates may result in unexpected credit assignment to preceding states. From this investigation emerges the concept of a novel value function, which we refer to as the ????????????? ????? ????????. Unlike traditional state value functions, bidirectional value functions account for both future expected returns (rewards anticipated from the current state onward) and past expected returns (cumulative rewards from the episode's start to the present). We derive principled update equations to learn this value function and, through experimentation, demonstrate its efficacy in enhancing the process of policy evaluation. In particular, our results indicate that the proposed learning approach can, in certain challenging contexts, perform policy evaluation more rapidly than TD(λ)–a method that learns forward value functions, v^π, ????????. Overall, our findings present a new perspective on eligibility traces and potential advantages associated with the novel value function it inspires, especially for policy evaluation.

Novel reinforcement learning algorithms, or improvements on existing ones, are commonly justified by evaluating their performance on benchmark environments and are compared to an ever-changing set of standard algorithms. However, despite numerous calls for improvements, experimental practices continue to produce misleading or unsupported claims. One reason for the ongoing substandard practices is that conducting rigorous benchmarking experiments requires substantial computational time. This work investigates the sources of increased computation costs in rigorous experiment designs. We show that conducting rigorous performance benchmarks will likely have computational costs that are often prohibitive. As a result, we argue for using an additional experimentation paradigm to overcome the limitations of benchmarking.

Evaluating policies using off-policy data is crucial for applying reinforcement learning to real-world problems such as healthcare and autonomous driving. Previous methods for *off-policy evaluation* (OPE) generally suffer from high variance or irreducible bias, leading to unacceptably high prediction errors. In this work, we introduce STAR, a framework for OPE that encompasses a broad range of estimators -- which include existing OPE methods as special cases -- that achieve lower mean squared prediction errors. STAR leverages state abstraction to distill complex, potentially continuous problems into compact, discrete models which we call *abstract reward processes* (ARPs). Predictions from ARPs estimated from off-policy data are provably consistent (asymptotically correct). Rather than proposing a specific estimator, we present a new framework for OPE and empirically demonstrate that estimators within STAR outperform existing methods. The best STAR estimator outperforms baselines in all twelve cases studied, and even the median STAR estimator surpasses the baselines in seven out of the twelve cases.

We introduce a principled method for performing zero-shot transfer in reinforcement learning (RL) by exploiting approximate models of the environment. Zero-shot transfer in RL has been investigated by leveraging methods rooted in generalized policy improvement (GPI) and successor features (SFs). Although computationally efficient, these methods are model-free: they analyze a library of policies---each solving a particular task---and identify which action the agent should take. We investigate the more general setting where, in addition to a library of policies, the agent has access to an approximate environment model. Even though model-based RL algorithms can identify near-optimal policies, they are typically computationally intensive. We introduce $h$-GPI, a multi-step extension of GPI that interpolates between these extremes---standard model-free GPI and fully model-based planning---as a function of a parameter, $h$, regulating the amount of time the agent has to reason. We prove that $h$-GPI's performance lower bound is strictly better than GPI's, and show that $h$-GPI generally outperforms GPI as $h$ increases. Furthermore, we prove that as $h$ increases, $h$-GPI's performance becomes arbitrarily less susceptible to sub-optimality in the agent's policy library. Finally, we introduce novel bounds characterizing the gains achievable by $h$-GPI as a function of approximation errors in both the agent's policy library and its (possibly learned) model. These bounds strictly generalize those known in the literature. We evaluate $h$-GPI on challenging tabular and continuous-state problems under value function approximation and show that it consistently outperforms GPI and state-of-the-art competing methods under various levels of approximation errors.

Multi-objective reinforcement learning algorithms (MORL) extend standard reinforcement learning (RL) to scenarios where agents must optimize multiple---potentially conflicting---objectives, each represented by a distinct reward function. To facilitate and accelerate research and benchmarking in multi-objective RL problems, we introduce a comprehensive collection of software libraries that includes: (i) MO-Gymnasium, an easy-to-use and flexible API enabling the rapid construction of novel MORL environments. It also includes more than 20 environments under this API. This allows researchers to effortlessly evaluate any algorithms on any existing domains; (ii) MORL-Baselines, a collection of reliable and efficient implementations of state-of-the-art MORL algorithms, designed to provide a solid foundation for advancing research. Notably, all algorithms are inherently compatible with MO-Gymnasium; and(iii) a thorough and robust set of benchmark results and comparisons of MORL-Baselines algorithms, tested across various challenging MO-Gymnasium environments. These benchmarks were constructed to serve as guidelines for the research community, underscoring the properties, advantages, and limitations of each particular state-of-the-art method.

