SPC: Evolving Self-Play Critic via Adversarial Games for LLM Reasoning
Authors: name: Jiaqi Chen, name: Bang Zhang, name: Ruotian Ma, name: Peisong Wang, name: Xiaodan Liang, name: Zhaopeng Tu, name: Xiaolong Li, name: Kwan-Yee K. Wong

Evaluating the step-by-step reliability of large language model (LLM)
reasoning, such as Chain-of-Thought, remains challenging due to the difficulty
and cost of obtaining high-quality step-level supervision. In this paper, we
introduce Self-Play Critic (SPC), a novel approach where a critic model evolves
its ability to assess reasoning steps through adversarial self-play games,
eliminating the need for manual step-level annotation. SPC involves fine-tuning
two copies of a base model to play two roles, namely a "sneaky generator" that
deliberately produces erroneous steps designed to be difficult to detect, and a
"critic" that analyzes the correctness of reasoning steps. These two models
engage in an adversarial game in which the generator aims to fool the critic,
while the critic model seeks to identify the generator's errors. Using
reinforcement learning based on the game outcomes, the models iteratively
improve; the winner of each confrontation receives a positive reward and the
loser receives a negative reward, driving continuous self-evolution.
Experiments on three reasoning process benchmarks (ProcessBench, PRM800K,
DeltaBench) demonstrate that our SPC progressively enhances its error detection
capabilities (e.g., accuracy increases from 70.8% to 77.7% on ProcessBench) and
surpasses strong baselines, including distilled R1 model. Furthermore, applying
SPC to guide the test-time search of diverse LLMs significantly improves their
mathematical reasoning performance on MATH500 and AIME2024, outperforming
state-of-the-art process reward models.