Reward Centering

Abstract: We show that discounted methods for solving continuing reinforcement learning problems can perform significantly better if they center their rewards by subtracting out the rewards' empirical average. The improvement is substantial at commonly used discount factors and increases further as the discount factor approaches one. In addition, we show that if a problem's rewards are shifted by a constant, then standard methods perform much worse, whereas methods with reward centering are unaffected. Estimating the average reward is straightforward in the on-policy setting; we propose a slightly more sophisticated method for the off-policy setting. Reward centering is a general idea, so we expect almost every reinforcement-learning algorithm to benefit by the addition of reward centering.

• The paper introduces reward centering, a method subtracting the empirical average reward, which theoretically and empirically improves discounted reinforcement learning algorithms, particularly for high discount factors, by reducing state-independent constant terms.
• Reward centering enhances the robustness of RL methods by making value estimates invariant to constant shifts in the reward signal, a common issue in dynamic environments.
• Empirical results across various domains demonstrate performance maintenance or improvement with centering, and the technique has broad potential applicability to various RL algorithms and future research directions like dynamic discount factors.

An Analysis of Reward Centering in Reinforcement Learning

This essay examines the paper on "Reward Centering" by Naik et al., which explores a method aimed at improving the efficiency of reinforcement learning (RL) algorithms, particularly those employing discount factors in continuing problems. The authors present a thorough investigation into how centering rewards can significantly enhance the performance of standard discounted-reward methods.

Summary of the Paper

The central thesis of the paper is that discounted reinforcement learning methods can benefit considerably from subtracting the empirical average of observed rewards—a process termed "reward centering." Theoretically backed by Blackwell's 1962 work, the authors illustrate that centering transforms the value estimates, removing a state-independent constant dependent on $1 - \gamma$, where $\gamma$ is the discount factor. This facilitates the focus on relative differences between states and actions, even when $\gamma$ is close to one, ameliorating common issues like numerical instability.

The paper further discusses the invariance of reward-centered methods to shifts in reward signals. Standard RL approaches exhibit diminished performance when the reward signal changes by a constant, whereas reward-centering methods remain unaffected. This feature enhances the robustness of RL algorithms in dynamic environments where reward characteristics may change.

Empirical and Theoretical Contributions

Empirically, the paper showcases several numerical results supporting their hypothesis. The study presents learning curves from experiments utilizing algorithms such as TD-learning and Q-learning with and without reward centering across various domains. For instance, in the Access-Control Queuing problem, reward centering enabled these algorithms to maintain or improve performance even at high discount factors, an area where uncentered methods typically struggle.

Theoretically, the authors leverage the Laurent-series decomposition of the discounted value function to elucidate the inherent benefits of reward centering. Their analysis points to the decomposition of the value function into constant and non-constant parts, with mean-centering effectively nullifying the influence of the constant component. This allows for simpler value estimation and improved stability as the discount factor approaches one.

Implications and Speculations on Future Work

The paper hints at a broad applicability of reward centering across various RL methods, suggesting potential improvements in actor-critic methods, policy-gradient approaches, and others. One intriguing direction for future research, as proposed by the authors, is the dynamic adjustment of discount factors during the learning process, enabled by simultaneous estimation of average rewards and centered values.

Additionally, reward centering's resilience to shifts in reward magnitude lays a foundation for augmenting RL algorithms with adaptive mechanisms that can smoothly handle changes in reward structures during agent-environment interactions.

Conclusion

In conclusion, Naik et al.'s paper presents a well-founded exploration of reward centering, demonstrating its utility in overcoming some of the intrinsic challenges faced by discounted-reward RL methods in continuing tasks. This technique offers a straightforward augmentation to existing algorithms, delivering increased robustness and efficiency, especially in environments characterized by complex and fluctuating reward dynamics. Reward centering, as articulated in this study, holds promise for broad applications within the reinforcement learning community, potentially catalyzing advancements in adaptive learning systems and RL algorithm designs.