aiqbench analysis
This paper provides rigorous theoretical proofs for the global linear convergence of PPO-Clip algorithms with KL-divergence regularization, addressing a critical gap in understanding the stability mechanisms behind modern LLM post-training methods. By establishing non-asymptotic convergence rates under general RL settings, the work offers essential mathematical guarantees that validate the empirical success of actor-only variants widely used in reinforcement learning from human feedback and fine-tuning pipelines.
Non-Asymptotic Global Convergence of PPO-Clip
arXiv:2512.16565v2 Announce Type: replace-cross Abstract: Reinforcement learning has gained attention for modern Large Language Model post-training. The actor-only variants of Proximal Policy Optimization (PPO) are widely applied for their efficiency. These algorithms incorporate a clipping mechanism to improve stability. Besides, a regularization term, such as the reverse KL-divergence or a more general \(f\)-divergence, is introduced to control excessive deviation from a reference policy. Despite their empirical success, a rigorous theoretical understanding of the problem and the algorithm's properties is limited. This paper advances the theoretical foundations of the PPO-Clip algorithm by analyzing a deterministic actor-only PPO algorithm within the general RL setting with \(f\)-divergence regularization under the softmax policy parameterization. We derive a non-uniform Lipschitz smoothness condition and a {\L}ojasiewicz inequality for the considered problem. Based on these properties, we establish non-asymptotic global linear convergence in value gap for the forward KL regularizer. For the reverse KL regularizer, we derive global linear convergence from any finite softmax initialization in both value gap and squared policy distance.
Abstract:Reinforcement learning has gained attention for modern Large Language Model post-training. The actor-only variants of Proximal Policy Optimization (PPO) are widely applied for their efficiency. These algorithms incorporate a clipping mechanism to improve stability. Besides, a regularization term, such as the reverse KL-divergence or a more general \(f\)-divergence, is introduced to control excessive deviation from a reference policy. Despite their empirical success, a rigorous theoretical understanding of the problem and the algorithm's properties is limited. This paper advances the theoretical foundations of the PPO-Clip algorithm by analyzing a deterministic actor-only PPO algorithm within the general RL setting with \(f\)-divergence regularization under the softmax policy parameterization. We derive a non-uniform Lipschitz smoothness condition and a Łojasiewicz inequality for the considered problem. Based on these properties, we establish non-asymptotic global linear convergence in value gap for the forward KL regularizer. For the reverse KL regularizer, we derive global linear convergence from any finite softmax initialization in both value gap and squared policy distance.
Optimization and Control (math.OC); Machine Learning (cs.LG)
arXiv:2512.16565 [math.OC]
(or arXiv:2512.16565v2 [math.OC] for this version)
https://doi.org/10.48550/arXiv.2512.16565 Focus to learn more arXiv-issued DOI via DataCite
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