Agents are minimally entities that are influenced by their past observations and act to influence future observations. This latter capacity is captured by empowerment, which has served as a vital framing concept across artificial intelligence and cognitive science. This former capacity, however, is equally foundational: In what ways, and to what extent, can an agent be influenced by what it observes? In this paper, we ground this concept in a universal agent-centric measure that we refer to as plasticity, and reveal a fundamental connection to empowerment. Following a set of desiderata on a suitable definition, we define plasticity using a new information-theoretic quantity we call the generalized directed information. We show that this new quantity strictly generalizes the directed information introduced by Massey (1990) while preserving all of its desirable properties. Under this definition, we find that plasticity is well thought of as the mirror of empowerment: The two concepts are defined using the same measure, with only the direction of influence reversed. Our main result establishes a tension between the plasticity and empowerment of an agent, suggesting that agent design needs to be mindful of both characteristics. We explore the implications of these findings, and suggest that plasticity, empowerment, and their relationship are essential to understanding agency.

We analyse quantile temporal-difference learning (QTD), a distributional reinforcement learning algorithm that has proven to be a key component in several successful large-scale applications of reinforcement learning. Despite these empirical successes, a theoretical understanding of QTD has proven elusive until now. Unlike classical TD learning, which can be analysed with standard stochastic approximation tools, QTD updates do not approximate contraction mappings, are highly non-linear, and may have multiple fixed points. The core result of this paper is a proof of convergence to the fixed points of a related family of dynamic programming procedures with probability 1, putting QTD on firm theoretical footing. The proof establishes connections between QTD and non-linear differential inclusions through stochastic approximation theory and non-smooth analysis.

In reinforcement learning (RL), state representations are key to dealing with large or continuous state spaces. While one of the promises of deep learning algorithms is to automatically construct features well-tuned for the task they try to solve, such a representation might not emerge from end-to-end training of deep RL agents. To mitigate this issue, auxiliary objectives are often incorporated into the learning process and help shape the learnt state representation. Bootstrapping methods are today's method of choice to make these additional predictions. Yet, it is unclear which features these algorithms capture and how they relate to those from other auxiliary-task-based approaches. In this paper, we address this gap and provide a theoretical characterization of the state representation learnt by temporal difference learning (Sutton, 1988). Surprisingly, we find that this representation differs from the features learned by Monte Carlo and residual gradient algorithms for most transition structures of the environment in the policy evaluation setting. We describe the efficacy of these representations for policy evaluation, and use our theoretical analysis to design new auxiliary learning rules. We complement our theoretical results with an empirical comparison of these learning rules for different cumulant functions on classic domains such as the four-room domain (Sutton et al, 1999) and Mountain Car (Moore, 1990).

Multi-step learning applies lookahead over multiple time steps and has proved valuable in policy evaluation settings. However, in the optimal control case, the impact of multi-step learning has been relatively limited despite a number of prior efforts. Fundamentally, this might be because multi-step policy improvements require operations that cannot be approximated by stochastic samples, hence hindering the widespread adoption of such methods in practice. To address such limitations, we introduce doubly multi-step off-policy VI (DoMo-VI), a novel oracle algorithm that combines multi-step policy improvements and policy evaluations. DoMo-VI enjoys guaranteed convergence speed-up to the optimal policy and is applicable in general off-policy learning settings. We then propose doubly multi-step off-policy actor-critic (DoMo-AC), a practical instantiation of the DoMo-VI algorithm. DoMo-AC introduces a bias-variance trade-off that ensures improved policy gradient estimates. When combined with the IMPALA architecture, DoMo-AC has showed improvements over the baseline algorithm on Atari-57 game benchmarks.

Reward is the driving force for reinforcement-learning agents. We here set out to understand the expressivity of Markov reward as a way to capture tasks that we would want an agent to perform. We frame this study around three new abstract notions of "task": (1) a set of acceptable behaviors, (2) a partial ordering over behaviors, or (3) a partial ordering over trajectories. Our main results prove that while reward can express many of these tasks, there exist instances of each task type that no Markov reward function can capture. We then provide a set of polynomial-time algorithms that construct a Markov reward function that allows an agent to perform each task type, and correctly determine when no such reward function exists.

