Action Gaps and Advantages in Continuous-Time Distributional Reinforcement Learning (2410.11022v1)

Abstract: When decisions are made at high frequency, traditional reinforcement learning (RL) methods struggle to accurately estimate action values. In turn, their performance is inconsistent and often poor. Whether the performance of distributional RL (DRL) agents suffers similarly, however, is unknown. In this work, we establish that DRL agents are sensitive to the decision frequency. We prove that action-conditioned return distributions collapse to their underlying policy's return distribution as the decision frequency increases. We quantify the rate of collapse of these return distributions and exhibit that their statistics collapse at different rates. Moreover, we define distributional perspectives on action gaps and advantages. In particular, we introduce the superiority as a probabilistic generalization of the advantage -- the core object of approaches to mitigating performance issues in high-frequency value-based RL. In addition, we build a superiority-based DRL algorithm. Through simulations in an option-trading domain, we validate that proper modeling of the superiority distribution produces improved controllers at high decision frequencies.

• The paper introduces a distributional action gap concept that evaluates the distinguishability of action-conditioned return distributions using optimal transport metrics.
• The study shows that as decision frequency increases, return means collapse faster than other statistics, revealing limitations of traditional DRL methods.
• The research develops a superiority-based DRL algorithm that enhances performance in high-frequency settings, validated through option-trading simulations.

Action Gaps and Advantages in Continuous-Time Distributional Reinforcement Learning

This paper explores the intricacies of high-frequency decision-making in distributional reinforcement learning (DRL) contexts, specifically focusing on continuous-time environments. It highlights that traditional reinforcement learning (RL) algorithms struggle to maintain performance consistency at high decision frequencies due to issues in estimating action values. The researchers extend this investigation to the domain of DRL, finding similar sensitivities.

Key Contributions

1. Distributional Action Gap: The paper introduces an extension of the action gap concept to DRL, evaluating the distinguishability of action-conditioned return distributions using metrics from probability theory, specifically $W_p$ distances from Optimal Transportation theory. Results demonstrate that these distributional action gaps collapse as decision intervals ($\timestep$) decrease, albeit more slowly than in traditional setting.
2. Collapse at High Frequencies: Tight bounds are established on the distributional action gaps of action-conditioned return distributions. As the decision frequency increases, it's shown that the means of the return distributions collapse at a faster rate than their other statistics, undermining straightforward transliterations of traditional RL solutions to DRL.
3. Distributional Superiority: Introducing a probabilistic generalization of the advantage function, termed the superiority, the authors outline its utility in remedying performance issues at high decision frequencies. This superiority metric, defined axiomatically, provides a more robust framework for action selection in varying frequency settings.
4. Algorithm Development: A superiority-based DRL algorithm is developed and tested within a simulation of an option-trading domain. These experiments indicate improved performance and controller robustness at high decision frequencies compared to existing algorithms.

Implications and Future Directions

The paper underscores the limitations of conventional RL and DRL techniques in contexts requiring rapid decision-making, pertinent to fields like robotics and finance. The introduction of distributional superiority presents a promising alternative approach, with empirical validation showing enhanced policy optimization capabilities.

Moving forward, the integration of superiority metrics into RL frameworks harbors potential for broad applicability across domains necessitating quick adaptive responses. Further research could include testing the superiority-based approaches across diverse environments and exploring synergies with other machine learning models to enhance decision-making under uncertainty.

Conclusion

This research delineates the sensitivity of DRL algorithms to decision frequencies, offers theoretical insights into action gaps and advantages in continuous-time settings, and proposes a novel metric—the superiority distribution—for improved policy learning. The superior performance of the proposed DRL algorithm in high-frequency settings solidifies its utility and prospects for future RL applications.