A Comedy of Estimators: On KL Regularization in RL Training of LLMs

• URL: http://arxiv.org/abs/2512.21852v1
• Date: Fri, 26 Dec 2025 04:20:58 GMT
• Title: A Comedy of Estimators: On KL Regularization in RL Training of LLMs
• Authors: Vedant Shah, Johan Obando-Ceron, Vineet Jain, Brian Bartoldson, Bhavya Kailkhura, Sarthak Mittal, Glen Berseth, Pablo Samuel Castro, Yoshua Bengio, Nikolay Malkin, Moksh Jain, Siddarth Venkatraman, Aaron Courville,
• Abstract summary: reinforcement learning (RL) can substantially improve the reasoning performance of large language models (LLMs)<n>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.<n>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.<n>We study the gradients of several estimators configurations, revealing how design choices shape gradient bias.
• Score: 81.7906270099878
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• Controllable Exploration in Hybrid-Policy RLVR for Multi-Modal Reasoning [88.42566960813438]
  CalibRL is a hybrid-policy RLVR framework that supports controllable exploration with expert guidance.<n>CalibRL increases policy entropy in a guided manner and clarifies the target distribution.<n>Experiments across eight benchmarks, including both in-domain and out-of-domain settings, demonstrate consistent improvements.
  arXiv  Detail & Related papers  (2026-02-22T07:23:36Z)
• Data Distribution as a Lever for Guiding Optimizers Toward Superior Generalization in LLMs [60.68927774057402]
  We show, for the first time, that a lower simplicity bias induces a better generalization.<n>Motivated by this insight, we demonstrate that the training data distribution by upsampling or augmenting examples learned later in training similarly reduces SB and leads to improved generalization.<n>Our strategy improves the performance of multiple language models including Phi2-2.7B, Llama3.2-1B, Gemma3-1B-PT, Qwen3-0.6B-Base-achieving relative accuracy gains up to 18% when fine-tuned with AdamW and Muon.
  arXiv  Detail & Related papers  (2026-01-31T07:40:36Z)
• Comparative Analysis and Parametric Tuning of PPO, GRPO, and DAPO for LLM Reasoning Enhancement [0.0]
  This study presents a systematic comparison of three Reinforcement Learning (RL) algorithms for improving complex reasoning in large language models (LLMs)<n>We find that RL-trained models outperform their corresponding base models, although the degree of improvement differs by benchmark.<n>Increasing the group size in GRPO and DAPO leads to more stable training dynamics and higher accuracy, while the impact of the KL-penalty coefficient is non-monotonic.
  arXiv  Detail & Related papers  (2025-12-08T14:58:19Z)
• Balancing Interpretability and Performance in Reinforcement Learning: An Adaptive Spectral Based Linear Approach [15.065437093352054]
  Reinforcement learning (RL) has been widely applied to sequential decision making.<n>Current approaches typically focus on performance and rely on post hoc explanations to account for interpretability.<n>We propose a spectral based linear RL method that extends the ridge regression-based approach through a spectral filter function.
  arXiv  Detail & Related papers  (2025-10-04T07:53:43Z)
• CurES: From Gradient Analysis to Efficient Curriculum Learning for Reasoning LLMs [53.749193998004166]
  Curriculum learning plays a crucial role in enhancing the training efficiency of large language models.<n>We propose CurES, an efficient training method that accelerates convergence and employs Bayesian posterior estimation to minimize computational overhead.
  arXiv  Detail & Related papers  (2025-10-01T15:41:27Z)
• Relative Trajectory Balance is equivalent to Trust-PCL [72.58731629381032]
  Relative Trajectory Balance (RTB) aims to improve fine-tuning in sequential generative models.<n>This paper establishes an equivalence between RTB and Trust-PCL, an off-policy RL method with KL regularization.
  arXiv  Detail & Related papers  (2025-09-01T17:17:25Z)
• KDRL: Post-Training Reasoning LLMs via Unified Knowledge Distillation and Reinforcement Learning [72.53466291156604]
  We present textbfKDRL, a textitunified post-training framework that jointly optimize a reasoning model through teacher supervision (KD) and self-exploration (RL)<n>We first formulate a unified objective that integrates GRPO and KD, and systematically explore how different KL approximations, KL coefficients, and reward-guided KD strategies affect the overall post-training dynamics and performance.
  arXiv  Detail & Related papers  (2025-06-02T19:46:41Z)
• On the Design of KL-Regularized Policy Gradient Algorithms for LLM Reasoning [59.11784194183928]
  Policy gradient algorithms have been successfully applied to enhance the reasoning capabilities of large language models (LLMs)<n>Regularized Policy Gradient (RPG) view shows that the widely-used $k_3$ penalty is exactly the unnormalized KL.<n>RPG-REINFORCE with RPG-Style Clip improves accuracy by up to $+6$ absolute percentage points over DAPO.
  arXiv  Detail & Related papers  (2025-05-23T06:01:21Z)
• RL in Name Only? Analyzing the Structural Assumptions in RL post-training for LLMs [14.78605805191225]
  Reinforcement learning-based post-training of large language models (LLMs) has recently gained attention.<n>We critically examine the formulation and assumptions underlying these methods.
  arXiv  Detail & Related papers  (2025-05-19T19:57:15Z)
• Statistically Efficient Variance Reduction with Double Policy Estimation for Off-Policy Evaluation in Sequence-Modeled Reinforcement Learning [53.97273491846883]
  We propose DPE: an RL algorithm that blends offline sequence modeling and offline reinforcement learning with Double Policy Estimation. We validate our method in multiple tasks of OpenAI Gym with D4RL benchmarks.
  arXiv  Detail & Related papers  (2023-08-28T20:46:07Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.