Efficient Dual Perturbation Robustness in Low-rank Markov Decision Processes

Core Concepts

The authors propose a novel robustness concept based on (ξ, η)-rectangularity that achieves efficient dual perturbation robustness in low-rank Markov decision processes (MDPs). They design an algorithm (R2PG) that provably converges to the optimal robust policy with bounded suboptimality.

Abstract

The paper addresses the challenge of achieving robustness in reinforcement learning (RL) agents trained in simulated environments, which often suffer from performance degradation when deployed in real-world environments due to distributional shift. The key insights are: The authors propose a new robustness concept based on (ξ, η)-rectangularity, which allows for efficient dual perturbation of both the feature maps and the factors in low-rank MDPs. This is in contrast to existing methods that only consider perturbation of either the features or the factors. They design the R2PG algorithm that iteratively evaluates and improves the robust policy. The policy evaluation step involves solving an optimization problem that can be reduced to a semi-definite program, making the algorithm computationally efficient. The authors provide a convergence guarantee for the R2PG algorithm, showing that the robust value of the output policy is close to that of the optimal robust policy. Numerical simulations on a toy model demonstrate the effectiveness of the proposed approach, where the output policies exhibit more conservative behavior as the perturbation radius increases. The paper makes a significant contribution by introducing a new robustness concept that is compatible with low-rank representations and enables the design of provably efficient and scalable algorithms for robust RL.

Stats

The paper does not contain any explicit numerical data or statistics. It focuses on the theoretical development of the robust low-rank MDP framework and the R2PG algorithm.

Quotes

None.

Key Insights Distilled From

Efficient Duple Perturbation Robustness in Low-rank MDPs

by Yang Hu,Hait... at arxiv.org 04-15-2024

https://arxiv.org/pdf/2404.08089.pdf

Deeper Inquiries

How can the proposed robustness concept be extended to handle other types of low-rank structures beyond the linear representation considered in this paper

The proposed robustness concept can be extended to handle other types of low-rank structures beyond linear representation by considering more complex feature and factor interactions. For example, one could explore non-linear feature mappings or incorporate additional latent variables into the low-rank MDP framework. By allowing for more flexible representations of the transition probabilities and rewards, the robustness concept can be adapted to capture a wider range of uncertainties in the system dynamics. This extension would involve defining appropriate ambiguity sets that account for the new structure of the low-rank MDPs and designing algorithms that can efficiently handle the increased complexity of the model.

Can the R2PG algorithm be further improved to achieve asymptotically accurate robust policy optimization, rather than the bounded suboptimality guarantee provided in the current analysis

To achieve asymptotically accurate robust policy optimization with the R2PG algorithm, one could explore techniques for improving the convergence properties of the algorithm. This could involve refining the optimization procedures used in policy evaluation and policy improvement steps to ensure that the algorithm converges to the optimal robust policy with higher precision. Additionally, incorporating advanced optimization methods, such as adaptive learning rates or more sophisticated policy update strategies, could help enhance the algorithm's performance and potentially lead to asymptotically accurate robust policy optimization.

What are the potential applications of the robust low-rank MDP framework in real-world domains, and how can the proposed approach be adapted to address the practical challenges in those domains

The robust low-rank MDP framework has various potential applications in real-world domains, such as robotics, autonomous systems, and decision-making under uncertainty. In robotics, the framework could be used to develop robust control policies for robotic agents operating in dynamic environments with uncertain dynamics. For autonomous systems, the framework could enable the design of resilient decision-making algorithms that can adapt to changing conditions and unforeseen events. To address practical challenges in these domains, the proposed approach could be adapted by incorporating domain-specific constraints, integrating sensor data for real-time decision-making, and optimizing the algorithm for efficient deployment on resource-constrained systems. Additionally, leveraging simulation environments and transfer learning techniques could help bridge the gap between simulated and real-world performance, enhancing the applicability of the framework in practical settings.