$f$-Divergence Regularized RLHF: Two Tales of Sampling and Unified Analyses

• URL: http://arxiv.org/abs/2605.06977v1
• Date: Thu, 07 May 2026 21:48:26 GMT
• Title: $f$-Divergence Regularized RLHF: Two Tales of Sampling and Unified Analyses
• Abstract summary: Reinforcement Learning from Human Feedback is a cornerstone technique for post-training large language models.<n>Recent empirical studies have begun exploring alternative divergences as regularizers in RLHF.<n>This work develops a comprehensive theoretical framework for online RLHF with a general $f$-divergence regularized objective.
• Score: 19.590316589389577
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Reinforcement Learning from Human Feedback (RLHF) has become a cornerstone technique for post-training large language models. While most existing approaches rely on the reverse KL-regularization, recent empirical studies have begun exploring alternative divergences (e.g., forward KL, chi-squared) as regularizers in RLHF. However, a unified theoretical understanding of general $f$-divergence regularization remains under-explored. To fill this gap, this work develops a comprehensive theoretical framework for online RLHF with a general $f$-divergence regularized objective. Rather than treating each possible divergence function individually, we adopt a holistic perspective across the entire function class and propose two algorithms based on distinct sampling principles. The first extends the classical optimism principle with a carefully designed exploration bonus, while the second introduces a new method that exploits the sensitivity of the optimal policy to reward perturbations under $f$-divergence regularization. Theoretical analysis shows that $O(\log T)$ regret and $O(1/T)$ sub-optimality gap are achievable, establishing provable efficiency of both algorithms and, to the best of our knowledge, the first performance bounds for online RLHF under general $f$-divergence regularization.

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