A0276
Title: Statistical learning of distributionally robust stochastic control in continuous state spaces
Authors: Nian Si - HKUST (Hong Kong) [presenting]
Abstract: The purpose is to explore the control of stochastic systems with potentially continuous state and action spaces, characterized by the state dynamics $X_{t+1} = f(X_t, A_t, W_t)$. X, A, and W represent the state, action, and exogenous random noise processes, respectively, with f denoting a known function that describes state transitions. Traditionally, the noise process $W_t$, is assumed to be independent and identically distributed, with a distribution that is either fully known or can be consistently estimated. However, the occurrence of distributional shifts, typical in engineering settings, necessitates the consideration of the robustness of the policy. A distributionally robust stochastic control paradigm is introduced that accommodates possibly adaptive adversarial perturbation to the noise distribution within a prescribed ambiguity set. Two adversary models are examined: current-action-aware and current-action unaware, leading to different dynamic programming equations. Furthermore, the optimal finite-sample minimax rates are characterized for achieving uniform learning of the robust value function across continuum states under both adversary types, considering ambiguity sets defined by fk-divergence and Wasserstein distance. Finally, the applicability of the framework is demonstrated across various real-world settings.