Abstract Reinforcement learning(RL) is a powerful learning paradigm in which agents can learn to maximize sparse and delayed reward signals. Although RL has had many impressive successes in complex domains, learning can take hours, days, or even years of training data. A major challenge of contemporary RL research is to discover how to learn with less data. Previous work has shown that domain information can be successfully used to shape the reward; by adding additional reward information, the agent can learn with much less data. Furthermore, if the reward is constructed from a potential function, the optimal policy is guaranteed to be unaltered. While suchpotential-based reward shaping(PBRS) holds promise, it is limited by the need for a well-defined potential function. Ideally, we would like to be able to take arbitrary advice from a human or other agent and improve performance without affecting the optimal policy. The recently introduceddynamic potential-based advice(DPBA) was proposed to tackle this challenge by predicting the potential function values as part of the learning process. However, this article demonstrates theoretically and empirically that, while DPBA can facilitate learning with good advice, it does in fact alter the optimal policy. We further show that when adding the correction term to “fix” DPBA it no longer shows effective shaping with good advice. We then present a simple method calledpolicy invariant explicit shaping(PIES) and show theoretically and empirically that PIES can use arbitrary advice, speed-up learning, and leave the optimal policy unchanged.

Credit assignment in reinforcement learning is the problem of measuring an action’s influence on future rewards. In particular, this requires separating skill from luck, i.e. disentangling the effect of an action on rewards from that of external factors and subsequent actions. To achieve this, we adapt the notion of counterfactuals from causality theory to a model-free RL setup. The key idea is to condition value functions on future events, by learning to extract relevant information from a trajectory. We formulate a family of policy gradient algorithms that use these future-conditional value functions as baselines or critics, and show that they are provably low variance. To avoid the potential bias from conditioning on future information, we constrain the hindsight information to not contain information about the agent’s actions. We demonstrate the efficacy and validity of our algorithm on a number of illustrative and challenging problems.

Reward is the driving force for reinforcement-learning agents. This paper is dedicated to understanding the expressivity of reward as a way to capture tasks that we would want an agent to perform. We frame this study around three new abstract notions of “task” that might be desirable: (1) a set of acceptable behaviors, (2) a partial ordering over behaviors, or (3) a partial ordering over trajectories. Our main results prove that while reward can express many of these tasks, there exist instances of each task type that no Markov reward function can capture. We then provide a set of polynomial-time algorithms that construct a Markov reward function that allows an agent to optimize tasks of each of these three types, and correctly determine when no such reward function exists. We conclude with an empirical study that corroborates and illustrates our theoretical findings.

The principal contribution of this paper is a conceptual framework for off-policy reinforcement learning, based on conditional expectations of importance sampling ratios. This framework yields new perspectives and understanding of existing off-policy algorithms, and reveals a broad space of unexplored algorithms. We theoretically analyse this space, and concretely investigate several algorithms that arise from this framework.

In this work, we consider the problem of autonomously discovering behavioral abstractions, or options, for reinforcement learning agents. We propose an algorithm that focuses on the termination function, as opposed to - as is common - the policy. The termination function is usually trained to optimize a control objective: an option ought to terminate if another has better value. We offer a different, information-theoretic perspective, and propose that terminations should focus instead on the compressibility of the option’s encoding - arguably a key reason for using abstractions. To achieve this algorithmically, we leverage the classical options framework, and learn the option transition model as a "critic" for the termination function. Using this model, we derive gradients that optimize the desired criteria. We show that the resulting options are non-trivial, intuitively meaningful, and useful for learning.

In order to solve complex problems an agent must be able to reason over a sufficiently long horizon. Temporal abstraction, commonly modeled through options, offers the ability to reason at many timescales, but the horizon length is still determined by the discount factor of the underlying Markov Decision Process. We propose a modification to the options framework that naturally scales the agent’s horizon with option length. We show that the proposed option-step discount controls a bias-variance trade-off, with larger discounts (counter-intuitively) leading to less estimation variance.

We consider the problem of efficient credit assignment in reinforcement learning. In order to efficiently and meaningfully utilize new data, we propose to explicitly assign credit to past decisions based on the likelihood of them having led to the observed outcome. This approach uses new information in hindsight, rather than employing foresight. Somewhat surprisingly, we show that value functions can be rewritten through this lens, yielding a new family of algorithms. We study the properties of these algorithms, and empirically show that they successfully address important credit assignment challenges, through a set of illustrative tasks.

