Jul 12, 2020
We study the exploration problem with approximate linear action-value functions in episodic reinforcement learning under the notion of low inherent Bellman error, a condition normally employed to show convergence of approximate value iteration. We relate this condition to other common frameworks and show that it is strictly more general than the low rank (or linear) MDP assumption of prior work. We provide an algorithm with a rate optimal regret bound for this setting. While computational tractability questions remain open, this enriches the class of MDPs with a linear representation for the action-value function where statistically efficient reinforcement learning is possible.
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