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Eduardo Pignatelli, Johan Ferret, Matthieu Geist, Thomas Mesnard, Hado van Hasselt, Laura Toni

The Credit Assignment Problem (CAP) refers to the longstanding challenge of Reinforcement Learning (RL) agents to associate actions with their long-term consequences. Solving the CAP is a crucial step towards the successful deployment of RL in the real world since most decision problems provide feedback that is noisy, delayed, and with little or no information about the causes. These conditions make it hard to distinguish serendipitous outcomes from those caused by informed decision-making. However, the mathematical nature of credit and the CAP remains poorly understood and defined. In this survey, we review the state of the art of Temporal Credit Assignment (CA) in deep RL. We propose a unifying formalism for credit that enables equitable comparisons of state of the art algorithms and improves our understanding of the trade-offs between the various methods. We cast the CAP as the problem of learning the influence of an action over an outcome from a finite amount of experience. We discuss the challenges posed by delayed effects, transpositions, and a lack of action influence, and analyse how existing methods aim to address them. Finally, we survey the protocols to evaluate a credit assignment method, and suggest ways to diagnoses the sources of struggle for different credit assignment methods. Overall, this survey provides an overview of the field for new-entry practitioners and researchers, it offers a coherent perspective for scholars looking to expedite the starting stages of a new study on the CAP, and it suggests potential directions for future research

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David Abel, André Barreto, Benjamin Van Roy, Doina Precup, Hado van Hasselt, Satinder Singh

In this paper we develop a foundation for continual reinforcement learning.

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David Abel, André Barreto, Hado van Hasselt, Benjamin Van Roy, Doina Precup, Satinder Singh

When has an agent converged? Standard models of the reinforcement learning problem give rise to a straightforward definition of convergence: An agent converges when its behavior or performance in each environment state stops changing. However, as we shift the focus of our learning problem from the environment's state to the agent's state, the concept of an agent's convergence becomes significantly less clear. In this paper, we propose two complementary accounts of agent convergence in a framing of the reinforcement learning problem that centers around bounded agents. The first view says that a bounded agent has converged when the minimal number of states needed to describe the agent's future behavior cannot decrease. The second view says that a bounded agent has converged just when the agent's performance only changes if the agent's internal state changes. We establish basic properties of these two definitions, show that they accommodate typical views of convergence in standard settings, and prove several facts about their nature and relationship. We take these perspectives, definitions, and analysis to bring clarity to a central idea of the field.

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Simon Schmitt, John Shawe-Taylor, Hado van Hasselt

How to efficiently explore in reinforcement learning is an open problem. Many exploration algorithms employ the epistemic uncertainty of their own value predictions -- for instance to compute an exploration bonus or upper confidence bound. Unfortunately the required uncertainty is difficult to estimate in general with function approximation. We propose epistemic value estimation (EVE): a recipe that is compatible with sequential decision making and with neural network function approximators. It equips agents with a tractable posterior over all their parameters from which epistemic value uncertainty can be computed efficiently. We use the recipe to derive an epistemic Q-Learning agent and observe competitive performance on a series of benchmarks. Experiments confirm that the EVE recipe facilitates efficient exploration in hard exploration tasks.

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Chentian Jiang, Nan Rosemary Ke, Hado van Hasselt

To generalize across tasks, an agent should acquire knowledge from past tasks that facilitate adaptation and exploration in future tasks. We focus on the problem of in-context adaptation and exploration, where an agent only relies on context, i.e., history of states, actions and/or rewards, rather than gradient-based updates. Posterior sampling (extension of Thompson sampling) is a promising approach, but it requires Bayesian inference and dynamic programming, which often involve unknowns (e.g., a prior) and costly computations. To address these difficulties, we use a transformer to learn an inference process from training tasks and consider a hypothesis space of partial models, represented as small Markov decision processes that are cheap for dynamic programming. In our version of the Symbolic Alchemy benchmark, our method's adaptation speed and exploration-exploitation balance approach those of an exact posterior sampling oracle. We also show that even though partial models exclude relevant information from the environment, they can nevertheless lead to good policies.

