Continuous state spaces and stochastic, switching dynamics characterize a number of rich, real world domains, such as robot navigation across varying terrain. We describe a reinforcement learning algorithm for learning in these domains and prove for certain environments the algorithm is probably approximately correct with a sample complexity that scales polynomially with the state-space dimension. Unfortunately, no optimal planning techniques exist in general for such problems; instead we use fitted value iteration to solve the learned MDP, and include the error due to approximate planning in our bounds. Finally, we report an experiment using a robotic car driving over varying terrain to demonstrate that these dynamics representations adequately capture real-world dynamics and that our algorithm can be used to efficiently solve such problems.