In this work, we address the problem of learning provably stable neural network policies for stochastic control systems.While recent work has demonstrated the feasibility of certifying given policies using martingale theory, the problem of how to learn such policies is little explored.Here, we study the effectiveness of jointly learning a policy together with a martingale certificate that proves its stability using a single learning algorithm.We observe that the joint optimization problem becomes easily stuck in local minima when starting from a randomly initialized policy. Our results suggest that some form of pre-training of the policy is required for the joint optimization to repair and verify the policy successfully.