Organizations: 1Meituan · 2Nanyang Technological University
Abstract
Reinforcement learning (RL) has become a central paradigm for large language model (LLM) post-training, but optimization toward new objectives can degrade capabilities already present in the base model. KL regularization is widely used to mitigate such forgetting by constraining policy drift toward a reference model. However, standard full-policy KL regularization constrains the entire response distribution and may unnecessarily restrict exploration and target-task learning. This raises a natural question: can a more precise constraint preserve existing capabilities while minimizing interference with learning new tasks? To this end, we propose \underline{Co}rrectness-Conditioned \underline{KL} Regularization (CoKL), a conditional regularization framework that narrows the preservation constraint from the full output distribution to correctness-conditioned response distributions. We instantiate CoKL with forward KL divergence and derive a practical finite-group training objective for RL-based LLM post-training. At the population level, CoKL decouples the total probability assigned to correct responses from their correctness-conditioned distribution, thereby regularizing the relative probability allocation among reference-supported correct responses without directly anchoring incorrect outputs or total correctness mass. We further show that full-policy forward and reverse KL regularization induce a strict optimal correctness gap when the reference policy is imperfect, whereas CoKL avoids this limitation. Experiments in controlled multi-solution environments and continual post-training settings across multiple model scales demonstrate that CoKL achieves a more favorable balance between target-task improvement and prior-capability retention than existing regularization methods. Our code is available at https://github.com/Lumina04/CoKL.
Reinforcement learning (RL) fine-tuning is widely used in language model training to improve model performance on a target task while limiting drift from a reference policy. A standard way to balance this trade-off is via a KL-regularized RL objective, although this formulation does not by itself provide a principled way to set the regularization coefficient. In practice, the coefficient is typically chosen heuristically or via hyperparameter search, which can lead to unnecessary overhead in training cost or undesirable reward-retention trade-offs. We instead propose a game-theoretic framework that gives this trade-off an explicit statistical interpretation. Specifically, we study a sequential game in which an agent chooses a policy to maximize cumulative reward while a monitor observes policy outputs over time and tests for deviations from the reference policy. Although not originating from the same perspective, we show that the resulting equilibrium policy can nonetheless be expressed as the solution to a KL-regularized RL problem for an optimal regularization parameter that can be viewed as maximizing reward per unit of statistical distinguishability. Drawing on classical results from concave-convex fractional programming, we provide a principled method for learning this equilibrium coefficient via reduction to the KL-regularized RL objective, thus allowing for flexible integration into standard fine-tuning pipelines. In experiments with Qwen3-8B and Llama-3.2-1B, we demonstrate that our methods result in competitive reward-retention trade-offs in a continual learning setting, and illustrate how our framework may be used to audit API providers serving open-source models.
The standard LLM training pipeline applies reinforcement learning (RL) only after pre-training and supervised fine-tuning (SFT). We question this status quo by training a LLM from scratch and applying RL, SFT, and SFT followed by RL directly to intermediate pre-training checkpoints. We find that RL is effective very early, and often matches the full SFT→RL pipeline early as well. Through experiments on harder problems, we find that targeted pre-training data composition is a strong lever for RL effectiveness, even more so than model scale. Beyond reasoning accuracy, applying RL directly to base checkpoints expands the model's distribution; the sharpening effect reported in recent work arises only when RL follows SFT. The general capabilities of the model remain essentially unchanged by RL, while they degrade following SFT. Finally, we merge RL and SFT objectives by parallel averaging, which outperforms across all other training methods discussed, across metrics, while preserving general capabilities. Together, these results suggest that LLM training might benefit from an expanded use of RL.
Large language model (LLM) post-training is essential for improving reasoning, adaptation, and alignment. Existing methods mainly follow two paradigms: reinforcement learning (RL) and on-policy distillation (OPD). However, RL relies on coarse-grained outcome supervision, resulting in difficult credit assignment and limited capability to acquire new knowledge. OPD, meanwhile, unconditionally matches teacher logits through KL divergence, which creates a dilemma: similar teachers provide little new knowledge, while substantially different teachers often yield ineffective guidance, largely restricting OPD to within-family distillation. We propose Distilled Reinforcement Learning (Distilled RL), which integrates teacher supervision into the RL objective to provide fine-grained guidance, selectively transfer new knowledge and avoid unconditional imitation. Distilled RL contains three components: reverse importance sampling with clipping, negative sample reset, and sequence-level geometric normalization. Through a concise and interpretable case study, we demonstrate that Distilled RL can effectively transfer previously unavailable knowledge from a teacher model to a student model. Extensive experiments across both within-family and cross-family distillation settings show that Distilled RL substantially outperforms standard RL and OPD in terms of both pass@1 and pass@k. Our code is available at https://github.com/597358816/Distilled-RL.