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arXiv 2007.11684cs.LGmath.OCstat.ML

Approximation Benefits of Policy Gradient Methods with Aggregated States

Columbia University(哥伦比亚大学)

Daniel Russo

英文摘要:

Folklore suggests that policy gradient can be more robust to misspecification than its relative, approximate policy iteration. This paper studies the case of state-aggregated representations, 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. Faced with inherent approximation error, methods that locally optimize the true decision-objective can be far more robust.

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