Motivated by the recent applications of game-theoretical learning to the design of distributed control systems, we study a class of control problems that can be formulated as potential games with continuous action sets. We propose an actor-critic reinforcement learning algorithm that adapts mixed strategies over continuous action spaces. To analyze the algorithm, we extend the theory of finite-dimensional two-timescale stochastic approximation to a Banach space setting, and prove that the continuous dynamics of the process converge to equilibrium in the case of potential games. These results combine to give a provably-convergent learning algorithm in which players do not need to keep track of the controls selected by other agents.