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3.10 proof of policy improvement bound 34 In the domain of robotic locomotion, we successfully learned controllers for swimming, walking and hopping in a physics simulator, using general purpose neural networks and minimally informative rewards. To our knowledge, no prior work has learned con- trollers from scratch for all of these tasks, using a generic policy search method and non-engineered, general-purpose policy representations. In the game-playing domain, we learned convolutional neural network policies that used raw images as inputs. This requires optimizing extremely high-dimensional policies, and only two prior methods report successful results on this task. Since the method we proposed is scalable and has strong theoretical foundations, we hope that it will serve as a jumping-off point for future work on training large, rich func- tion approximators for a range of challenging problems. At the intersection of the two experimental domains we explored, there is the possibility of learning robotic control policies that use vision and raw sensory data as input, providing a unified scheme for training robotic controllers that perform both perception and control. The use of more so- phisticated policies, including recurrent policies with hidden state, could further make it possible to roll state estimation and control into the same policy in the partially-observed setting. By combining our method with model learning, it would also be possible to sub- stantially reduce its sample complexity, making it applicable to real-world settings where samples are expensive. 3.10 proof of policy improvement bound This proof uses techniques from the proof of Theorem 4.1 in [KL02], adapting them to the more general setting considered in this chapter. Lemma 1. Given two policies π,π ̃, ∞ γtAπ(st, at) t=0 This expectation is taken over trajectories τ := (s0, a0, s1, a0, . . . ), and the notation Eτ∼π ̃ [. . . ] indicates that actions are sampled from π ̃ to generate τ. η(π ̃) = η(π)+Eτ∼π ̃PDF Image | OPTIMIZING EXPECTATIONS: FROM DEEP REINFORCEMENT LEARNING TO STOCHASTIC COMPUTATION GRAPHS
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