Autonomous learning of robotic skills can allow general-purpose robots to learn wide behavioral repertoires without requiring extensive manual engineering. However, robotic skill learning methods typically make one of several trade-offs to enable practical real-world learning, such as requiring manually designed policy or value function representations, initialization from human-provided demonstrations, instrumentation of the training environment, or extremely long training times. In this paper, we propose a new reinforcement learning algorithm for learning manipulation skills that can train general-purpose neural network policies with minimal human engineering, while still allowing for fast, efficient learning in stochastic environments. Our approach builds on the guided policy search (GPS) algorithm, which transforms the reinforcement learning problem into supervised learning from a computational teacher (without human demonstrations). In contrast to prior GPS methods, which require a consistent set of initial states to which the system must be reset after each episode, our approach can handle randomized initial states, allowing it to be used in environments where deterministic resets are impossible. We compare our method to existing policy search techniques in simulation, showing that it can train high-dimensional neural network policies with the same sample efficiency as prior GPS methods, and present real-world results on a PR2 robotic manipulator.