A temporally abstract action, or an option, is specified by a policy and a termination condition: the policy guides the option behavior, and the termination condition roughly determines its length. Generally, learning with longer options (like learning with multi-step returns) is known to be more efficient. However, if the option set for the task is not ideal, and cannot express the primitive optimal policy well, shorter options offer more flexibility and can yield a better solution. Thus, the termination condition puts learning efficiency at odds with solution quality. We propose to resolve this dilemma by decoupling the behavior and target terminations, just like it is done with policies in off-policy learning. To this end, we give a new algorithm, Q(beta), that learns the solution with respect to any termination condition, regardless of how the options actually terminate. We derive Q(beta) by casting learning with options into a common framework with well-studied multi-step off policy learning. We validate our algorithm empirically, and show that it holds up to its motivating claims.

Many real-world reinforcement learning problems have a hierarchical nature, and often exhibit some degree of partial observability. While hierarchy and partial observability are usually tackled separately (for instance by combining recurrent neural networks and options), we show that addressing both problems simultaneously is simpler and more efficient in many cases. More specifically, we make the initiation set of options conditional on the previously-executed option, and show that options with such Option-Observation Initiation Sets (OOIs) are at least as expressive as Finite State Controllers (FSCs), a state-of-the-art approach for learning in POMDPs. OOIs are easy to design based on an intuitive description of the task, lead to explainable policies and keep the top-level and option policies memoryless. Our experiments show that OOIs allow agents to learn optimal policies in challenging POMDPs, while being much more sample-efficient than a recurrent neural network over options.

In this work, we take a fresh look at some old and new algorithms for off-policy, return-based reinforcement learning. Expressing these in a common form, we derive a novel algorithm, Retrace(lambda), with three desired properties: (1) it has low variance; (2) it safely uses samples collected from any behaviour policy, whatever its degree of "off-policyness"; and (3) it is efficient as it makes the best use of samples collected from near on-policy behaviour policies. We analyse the contractive nature of the related operator under both off-policy policy evaluation and control settings and derive online sample-based algorithms. We believe this is the first return-based off-policy control algorithm converging a.s. to Q* without the GLIE assumption (Greedy in the Limit with Infinite Exploration). As a corollary, we prove the convergence of Watkins' Q(lambda), which was an open problem since 1989. We illustrate the benefits of Retrace(lambda) on a standard suite of Atari 2600 games.

Effectively incorporating external advice is an important problem in reinforcement learning, especially as it moves into the real world. Potential-based reward shaping is a way to provide the agent with a specific form of additional reward, with the guarantee of policy invariance. In this work we give a novel way to incorporate an arbitrary reward function with the same guarantee, by implicitly translating it into the specific form of dynamic advice potentials, which are maintained as an auxiliary value function learnt at the same time. We show that advice provided in this way captures the input reward function in expectation, and demonstrate its efficacy empirically.

In this work we propose learning an ensemble of policies related through potential-based shaping rewards via the off-policy Horde framework.

Multi-objectivization is the process of transforming a single objective problem into a multi-objective problem. Research in evolutionary optimization has demonstrated that the addition of objectives that are correlated with the original objective can make the resulting problem easier to solve compared to the original single-objective problem. In this paper we investigate the multi-objectivization of reinforcement learning problems. We propose a novel method for the multi-objectivization of Markov Decision problems through the use of multiple reward shaping functions. Reward shaping is a technique to speed up reinforcement learning by including additional heuristic knowledge in the reward signal. The resulting composite reward signal is expected to be more informative during learning, leading the learner to identify good actions more quickly. Good reward shaping functions are by definition correlated with the target value function for the base reward signal, and we show in this paper that adding several correlated signals can help to solve the basic single objective problem faster and better. We prove that the total ordering of solutions, and by consequence the optimality of solutions, is preserved in this process, and empirically demonstrate the usefulness of this approach on two reinforcement learning tasks: a pathfinding problem and the Mario domain.

Users often need to test, debug or reuse spreadsheets. We present a new algorithm that can identify differences between two spreadsheets, providing a basis for future tools to help users compare two versions of a spreadsheet (thereby seeing what is new and needs testing) or two different spreadsheets (thereby seeing which is more appropriate for reuse in a situation). This algorithm, RowColAlign, is a two-dimensional generalization of the classic dynamic programming algorithm for solving the one-dimensional longest common subsequence problem. In addition, we present a new planted model for generating test cases to evaluate this algorithm and others like it, including the greedy SheetDiff algorithm presented in prior work. In our evaluation, our new RowColAlign algorithm made no errors at all on test cases, including test cases comparable to relatively large spreadsheets. Moreover, further analysis revealed that it is unexpected for our new algorithm to make errors except when spreadsheets contain an unrealistically small number of distinct values. These results are extremely encouraging, revealing our algorithm's potential as the basis for future spreadsheet tools.