aiqbench analysis
This paper identifies a critical implementation gap in reinforcement learning for large language models, where common KL divergence estimators introduce gradient bias that degrades reasoning performance. The authors demonstrate that switching to unbiased estimator configurations significantly improves model stability and generalization across both in-domain and out-of-distribution tasks. For practitioners fine-tuning LLMs via RL, this work provides essential guidance on correcting objective-function mismatches currently prevalent in open-source libraries.
A Comedy of Estimators: On KL Regularization in RL Training of LLMs
arXiv:2512.21852v4 Announce Type: replace-cross Abstract: The reasoning performance of large language models (LLMs) can be substantially improved by training them with reinforcement learning (RL). The RL objective for LLM training involves a regularization term, which is the reverse Kullback-Leibler (KL) divergence between the trained policy and the reference policy. Since computing the KL divergence exactly is intractable, various estimators are used in practice to estimate it from on-policy samples. Despite its wide adoption, including in several open-source libraries, there is no systematic study analyzing the numerous ways of incorporating KL estimators in the objective and their effect on the downstream performance of RL-trained models. Recent works show that prevailing practices for incorporating KL regularization do not provide correct gradients for stated objectives, creating a discrepancy between the objective and its implementation. In this paper, we further analyze these practices and study the gradients of several estimators configurations, revealing how design choices shape gradient bias. We substantiate these findings with empirical observations by RL fine-tuning \texttt{Qwen2.5-7B}, \texttt{Llama-3.1-8B-Instruct} and \texttt{Qwen3-4B-Instruct-2507} with different configurations and evaluating their performance on both in- and out-of-distribution tasks. Through our analysis, we observe that, in on-policy settings: (1) estimator configurations with biased gradients can result in training instabilities; and (2) using estimator configurations resulting in unbiased gradients leads to better performance on in-domain as well as out-of-domain tasks. We also investigate the performance resulting from different KL configurations in off-policy settings and observe that KL regularization can help stabilize off-policy RL training resulting from asynchronous setups.
Authors:Vedant Shah, Johan Obando-Ceron, Vineet Jain, Brian Bartoldson, Bhavya Kailkhura, Sarthak Mittal, Glen Berseth, Pablo Samuel Castro, Yoshua Bengio, Esmeralda S. Whitammer, Moksh Jain, Siddarth Venkatraman, Aaron Courville
Abstract:The reasoning performance of large language models (LLMs) can be substantially improved by training them with reinforcement learning (RL). The RL objective for LLM training involves a regularization term, which is the reverse Kullback-Leibler (KL) divergence between the trained policy and the reference policy. Since computing the KL divergence exactly is intractable, various estimators are used in practice to estimate it from on-policy samples. Despite its wide adoption, including in several open-source libraries, there is no systematic study analyzing the numerous ways of incorporating KL estimators in the objective and their effect on the downstream performance of RL-trained models. Recent works show that prevailing practices for incorporating KL regularization do not provide correct gradients for stated objectives, creating a discrepancy between the objective and its implementation. In this paper, we further analyze these practices and study the gradients of several estimators configurations, revealing how design choices shape gradient bias. We substantiate these findings with empirical observations by RL fine-tuning \texttt{Qwen2.5-7B}, \texttt{Llama-3.1-8B-Instruct} and \texttt{Qwen3-4B-Instruct-2507} with different configurations and evaluating their performance on both in- and out-of-distribution tasks. Through our analysis, we observe that, in on-policy settings: (1) estimator configurations with biased gradients can result in training instabilities; and (2) using estimator configurations resulting in unbiased gradients leads to better performance on in-domain as well as out-of-domain tasks. We also investigate the performance resulting from different KL configurations in off-policy settings and observe that KL regularization can help stabilize off-policy RL training resulting from asynchronous setups.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2512.21852 [cs.LG]
(or arXiv:2512.21852v4 [cs.LG] for this version)
Full text under the publisher's open licence · 286 words
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