Variance-Aware Fine-Grained Gap-Dependent Bounds for Online Reinforcement Learning
We study model-free online reinforcement learning (RL) for episodic tabular Markov decision processes, focusing on both gap-dependent regret and policy switching cost. While fine-grained gap-dependent analysis has been established for model-free RL algorithms using Hoeffding-type exploration bonuses, such results for model-free algorithms with variance-based exploration bonuses remain unknown, despite their superior worst-case and coarse-grained gap-dependent guarantees. In this paper, we resolve this open problem by establishing the first fine-grained gap-dependent regret upper bound for UCB-Bernstein+, a refined UCB-Bernstein algorithm, in variance-aware model-free online RL. Moreover, ...
| Authors | Haochen Zhang, Lingzhou Xue, Zhong Zheng |
|---|---|
| Primary category | stat.ML |
| Published | 3 October 2026 |
| Last updated at source | 3 October 2026 |
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