Contrastingly, others have observed that larger batch sizes tend to converge to "sharper" optimization

Since the policy used to collect transitions is changing throughout learning, the replay memory contains data coming from a mixture of policies (that differ from the agent's current policy), and

We study the multi-step off-policy learning approach to distributional RL.

The last decade has seen an upswing in interest and adoption of reinforcement learning (RL) techniques, in large part due to its demonstrated capabilities at performing certain tasks at "super-human levels". This has incentivized the community to prioritize research that demonstrates RL agent performance, often at the expense of research aimed at understanding their learning dynamics. Performance-focused research runs the risk of overfitting on academic benchmarks -- thereby rendering them less useful -- which can make it difficult to transfer proposed techniques to novel problems. Further, it implicitly diminishes work that does not push the performance-frontier, but aims at improving our understanding of these techniques. This paper argues two points: (i) RL research should stop focusing solely on demonstrating agent capabilities, and focus more on advancing the science and understanding of reinforcement learning; and (ii) we need to be more precise on how our benchmarks map to the underlying mathematical formalisms. We use the popular Arcade Learning Environment (ALE; Bellemare et al., 2013) as an example of a benchmark that, despite being increasingly considered "saturated", can be effectively used for developing this understanding, and facilitating the deployment of RL techniques in impactful real-world problems.

In the era of deep reinforcement learning, making progress is more complex, as the collected experience must be compressed into a deep model for future exploitation and sampling. Many papers have shown that training a deep learning policy under the changing state and action distribution leads to sub-optimal performance, or even collapse. This naturally leads to the concern that even if the community creates improved exploration algorithms or reward objectives, will those improvements fall on the \textit{deaf ears} of optimization difficulties. This work proposes a new \textit{practical} sub-optimality estimator to determine optimization limitations of deep reinforcement learning algorithms. Through experiments across environments and RL algorithms, it is shown that the difference between the best experience generated is 2-3$\times$ better than the policies' learned performance. This large difference indicates that deep RL methods only exploit half of the good experience they generate.

In reinforcement learning (RL), the long-term behavior of decision-making policies is evaluated based on their average returns. Distributional RL has emerged, presenting techniques for learning return distributions, which provide additional statistics for evaluating policies, incorporating risk-sensitive considerations. When the passage of time cannot naturally be divided into discrete time increments, researchers have studied the continuous-time RL (CTRL) problem, where agent states and decisions evolve continuously. In this setting, the Hamilton-Jacobi-Bellman (HJB) equation is well established as the characterization of the expected return, and many solution methods exist. However, the study of distributional RL in the continuous-time setting is in its infancy. Recent work has established a distributional HJB (DHJB) equation, providing the first characterization of return distributions in CTRL. These equations and their solutions are intractable to solve and represent exactly, requiring novel approximation techniques. This work takes strides towards this end, establishing conditions on the method of parameterizing return distributions under which the DHJB equation can be approximately solved. Particularly, we show that under a certain topological property of the mapping between statistics learned by a distributional RL algorithm and corresponding distributions, approximation of these statistics leads to close approximations of the solution of the DHJB equation. Concretely, we demonstrate that the quantile representation common in distributional RL satisfies this topological property, certifying an efficient approximation algorithm for continuous-time distributional RL.

Value functions are a central component of deep reinforcement learning (RL). These functions, parameterized by neural networks, are trained using a mean squared error regression objective to match bootstrapped target values. However, scaling value-based RL methods that use regression to large networks, such as high-capacity Transformers, has proven challenging. This difficulty is in stark contrast to supervised learning: by leveraging a cross-entropy classification loss, supervised methods have scaled reliably to massive networks. Observing this discrepancy, in this paper, we investigate whether the scalability of deep RL can also be improved simply by using classification in place of regression for training value functions. We demonstrate that value functions trained with categorical cross-entropy significantly improves performance and scalability in a variety of domains. These include: single-task RL on Atari 2600 games with SoftMoEs, multi-task RL on Atari with large-scale ResNets, robotic manipulation with Q-transformers, playing Chess without search, and a language-agent Wordle task with high-capacity Transformers, achieving state-of-the-art results on these domains. Through careful analysis, we show that the benefits of categorical cross-entropy primarily stem from its ability to mitigate issues inherent to value-based RL, such as noisy targets and non-stationarity. Overall, we argue that a simple shift to training value functions with categorical cross-entropy can yield substantial improvements in the scalability of deep RL at little-to-no cost.