Designing reward functions for efficiently guiding reinforcement learning (RL) agents toward specific behaviors is a complex task. This is challenging since it requires the identification of reward structures that are not sparse and that avoid inadvertently inducing undesirable behaviors. Naively modifying the reward structure to offer denser and more frequent feedback can lead to unintended outcomes and promote behaviors that are not aligned with the designer's intended goal. Although potential-based reward shaping is often suggested as a remedy, we systematically investigate settings where deploying it often significantly impairs performance. To address these issues, we introduce a new framework that uses a bi-level objective to learn \emph{behavior alignment reward functions}. These functions integrate auxiliary rewards reflecting a designer's heuristics and domain knowledge with the environment's primary rewards. Our approach automatically determines the most effective way to blend these types of feedback, thereby enhancing robustness against heuristic reward misspecification. Remarkably, it can also adapt an agent's policy optimization process to mitigate suboptimalities resulting from limitations and biases inherent in the underlying RL algorithms. We evaluate our method's efficacy on a diverse set of tasks, from small-scale experiments to high-dimensional control challenges. We investigate heuristic auxiliary rewards of varying quality---some of which are beneficial and others detrimental to the learning process. Our results show that our framework offers a robust and principled way to integrate designer-specified heuristics. It not only addresses key shortcomings of existing approaches but also consistently leads to high-performing solutions, even when given misaligned or poorly-specified auxiliary reward functions.

In many real-world applications, reinforcement learning (RL) agents might have to solve multiple tasks, each one typically modeled via a reward function. If reward functions are expressed linearly, and the agent has previously learned a set of policies for different tasks, successor features (SFs) can be exploited to combine such policies and identify reasonable solutions for new problems. However, the identified solutions are not guaranteed to be optimal. We introduce a novel algorithm that addresses this limitation. It allows RL agents to combine existing policies and directly identify optimal policies for arbitrary new problems, without requiring any further interactions with the environment. We first show (under mild assumptions) that the transfer learning problem tackled by SFs is equivalent to the problem of learning to optimize multiple objectives in RL. We then introduce an SF-based extension of the Optimistic Linear Support algorithm to learn a set of policies whose SFs form a convex coverage set. We prove that policies in this set can be combined via generalized policy improvement to construct optimal behaviors for any new linearly-expressible tasks, without requiring any additional training samples. We empirically show that our method outperforms state-of-the-art competing algorithms both in discrete and continuous domains under value function approximation.

In this work we introduce Constrained Offline Policy Optimization (COPO), an offline policy optimization algorithm for learning in MDPs with cost constraints. COPO is built upon a novel offline cost-projection method, which we formally derive and analyze. Our method improves upon the state-of-the-art in offline constrained policy optimization by explicitly accounting for distributional shift and by offering non-asymptotic confidence bounds on the cost of a policy. These formal properties are superior to those of existing techniques, which only guarantee convergence to a point estimate. We formally analyze our method and empirically demonstrate that it achieves state-of-the-art performance on discrete and continuous control problems, while offering the aforementioned improved, stronger, and more robust theoretical guarantees.

Given the growth in complexity and scale of computer networks and considering that the leading cause of failures is human error, there is an increasing interest in minimizing the role of humans in network management. In this context, we propose a two-step, machine learning approach for automatically balancing network flows. Firstly, we rely on identifying flows that can more heavily impact the network, i.e., elephant flows. Sec-ondly, we use reinforcement learning to determine the best action to be performed in the network, given its state. The intuition for this two-step approach is to amortize the computational costs of reinforcement learning and apply it only to flows that can cause a high impact on network performance. Our main contributions are (i) problem modeling as a function of states and actions to balance network traffic and (ii) an architecture that more judiciously uses reinforcement learning on flows of interest for load balancing.

