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Sample-Efficient Reinforcement Learning Is Feasible for Linearly Realizable MDPs with Limited Revisiting

NeurIPS 2021 · Reinforcement learning › MDPs and planning · approach: Function approximation in RL theory · 6 citations (OpenAlex)

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Measured effects reported in the paper

What was changedWhereMeasuredEffect
Allow controlled state revisiting during online explorationRL with linearly realizable Q* · Finite-horizon MDP with a sub-optimality gapsample complexity scaling: polynomially in the feature dimension d, the horizon H, and the inverse sub-optimality gap 1/\taugap, but otherwise indeHelped
Permit state revisiting rather than restrict sampling to standard online RLRL with linearly realizable Q* · Online RL with a large sub-optimality gapfeasibility of sample-efficient learningHelped
Use the sub-optimality gap to trigger backtracking when the UCB bonus is too largeLinQ-LSVI-UCB · Finite-horizon MDP with linearly realizable Q*number of state revisits: K - N \le \frac{4c_{\beta}^2d^2H^5\log^2 \frac{KH}{\delta}}{\taugap^2}Helped
Use gap-based revisiting with LinQ-LSVI-UCBLinQ-LSVI-UCB · Finite-horizon MDP with linearly realizable Q*expected regret: \frac{17c_{\beta}^{2}d^{2}H^{7}\log^{2}(KH)}{\Delta_{\mathsf{gap}}^{2}}Helped
Use linear realizability of Q* without the stronger linear MDP assumptionRL with value-based linear representation · Finite-horizon MDPassumption strengthHelped
Estimate the next-step Q-value without adding its UCB bonus in the theta updateLinQ-LSVI-UCB · Finite-horizon MDP with linearly realizable Q*validity of the analysisHelped

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