KLPO: a critic-free, KL-regularized policy optimization method for LLM agents
A new arXiv paper, "On KL-Regularized Policy Optimization" by Yifan Zhang (submitted 6 Oct 2026), proposes KLPO, which anchors the KL regularizer at the sampler so asynchronous RL for LLM agents can train on trajectories from stale checkpoints and mismatched inference probabilities without importance weights. The paper says the regularized improvement step has a closed-form Gibbs solution, and that for token-level policy mirror descent targets the gradient can be computed from terminal returns without a critic, using one rollout per prompt. It further proves independent Monte Carlo estimates of the KL term keep gradients unbiased and shows SPPO, GPO, REBEL and BPO arise as special cases of KLPO.
Why it matters: If it holds up, it could simplify asynchronous RL training for LLM agents by removing critic networks and per-prompt response groups — though the claims are theoretical and the paper reports no experiments.
Computer Science > Machine Learning
arXiv:2610.08963 (cs)
[Submitted on 6 Oct 2026]
Title:On KL-Regularized Policy Optimization
Authors:Yifan Zhang
View a PDF of the paper titled On KL-Regularized Policy Optimization, by Yifan Zhang
View PDFAbstract:Asynchronous reinforcement learning (RL) for large language model (LLM) agents trains one policy on trajectories generated by another: rollouts come from stale checkpoints, and the inference engine's probabilities differ from the trainer's even at identical parameters. Standard remedies either clip importance ratios, which biases the update, or, as in GRPO, sample a group of responses per prompt, which is costly when episodes are long. We propose KL-Regularized Policy Optimization (KLPO), a framework that anchors the KL regularizer at the sampler. The regularized improvement step then has a closed-form Gibbs solution, and KLPO fits its log-ratio optimality condition by least squares on the sampler's own trajectories, so the sampler probability enters through a log-ratio and no importance weights are needed. Profiling out the regression intercept replaces the intractable log-partition function with the signal's sampler mean plus a sampler-to-trainer KL divergence. For token-level policy mirror descent targets, we show that the resulting gradient can be computed from terminal returns without a critic, via sampler-centered scores or a single trajectory residual, even under stochastic tool outputs. We further prove that independent Monte Carlo estimates of the KL term keep these gradients unbiased, derive the exact KL gap of cheaper top-$K$ and binary approximations, and show that SPPO, GPO, REBEL, and BPO arise as special cases of KLPO. The result is a critic-free update that uses one rollout per prompt and requires neither a learned normalizer nor a group of responses.
| Comments: | Project Page: this https URL |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Computation and Language (cs.CL) |
| Cite as: | arXiv:2610.08963 [cs.LG] |
| (or arXiv:2610.08963v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.08963 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Yifan Zhang [view email][v1] Tue, 6 Oct 2026 18:30:42 UTC (60 KB)
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- HiPLEX: Hierarchical Policy Factorization for Full-Duplex Speech Language ModelsHugging Face · Papers · GRPO