Methods for sequential decision-making are often built upon a foundational assumption that the underlying decision process is stationary. This limits the application of such methods because real-world problems are often subject to changes due to external factors (\textit{passive} non-stationarity), changes induced by interactions with the system itself (\textit{active} non-stationarity), or both (\textit{hybrid} non-stationarity). In this work, we take the first steps towards the fundamental challenge of on-policy and off-policy evaluation amidst structured changes due to active, passive, or hybrid non-stationarity. Towards this goal, we make a \textit{higher-order stationarity} assumption such that non-stationarity results in changes over time, but the way changes happen is fixed. We propose, OPEN, an algorithm that uses a double application of counterfactual reasoning and a novel importance-weighted instrument-variable regression to obtain both a lower bias and a lower variance estimate of the structure in the changes of a policy's past performances. Finally, we show promising results on how OPEN can be used to predict future performances for several domains inspired by real-world applications that exhibit non-stationarity.

Hindsight allows reinforcement learning agents to leverage new observations to make inferences about earlier states and transitions. In this paper, we exploit the idea of hindsight and introduce posterior value functions. Posterior value functions are computed by inferring the posterior distribution over hidden components of the state in previous timesteps and can be used to construct novel unbiased baselines for policy gradient methods. Importantly, we prove that these baselines reduce (and never increase) the variance of policy gradient estimators compared to traditional state value functions. While the posterior value function is motivated by partial observability, we extend these results to arbitrary stochastic MDPs by showing that hindsight-capable agents can model stochasticity in the environment as a special case of partial observability. Finally, we introduce a pair of methods for learning posterior value functions and prove their convergence.

When faced with sequential decision-making problems, it is often useful to be able to predict what would happen if decisions were made using a new policy. Those predictions must often be based on data collected under some previously used decision-making rule. Many previous methods enable such off-policy (or counterfactual) estimation of the expected value of a performance measure called the return. In this paper, we take the first steps towards a 'universal off-policy estimator' (UnO)---one that provides off-policy estimates and high-confidence bounds for any parameter of the return distribution. We use UnO for estimating and simultaneously bounding the mean, variance, quantiles/median, inter-quantile range, CVaR, and the entire cumulative distribution of returns. Finally, we also discuss UnO's applicability in various settings, including fully observable, partially observable (i.e., with unobserved confounders), Markovian, non-Markovian, stationary, smoothly non-stationary, and discrete distribution shifts.

Finding the ideal number of layers and size for each layer is a key challenge in deep neural network design. Two approaches for such networks exist: filter learning and architecture learning. While the first one starts with a given architecture and optimizes model weights, the second one aims to find the best architecture. Recently, several visual analytics (VA) techniques have been proposed to understand the behavior of a network, but few VA techniques support designers in architectural decisions. We propose a hybrid methodology based on VA to improve the architecture of a pre-trained network by reducing/increasing the size and number of layers. We introduce Activation Occurrence Maps that show how likely each image position of a convolutional kernel’s output activates for a given class, and Class Selectivity Maps, that show the selectiveness of different positions in a kernel’s output for a given label. Both maps help in the decision to drop kernels that do not significantly add to the network’s performance, increase the size of a layer having too few kernels, and add extra layers to the model. The user interacts from the first to the last layer, and the network is retrained after each layer modification. We validate our approach with experiments in models trained with two widely-known image classification datasets and show how our method helps to make design decisions to improve or to simplify the architectures of such models.

Defining a reward function that, when optimized, results in a rapid acquisition of an optimal policy, is one of the most challenging problems involved when deploying reinforcement learning algorithms. The existing works on the optimal reward problem (ORP) propose mechanisms to design reward functions but their application is limited to specific sub-classes of single or multi-agent reinforcement learning problems. Moreover, these methods identify which rewards should be given in which situation, but not which aspects of the state or environment should be used when defining the reward function. Those methods also do not directly model how quickly an optimal policy can be learned by optimizing a given candidate reward function. In this paper, we define the extended optimal reward problem (EORP) which: i) can identify both reward features and reward weights that compose the reward function; ii) is general enough to deal with single and multi-agent reinforcement learning problems; iii) is scalable to problems with large number of agents learning simultaneously; iv) incorporates a learning effort metric in the evaluation of reward functions allowing the discovery of reward functions that result in faster learning. Experimental results on gridworld-like and traffic assignment scenarios are used to evaluate the efficiency of our approach in designing effective reward functions.

