Tighter Regret Bounds for Contextual Action-Set Reinforcement Learning
Authors: Zijun Chen, Zihan Zhang
Summary
arXiv:2605. 15692v1 Announce Type: cross 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.
Relevance
Read next because Tighter Regret Bounds for Contextual Action-Set Reinforcement Learning overlaps with clean result "LoRA persona trained on alone emits at 23.5% when a co-trained partner learns ..., vs 0% control on Qwen2.5-7B-Instruct (MODERATE confidence)", clean result "Leakage rate is a usable signal for recovering trigger-shaped phrases on Gaperon-1125-1B without knowing the hidden trigger itself (MODERATE confidence)", clean result "Language-mismatch LoRA SFT on Qwen2.5-7B leaks the trained completion language into bystander directives the model was never trained on, absent under same-language SFT (LOW confidence)". Matching terms: strong, text, rate, contexts. Source: arxiv stat.ML (Machine Learning).
Threat model
Potential threat/caveat for clean result "LoRA persona trained on alone emits at 23.5% when a co-trained partner learns ..., vs 0% control on Qwen2.5-7B-Instruct (MODERATE confidence)": this item discusses adversarial.
Abstract
arXiv:2605.15692v1 Announce Type: cross 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, $\sum_{k=1}^K [V^{*,M^k} - V^{\pi^k,M^k}]$, 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 $\widetilde{O}(SAH^3/\epsilon^2)$ 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}{\Delta_{\min}^{p}} + pK\Delta_{\min}^{p} \right)\log K \cdot \mathrm{poly}(S,A,H) \right), ] where $\Delta_{\min}^{p}$ 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.