Distributional Reinforcement Learning with Quantile Regression (1710.10044v1)

Abstract: In reinforcement learning an agent interacts with the environment by taking actions and observing the next state and reward. When sampled probabilistically, these state transitions, rewards, and actions can all induce randomness in the observed long-term return. Traditionally, reinforcement learning algorithms average over this randomness to estimate the value function. In this paper, we build on recent work advocating a distributional approach to reinforcement learning in which the distribution over returns is modeled explicitly instead of only estimating the mean. That is, we examine methods of learning the value distribution instead of the value function. We give results that close a number of gaps between the theoretical and algorithmic results given by Bellemare, Dabney, and Munos (2017). First, we extend existing results to the approximate distribution setting. Second, we present a novel distributional reinforcement learning algorithm consistent with our theoretical formulation. Finally, we evaluate this new algorithm on the Atari 2600 games, observing that it significantly outperforms many of the recent improvements on DQN, including the related distributional algorithm C51.

• The paper introduces a quantile regression-based RL algorithm that models full return distributions and proves that its distributional Bellman operator is a contraction.
• The method assigns fixed probabilities to adjustable quantile locations, simplifying distribution estimation and effectively reducing the Wasserstein distance.
• Empirical results on Atari games demonstrate a 33% performance boost over C51, validating the practical advantages of this approach.

Distributional Reinforcement Learning with Quantile Regression

The paper "Distributional Reinforcement Learning with Quantile Regression," authored by Will Dabney, Mark Rowland, Marc G. Bellemare, and Remi Munos, builds on recent advancements in reinforcement learning (RL) by focusing on a distributional approach. By leveraging quantile regression, the authors provide a novel perspective on modeling the distribution over returns, offering significant improvements in algorithmic performance and theoretical understanding.

Background and Motivation

Traditional RL methods prioritize estimating the expected value of the return, averaging over the inherent randomness in future rewards. This paper extends the distributional RL perspective, initially introduced by the C51 algorithm, which models the entire distribution of returns instead of merely their expectation. Such an approach facilitates a better representation of the uncertainties within the environment.

Contribution and Methodology

The paper's primary contribution is the introduction of a new distributional RL algorithm that capitalizes on quantile regression. This approach provides a theoretical and practical framework for RL algorithms to work directly over the Wasserstein metric. Key developments include:

1. Quantile-based Parametrization: Instead of fixing support locations and adjusting probabilities, as in C51, the new method assigns fixed probabilities to adjustable locations. This choice simplifies the implementation and aligns directly with quantile regression techniques.
2. Quantile Regression Application: The authors demonstrate how quantile regression can be used to approximate distributions by adjusting locations, effectively minimizing Wasserstein distance.
3. Theoretical Validation: The paper rigorously proves that the combined operator of quantile regression and the distributional BeLLMan update is a contraction, ensuring convergence to an optimal policy.
4. Numerical Validation: The proposed QR-DQN algorithm significantly outperformed its predecessors on the Atari 2600 suite, achieving improved scores due to the effective representation of return distributions.

Results and Implications

Experimental results indicate a substantial enhancement in performance over existing algorithms. By applying their approach to Atari games, the authors observed a marked 33% improvement over C51 in terms of median score increments. Such empirical evidence supports the assertion that explicitly modeling value distributions can lead to superior policy performance.

Theoretical and Practical Implications

The implications of this work are manifold:

• Theoretical: This approach bridges the previous disconnect between theory and practice in distributional RL. By leveraging the properties of the Wasserstein metric and quantile regression, the algorithm achieves both stability and effectiveness.
• Practical: Enhanced robustness and reduced sample complexity position this method as a compelling alternative for various RL applications. Furthermore, the ability to model the entire distribution allows for more nuanced control policies, potentially improving decision-making in high-risk environments.

Future Directions

Several avenues for further research emerge from this paper:

• Combining with Advanced Architectures: Incorporating techniques like Double DQN or dueling architectures might amplify the benefits of QR-DQN.
• Risk-sensitive Policies: The quantile-based approach offers a pathway to develop risk-sensitive policies, leveraging the richer information provided by value distributions.
• Broader Applications: Extending this framework beyond game environments to real-world scenarios could uncover additional opportunities and challenges, such as robotics or financial modeling.

Conclusion

This paper presents a significant advancement in distributional reinforcement learning by integrating quantile regression, effectively enhancing both theoretical foundations and practical applications. The proposed algorithmic approach not only advances the performance of RL systems but also clarifies the utility of considering value distributions outright. As such, it sets a promising stage for future exploration of distributional methods in reinforcement learning.