The multi-armed bandit (MAB) problem is concerned with an agent choosing which arm of a slot machine to play in order to optimize its reward. A family of reinforcement learning algorithms exists to tackle this problem, including a few variants that consider more than one agent (thus, characterizing a repeated game) and non-stationary variants. In this paper, we seek to evaluate the performance of some of these MAB algorithms and compare them with Q-learning when applied to a non-stationary repeated game, where commuter agents face thetask of learning how to choose a route that minimizes their travel times.

Machine learning algorithms can be expensive to deploy, in particular, those used in robotics applications that perform many variations of the same task. Solutions to one variation of a task may be found via Reinforcement Learning algorithms, and are typically modeled as a vector of N parameters encoding the robot's behavior policy. When N is large or executing robot trials is time-consuming, searching in the space of solutions becomes prohibitively expensive. In this paper, we introduce a method that allows robots to generalize behaviors by analyzing solutions to a small number of previously-trained related tasks. This allows for approximate policies for novel tasks to be rapidly estimated. We present a method that achieves this type of generalization by performing nonlinear regression directly on the policy manifold — i.e., the solution space spanned as we change the parameters describing tasks. Because tasks are typically described by few parameters, the corresponding policy manifold has few degrees of freedom, which leads to low-dimensional surfaces. We exploit this property to construct a function that maps task parameters to policy parameters (a parameterized skill). Our method uses manifold clustering techniques to deal with discontinuous manifolds, a challenging situation arising from physical obstacles or robot constraints. We evaluate our method on a set of robot manipulation tasks and show that it can efficiently estimate policies for novel tasks from a small number of training examples.

We propose a new class of algorithms for minimizing or maximizing functions of parametric probabilistic models. These new algorithms are natural gradient algorithms that leverage more information than prior methods by using a new metric tensor in place of the commonly used Fisher information matrix. This new metric tensor is derived by computing directions of steepest ascent where the distance between distributions is measured using an approximation of energy distance (as opposed to Kullback-Leibler divergence, which produces the Fisher information matrix), and so we refer to our new ascent direction as the energetic natural gradient.

We introduce a method for actively learning parameterized skills. Parameterized skills are flexible behaviors that can solve any task drawn from a distribution of parameterized reinforcement learning problems. Approaches to learning such skills have been proposed, but limited attention has been given to identifying which training tasks allow for rapid skill acquisition. We construct a non-parametric Bayesian model of skill performance and derive analytical expressions for a novel acquisition criterion capable of identifying tasks that maximize expected improvement in skill performance. We also introduce a spatiotemporal kernel tailored for non-stationary skill performance models. The proposed method is agnostic to policy and skill representation and scales independently of task dimensionality. We evaluate it on a non-linear simulated catapult control problem over arbitrarily mountainous terrains.

We demonstrate a sample-efficient method for constructing reusable parameterized skills that can solve families of related motor tasks. Our method uses learned policies to analyze the policy space topology and learn a set of regression models which, given a novel task, appropriately parameterizes an underlying low-level controller. By identifying the disjoint charts that compose the policy manifold, the method can separately model the qualitatively different sub-skills required for solving distinct classes of tasks. Such sub-skills are useful because they can be treated as new discrete, specialized actions by higher-level planning processes. We also propose a method for reusing seemingly unsuccessful policies as additional, valid training samples for synthesizing the skill, thus accelerating learning. We evaluate our method on a humanoid iCub robot tasked with learning to accurately throw plastic balls at parameterized target locations.

We study the problem of finding efficient exploration policies for the case in which an agent is momentarily not concerned with exploiting, and instead tries to compute a policy for later use. We first formally define the Optimal Exploration Problem as one of sequential sampling and show that its solutions correspond to paths of minimum expected length in the space of policies. We derive a model-free, local linear approximation to such solutions and use it to construct efficient exploration policies. We compare our model-free approach to other exploration techniques, including one with the best known PAC bounds, and show that ours is both based on a well-defined optimization problem and empirically efficient.

In this paper we introduce RL-CD, a method for solving reinforcement learning problems in non-stationary environments. The method is based on a mechanism for creating, updating and selecting one among several partial models of the environment. The partial models are incrementally built according to the system's capability of making predictions regarding a given sequence of observations. We propose, formalize and show the efficiency of this method both in a simple non-stationary environment and in a noisy scenario. We show that RL-CD performs better than two standard reinforcement learning algorithms and that it has advantages over methods specifically designed to cope with non-stationarity. Finally, we present known limitations of the method and future works.