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Sebastian Flennerhag, Tom Zahavy, Brendan O'Donoghue, Hado van Hasselt, András György, Satinder Singh

We study the connection between gradient-based meta-learning and convex op-timisation. We observe that gradient descent with momentum is a special case of meta-gradients, and building on recent results in optimisation, we prove convergence rates for meta-learning in the single task setting. While a meta-learned update rule can yield faster convergence up to constant factor, it is not sufficient for acceleration. Instead, some form of optimism is required. We show that optimism in meta-learning can be captured through Bootstrapped Meta-Gradients (Flennerhag et al., 2022), providing deeper insight into its underlying mechanics.

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Steven Kapturowski, Víctor Campos, Ray Jiang, Nemanja Rakićević, Hado van Hasselt, Charles Blundell, Adrià Puigdomènech Badia

The task of building general agents that perform well over a wide range of tasks has been an important goal in reinforcement learning since its inception. The problem has been subject of research of a large body of work, with performance frequently measured by observing scores over the wide range of environments contained in the Atari 57 benchmark. Agent57 was the first agent to surpass the human benchmark on all 57 games, but this came at the cost of poor data-efficiency, requiring nearly 80 billion frames of experience to achieve. Taking Agent57 as a starting point, we employ a diverse set of strategies to achieve a 200-fold reduction of experience needed to out perform the human baseline. We investigate a range of instabilities and bottlenecks we encountered while reducing the data regime, and propose effective solutions to build a more robust and efficient agent. We also demonstrate competitive performance with high-performing methods such as Muesli and MuZero. The four key components to our approach are (1) an approximate trust region method which enables stable bootstrapping from the online network, (2) a normalisation scheme for the loss and priorities which improves robustness when learning a set of value functions with a wide range of scales, (3) an improved architecture employing techniques from NFNets in order to leverage deeper networks without the need for normalization layers, and (4) a policy distillation method which serves to smooth out the instantaneous greedy policy overtime.

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Veronica Chelu, Diana Borsa, Doina Precup, Hado van Hasselt

Efficient credit assignment is essential for reinforcement learning algorithms in both prediction and control settings. We describe a unified view on temporal-difference algorithms for selective credit assignment. These selective algorithms apply weightings to quantify the contribution of learning updates. We present insights into applying weightings to value-based learning and planning algorithms, and describe their role in mediating the backward credit distribution in prediction and control. Within this space, we identify some existing online learning algorithms that can assign credit selectively as special cases, as well as add new algorithms that assign credit backward in time counterfactually, allowing credit to be assigned off-trajectory and off-policy.

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Simon Schmitt, John Shawe-Taylor, Hado van Hasselt

To accumulate knowledge and improve its policy of behaviour, a reinforcement learning agent can learn `off-policy' about policies that differ from the policy used to generate its experience. This is important to learn counterfactuals, or because the experience was generated out of its own control. However, off-policy learning is non-trivial, and standard reinforcement-learning algorithms can be unstable and divergent. In this paper we discuss a novel family of off-policy prediction algorithms which are convergent by construction. The idea is to first learn on-policy about the data-generating behaviour, and then bootstrap an off-policy value estimate on this on-policy estimate, thereby constructing a value estimate that is partially off-policy. This process can be repeated to build a chain of value functions, each time bootstrapping a new estimate on the previous estimate in the chain. Each step in the chain is stable and hence the complete algorithm is guaranteed to be stable. Under mild conditions this comes arbitrarily close to the off-policy TD solution when we increase the length of the chain. Hence it can compute the solution even in cases where off-policy TD diverges. We prove that the proposed scheme is convergent and corresponds to an iterative decomposition of the inverse key matrix. Furthermore it can be interpreted as estimating a novel objective -- that we call a `k-step expedition' -- of following the target policy for finitely many steps before continuing indefinitely with the behaviour policy. Empirically we evaluate the idea on challenging MDPs such as Baird's counter example and observe favourable results.

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