Unsupervised Basis Function Adaptation for Reinforcement Learning
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When using reinforcement learning (RL) algorithms to evaluate a policy it is common, given a large state space, to introduce some form of approximation architecture for the value function (VF). The exact form of this architecture can have a significant effect on the accuracy of the VF estimate, however, and determining a suitable approximation architecture can often be a highly complex task. Consequently there is a large amount of interest in the potential for allowing RL algorithms to adaptively generate (i.e. to learn) approximation architectures. We investigate a method of adapting approximation architectures which uses feedback regarding the frequency with which an agent has visited certain states to guide which areas of the state space to approximate with greater detail. We introduce an algorithm based upon this idea which adapts a state aggregation approximation architecture on-line. Assuming S states, we demonstrate theoretically that - provided the following relatively non-restrictive assumptions are satisfied: (a) the number of cells X in the state aggregation architecture is of order √(S)S_2S or greater, (b) the policy and transition function are close to deterministic, and (c) the prior for the transition function is uniformly distributed - our algorithm can guarantee, assuming we use an appropriate scoring function to measure VF error, error which is arbitrarily close to zero as S becomes large. It is able to do this despite having only O(X_2S) space complexity (and negligible time complexity). We conclude by generating a set of empirical results which support the theoretical results.
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