Title: Accelerating Safe Reinforcement Learning with Constraint-mismatched Policies. Abstract: We consider the problem of reinforcement learning when provided with (1) a baseline control policy and (2) a set of constraints that the controlled system must satisfy. The baseline policy can arise from a teacher agent, demonstration data or even a heuristic while the constraints might encode safety, fairness or other application-specific requirements. Importantly, the baseline policy may be sub-optimal for the task at hand, and is not guaranteed to satisfy the specified constraints. The key challenge therefore lies in effectively leveraging the baseline policy for faster learning, while still ensuring that the constraints are minimally violated. To reconcile these potentially competing aspects, we propose an iterative policy optimization algorithm that alternates between maximizing expected return on the task, minimizing distance to the baseline policy, and projecting the policy onto the constraint-satisfying set. We analyze the convergence of our algorithm theoretically and provide a finite-sample guarantee. In our empirical experiments on five different control tasks, our algorithm consistently outperforms several state-of-the-art methods, achieving 10 times fewer constraint violations and 40% higher reward on average.