A Distributional Perspective on Reinforcement Learning (1707.06887v1)

Abstract: In this paper we argue for the fundamental importance of the value distribution: the distribution of the random return received by a reinforcement learning agent. This is in contrast to the common approach to reinforcement learning which models the expectation of this return, or value. Although there is an established body of literature studying the value distribution, thus far it has always been used for a specific purpose such as implementing risk-aware behaviour. We begin with theoretical results in both the policy evaluation and control settings, exposing a significant distributional instability in the latter. We then use the distributional perspective to design a new algorithm which applies BeLLMan's equation to the learning of approximate value distributions. We evaluate our algorithm using the suite of games from the Arcade Learning Environment. We obtain both state-of-the-art results and anecdotal evidence demonstrating the importance of the value distribution in approximate reinforcement learning. Finally, we combine theoretical and empirical evidence to highlight the ways in which the value distribution impacts learning in the approximate setting.

• The paper establishes that modeling entire return distributions yields a contraction in the Wasserstein metric for policy evaluation.
• The paper introduces a novel RL algorithm using a categorical approach to approximate value distributions, achieving state-of-the-art results on Atari benchmarks.
• The paper highlights that instability in control settings due to non-contractive properties calls for innovative methods to ensure robust and stable learning.

A Distributional Perspective on Reinforcement Learning

The paper "A Distributional Perspective on Reinforcement Learning" by Marc G. Bellemare, Will Dabney, and Rémi Munos proposes a fundamental shift in reinforcement learning (RL) from traditional value expectation models to distributional models of return. This approach is premised on the notion that reinforcement learning agents can benefit from modeling the entire distribution of returns, rather than focusing solely on expected returns.

Key Contributions

The paper presents several key theoretical and practical contributions:

1. Theoretical Foundation:
   • The authors establish that the distributional BeLLMan operator, which defines the evolution of value distributions, is a contraction in the Wasserstein metric for policy evaluation. This confirms the stability of the distributional approach.
2. Instability in Control Setting:
   • In the control setting, the distributional BeLLMan operator does not exhibit contraction properties in any common metric over distributions. This highlights a significant instability that contrasts with the policy evaluation case. The authors suggest that learning algorithms need to be designed to account for the effects of nonstationary policies.
3. Algorithmic Advancement:
   • The paper introduces a novel RL algorithm that approximates value distributions using a parameterized distribution. This algorithm applies the distributional BeLLMan equation and employs a categorical approach to project distributions onto a discrete support.
4. Empirical Success:
   • Through experiments on the Arcade Learning Environment, the proposed algorithm achieves state-of-the-art results on several benchmark games. This empirical evidence demonstrates the practical viability and strengths of modeling value distributions.

Numerical Results and Empirical Validation

The algorithm was rigorously tested on Atari 2600 games, showcasing improved performance over traditional and recent algorithms. Specifically, the distributional approach achieved significant performance boosts in games like Seaquest, where it reached state-of-the-art levels.

The detailed empirical results indicate that approximation of value distributions rather than expected values delivers more stable and robust learning, especially in complex environments like those found in Atari games. For example, the empirical results indicated increased performance on a number of games compared to other state-of-the-art algorithms like Double DQN and Prioritized Experience Replay.

Implications and Future Directions

The distributional perspective on RL introduces both practical and theoretical implications:

• Robust Learning: Modeling the full distribution of returns helps in capturing the risk and variability in returns, which is critical in environments with high uncertainty or variability.
• Stability Issues: The observed instabilities in contraction properties of the control setting imply that further research is needed to develop methods that mitigate such instabilities.
• Approximation Benefits: The empirical success demonstrates that distributional approaches can yield better approximations and, consequently, enhanced performance in practical scenarios.

From a theoretical standpoint, this approach opens new avenues for research in contraction properties of operators and the impact of distribution modeling on algorithmic stability. Practically, future work may explore richer parametric models and further optimization of the distribution approximation techniques.

Conclusion

In summary, this paper substantiates the importance of adopting a distributional perspective in reinforcement learning. The presented theoretical foundations and empirical validations suggest that focusing on the entirety of value distributions offers substantial improvements over conventional expectation-based methods. As RL continues to evolve, embracing such distributional methodologies promises to enhance both the stability and performance of learning agents in varied and complex environments.