Tighter Regret Bounds for Contextual Action-Set Reinforcement Learning

• URL: http://arxiv.org/abs/2605.15692v1
• Date: Fri, 15 May 2026 07:28:42 GMT
• Title: Tighter Regret Bounds for Contextual Action-Set Reinforcement Learning
• Abstract summary: We study episodic reinforcement learning with fixed reward and transition functions, but with episode-dependent admissible action sets.<n>Performance is measured by cumulative regret against the episode-wise optimal value, $sum_k=1K [V*,Mk - Vk,Mk]$.<n>We show that the MVP algorithm naturally extends to this framework and enjoys strong theoretical guarantees.
• Score: 17.131069269126776
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study episodic reinforcement learning with fixed reward and transition functions, but with episode-dependent admissible action sets that are observed at the start of each episode. Performance is measured by cumulative regret against the episode-wise optimal value, $\sum_{k=1}^K [V^{*,M^k} - V^{π^k,M^k}]$, where $M^k$ represents the action context in the $k$-th episode. We show that the MVP algorithm naturally extends to this framework and enjoys strong theoretical guarantees. In particular, we establish a minimax regret bound of $\widetilde{O}(\sqrt{SAH^3K\log L})$ for adversarial contexts, where $L$ denotes the number of possible contexts. This result implies a regret bound of $\widetilde{O}(\sqrt{SAH^3K})$ for stochastic contexts. We further translate the stochastic regret guarantee into a sample complexity bound of $\widetilde{O}(SAH^3/ε^2)$ for a fixed context distribution. In addition, we derive a gap-dependent regret bound of \[ \widetilde O\left( \inf_{p\in [0,1)} \left( \frac{1}{Δ_{\min}^{p}} + pKΔ_{\min}^{p} \right)\log K \cdot \mathrm{poly}(S,A,H) \right), \] where $Δ_{\min}^{p}$ is the global $p$-trimmed positive-gap floor over suboptimal $(h,s,a)$ triples. This bound can substantially improve upon the minimax rate when the relevant suboptimality gaps are large.

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