Approximation Benefits of Policy Gradient Methods with Aggregated States
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Folklore suggests that policy gradient can be more robust to misspecification than its relative, approximate policy iteration. This paper studies the case of state-aggregation, where the state space is partitioned and either the policy or value function approximation is held constant over partitions. This paper shows a policy gradient method converges to a policy whose regret per-period is bounded by ϵ, the largest difference between two elements of the state-action value function belonging to a common partition. With the same representation, both approximate policy iteration and approximate value iteration can produce policies whose per-period regret scales as ϵ/(1-γ), where γ is a discount factor. Theoretical results synthesize recent analysis of policy gradient methods with insights of Van Roy (2006) into the critical role of state-relevance weights in approximate dynamic programming.
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