Title: Monotonic Robust Policy Optimization with Model Discrepancy. Abstract: State-of-the-art deep reinforcement learning (DRL) algorithms tend to overfit in some specific environments due to the lack of data diversity in training. To mitigate the model discrepancy between training and target (testing) environments, domain randomization (DR) can generate plenty of environments with a sufficient diversity by randomly sampling environment parameters in simulator. Though standard DR using a uniform distribution improves the average performance on the whole range of environments, the worst-case environment is usually neglected without any performance guarantee. Since the average and worst-case performance are equally important for the generalization in RL, in this paper, we propose a policy optimization approach for concurrently improving the policy's performance in the average case (i.e., over all possible environments) and the worst-case environment. We theoretically derive a lower bound for the worst-case performance of a given policy over all environments. Guided by this lower bound, we formulate an optimization problem which aims to optimize the policy and sampling distribution together, such that the constrained expected performance of all environments is maximized. We prove that the worst-case performance is monotonically improved by iteratively solving this optimization problem. Based on the proposed lower bound, we develop a practical algorithm, named monotonic robust policy optimization (MRPO), and validate MRPO on several robot control tasks. By modifying the environment parameters in simulation, we obtain environments for the same task but with different transition dynamics for training and testing. We demonstrate that MRPO can improve both the average and worst-case performance in the training environments, and facilitate the learned policy with a better generalization capability in unseen testing environments.