Start Classifying: Categorical Critics for LLM Reinforcement Learning
Authors: Zhijian Zhou, Long Li, Xuan Zhang, Zongkai Liu, Yulei Qin, Ke Li, Xing Sun, Xiaoyu Tan, +2 more
Organizations: Fudan University · Shanghai Innovation Institute · Tencent YoutuLab · Griffith University · Shanghai Academy of Artificial Intelligence for Science
Abstract
Proximal Policy Optimization (PPO) for large language models typically trains its critic by mean-squared-error (MSE) regression on scalar value targets. Although scalar MSE is statistically valid for estimating the conditional expected return, sparse binary rewards in reinforcement learning with verifiable rewards (RLVR) make critic optimization and calibration especially consequential: small value errors directly distort the scalar advantages used by PPO. We study whether a classification-based training objective can improve this critic signal. HL-Gauss PPO replaces the scalar MSE head with a categorical predictor over a discretized value support, trained by cross-entropy against smoothed HL-Gauss targets. Its output is decoded to a scalar expectation for standard GAE and PPO; the actor update is therefore unchanged and is not distributional. Across mathematical reasoning, tool-augmented math, and Search-R1, and on both Qwen2.5 and Qwen3 backbones, HL-Gauss PPO consistently improves over strong PPO and DAPO baselines. Controls with one-hot, two-hot, and Bernoulli two-bin critics show that neither a larger output head nor binary classification alone explains the gains. On a common collection of reasoning prefixes, HL-Gauss improves Brier score and calibration error and yields more symmetric, lower-variance advantages. These results position categorical value learning as an effective optimization surrogate for PPO critics in RLVR.
Reinforcement learning substantially improves pretrained language models, but it remains understudied why critic-free methods such as PPO and GRPO work as well as they do, and when they should provide the largest gains. We develop a value-gradient perspective of critic-free RL for LLM post-training. First, under a differentiable rollout and additive-noise parameterization, we show that the actor update is value-gradient-like in expectation: the backward pass propagates costates whose conditional expectation equals the value gradient. Second, for discrete transformer policies, we show that autodifferentiation through attention produces empirical costates that approximate this value signal, with an error controlled by the sampling gap and policy entropy. These results motivate a decomposition of RL impact into value gradient signal and reachable reward headroom, yielding a criterion for when RL should be most effective along a pretraining trajectory.
Reinforcement learning with verifiable rewards (RLVR) has become a dominant paradigm for improving the reasoning capabilities of large language models (LLMs). Recent tree-based methods such as TreeRPO extend flat trajectory sampling with tree-structured rollouts to obtain dense, step-level reward signals without a separate process reward model. However, not all trees are equally informative: trees where all leaves succeed, all leaves fail, or the policy already predicts the reward distribution contribute little to gradient updates, wasting compute. We introduce CATPO (Critique-Augmented Tree Policy Optimization), which diagnoses and addresses this waste at the tree level. CATPO first scores each tree via a tree informativeness score, F(T), combining leaf-outcome diversity with policy-reward decorrelation at zero extra compute. For dead-wrong trees where all branches fail, CATPO applies critique-guided healing: it locates the shallowest failure point, generates a natural-language critique, and grafts refined continuations to recover training signal. Finally, an informativeness-weighted loss scales each tree's gradient contribution by its normalized score, concentrating parameter updates on the most informative trees while preserving overall gradient magnitude. Experiments on Qwen2.5-Math-1.5B trained with the MATH dataset show that CATPO achieves 37.5% macro accuracy across four benchmarks (AIME24, MATH-500, OlympiadBench, and MinervaMath), improving over TreeRPO by 1.9% and GRPO by 4.8%.
Reinforcement learning with verifiable rewards (RLVR) for Large Reasoning Models hinges on baseline estimation for variance reduction, but existing approaches pay a heavy price: PPO requires a policy-model scale critic, while GRPO needs multiple rollouts per prompt to keep its empirical group mean stable. We introduce Policy Optimization with Internal State Value Estimation), which obtains a baseline at negligible cost by using the policy model's internal signals already computed during the policy forward pass. A lightweight probe predicts the expected verifiable reward from the hidden states of the prompt and generated trajectory, as well as token-entropy statistics, and is trained online alongside the policy. To preserve gradient unbiasedness despite using trajectory-conditioned features, we introduce a cross-rollout construction that predicts each rollout's value from an independent rollout's internal states. Because POISE estimates prompt value using only a single rollout, it enables higher prompt diversity for a fixed compute budget during training. This reduces gradient variance for more stable learning and also eliminates the compute overhead of sampling costs for detecting zero-advantage prompts. On Qwen3-4B and DeepSeek-R1-Distill-Qwen-1.5B across math reasoning benchmarks, POISE matches DAPO while requiring less compute. Moreover, its value estimator shows similar performance to a separate LLM-scale value model and generalizes to various verifiable tasks. By leveraging the model's own internal representations, POISE enables more stable and efficient policy optimization.