  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.

Machine Learning