Robust Offline Reinforcement Learning with Heavy-Tailed Rewards: Enhancing Policy Evaluation and Optimization

Core Concepts

This paper proposes two algorithmic frameworks, ROAM and ROOM, to enhance the robustness of offline reinforcement learning (RL) in scenarios with heavy-tailed rewards, a prevalent issue in real-world applications. The key idea is to strategically incorporate the median-of-means method with offline RL, enabling straightforward uncertainty estimation for the value function estimator and effectively managing heavy-tailed rewards.

Abstract

The paper addresses the challenge of heavy-tailed rewards in offline reinforcement learning (RL), which poses great difficulties for existing methods. The authors propose two frameworks: ROAM (Robust Off-policy Evaluation via Median-of-means) for off-policy evaluation (OPE): ROAM leverages the median-of-means (MM) estimator to robustly estimate the Q-function and value of a target policy. ROAM provides a natural way to quantify the uncertainty of the value estimation, which is crucial in high-risk applications. Theoretical analysis shows ROAM outperforms existing methods when rewards are heavy-tailed. ROOM (Robust OPO via Median-of-means) for offline policy optimization (OPO): ROOM extends the MM approach to value-based OPO algorithms, enabling robust Q-function estimation. ROOM naturally incorporates the principle of pessimism to address insufficient data coverage, further enhancing performance in heavy-tailed environments. Theoretical results demonstrate ROOM provides a robust lower bound for the optimal Q-function. The authors conduct extensive experiments on benchmark environments, demonstrating the superiority of ROAM and ROOM over existing methods when rewards exhibit heavy-tailed distributions.

Stats

"The heavy-tailedness pose great challenges to existing offline RL methods." "In a two-armed bandit example, the large variance in estimating the expected reward causes a non-negligible probability of selecting the sub-optimal arm. In settings with heavy-tailed rewards, the empirical mean of the sub-optimal arm is subject to an even larger variance, leading to a higher probability of selecting the sub-optimal arm."

Quotes

"To accommodate the heavy-tailed rewards in offline RL, we propose new frameworks for both OPE and OPO by leveraging the median-of-means (MM) estimator in robust statistics." "The proposed approach also provides a natural way for qualifying the uncertainty of value estimation, which is crucial in both OPE and OPO."

Key Insights Distilled From

Robust Offline Reinforcement learning with Heavy-Tailed Rewards

by Jin Zhu,Runz... at arxiv.org 04-02-2024

https://arxiv.org/pdf/2310.18715.pdf

Deeper Inquiries

How can the proposed frameworks be extended to handle other types of distributional shift, such as covariate shift, in offline RL

The proposed frameworks, ROAM and ROOM, can be extended to handle other types of distributional shift, such as covariate shift, in offline RL by incorporating techniques from domain adaptation and transfer learning. Covariate shift occurs when the distribution of input features changes between the training and testing data. To address this, one approach could be to adapt the MM estimator to handle shifts in the feature space. By incorporating domain adaptation methods into the MM framework, the algorithms can learn to adjust for changes in the input distribution. Additionally, techniques like importance weighting or domain adversarial training can be integrated into the MM estimator to account for covariate shift in the offline RL setting.

What are the potential limitations of the median-of-means approach, and how can they be addressed in future research

One potential limitation of the median-of-means approach is its sensitivity to the choice of the number of partitions (K) and the block size within each partition. If these parameters are not chosen optimally, it can affect the robustness and performance of the estimator. To address this limitation, future research could focus on developing adaptive methods that automatically determine the optimal values for K and the block size based on the characteristics of the dataset. Additionally, exploring the use of different robust estimators in conjunction with the MM approach could provide more flexibility and potentially improve performance in handling heavy-tailed data.

Can the ideas behind ROAM and ROOM be applied to other areas of machine learning beyond reinforcement learning to enhance robustness against heavy-tailed data

The ideas behind ROAM and ROOM can be applied to other areas of machine learning beyond reinforcement learning to enhance robustness against heavy-tailed data. For example, in supervised learning tasks such as classification or regression, where heavy-tailed data distributions can lead to model instability, incorporating the MM estimator could help in improving the robustness of the models. By integrating the MM approach into existing algorithms for supervised learning, researchers can develop methods that are more resilient to outliers and heavy-tailed data. Additionally, the principles of pessimism and uncertainty quantification from ROAM and ROOM can be valuable in various machine learning applications to improve model performance in the presence of challenging data distributions.