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

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 both expectation-based and 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. Beyond SN-MDP, 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 histogram density estimation. 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 games verified the convergence of both expectation-based and distributional RL in the SN-MDP-like setting under different strengths of state observation noises. More importantly, in noisy settings beyond SN-MDP, distributional RL is less vulnerable against noisy state observations compared with its expectation-based counterpart.