Title: Variance Reduced Domain Randomization for Policy Gradient. Abstract: By introducing randomness on environment parameters that fundamentally affect the dynamics, domain randomization (DR) imposes diversity to the policy trained by deep reinforcement learning, and thus improves its capability of generalization. The randomization of environments, however, introduces another source of variability for the estimate of policy gradients, in addition to the already high variance due to trajectory sampling. Therefore, with standard state-dependent baselines, the policy gradient methods may still suffer high variance, causing low sample efficiency during the training of DR. In this paper, we theoretically derive a bias-free and state/environment-dependent optimal baseline for DR, and analytically show its ability to achieve further variance reduction over the standard constant and state-dependent baselines for DR. We further propose a variance reduced domain randomization (VRDR) approach for policy gradient methods, to strike a tradeoff between the variance reduction and computational complexity in practice. By dividing the entire space of environments into some subspaces and estimating the state/subspace-dependent baseline, VRDR enjoys a theoretical guarantee of faster convergence than the state-dependent baseline. We conduct empirical evaluations on six robot control tasks with randomized dynamics. The results demonstrate that VRDR can consistently accelerate the convergence of policy training in all tasks, and achieve even higher rewards in some specific tasks.   