Hista and Numca: Estimate State Value Effectively for Large Language Model Reinforcement Learning

Abstract

Reinforcement Learning (RL) refines large language models (LLMs) by directly optimizing model behavior with reward signals. Although accurate state value estimation is essential for stable training in classical RL settings, it remains an understudied challenge in LLM post-training. In this work, we demonstrate that accurate value estimation can stabilize and improve post-training. First, we construct State Value Estimation Benchmark (SVEB) and show that critics of standard approaches like PPO simply degenerate toward a coarse group-average baseline. To overcome this, we propose two techniques. One is a heuristic method *Numca*, which uses numbers in responses as state representation to calculate state value. Another is a general hidden-state-based framework *Hista*, which utilize the semantic information in hidden states to group disjoint responses. Experiments show that when equipped with these improved estimates, training gains better performance consistently with different RL algorithms.