Minimax Optimal and Computationally Efficient Algorithms for
  Distributionally Robust Offline Reinforcement Learning
Zhishuai Liu Pan Xu
Distributionally robust offline reinforcement learning (RL), which seeks
robust policy training against environment perturbation by modeling dynamics
uncertainty, calls for function approximations when facing large state-action
spaces. However, the consideration of dynamics uncertainty introduces essential
nonlinearity and computational burden, posing unique challenges for analyzing
and practically employing function approximation. Focusing on a basic setting
where the nominal model and perturbed models are linearly parameterized, we
propose minimax optimal and computationally efficient algorithms realizing
function approximation and initiate the study on instance-dependent
suboptimality analysis in the context of robust offline RL. Our results uncover
that function approximation in robust offline RL is essentially distinct from
and probably harder than that in standard offline RL. Our algorithms and
theoretical results crucially depend on a variety of new techniques, involving
a novel function approximation mechanism incorporating variance information, a
new procedure of suboptimality and estimation uncertainty decomposition, a
quantification of the robust value function shrinkage, and a meticulously
designed family of hard instances, which might be of independent interest.