Exploring the Training Robustness of Distributional Reinforcement Learning against Noisy State Observations

TL;DR

This paper investigates the robustness of distributional reinforcement learning to noisy state observations, demonstrating its superior stability and lower vulnerability compared to expectation-based methods through theoretical analysis and extensive experiments.

Contribution

It provides a theoretical analysis of distributional RL's robustness to noisy observations and empirically shows its advantages over expectation-based RL.

Findings

Distributional RL maintains stable gradients under noisy conditions.

Distributional RL is less vulnerable to random and adversarial state noise.

Theoretical characterization of bounded gradient norms explains robustness.

Abstract

In real scenarios, state observations that an agent observes may contain measurement errors or adversarial noises, misleading the agent to take suboptimal actions or even collapse while training. In this paper, we study the training robustness of distributional Reinforcement Learning (RL), a class of state-of-the-art methods that estimate the whole distribution, as opposed to only the expectation, of the total return. Firstly, we validate the contraction of distributional Bellman operators in the State-Noisy Markov Decision Process (SN-MDP), a typical tabular case that incorporates both random and adversarial state observation noises. In the noisy setting with function approximation, we then analyze the vulnerability of least squared loss in expectation-based RL with either linear or nonlinear function approximation. By contrast, we theoretically characterize the bounded gradient norm of distributional RL loss based on the categorical parameterization equipped with the KL divergence. The resulting stable gradients while the optimization in distributional RL accounts for its better training robustness against state observation noises. Finally, extensive experiments on the suite of environments verified that distributional RL is less vulnerable against both random and adversarial noisy state observations compared with its expectation-based counterpart.