DisCO: Reinforcing Large Reasoning Models with Discriminative Constrained Optimization

• URL: http://arxiv.org/abs/2505.12366v2
• Date: Tue, 10 Jun 2025 03:47:30 GMT
• Title: DisCO: Reinforcing Large Reasoning Models with Discriminative Constrained Optimization
• Authors: Gang Li, Ming Lin, Tomer Galanti, Zhengzhong Tu, Tianbao Yang,
• Abstract summary: Group Relative Policy Optimization is a reinforcement learning method for large reasoning models (LRMs)<n>In this work, we analyze the GRPO objective under a binary reward setting and reveal an inherent limitation of question-level difficulty bias.<n>We introduce a new Discriminative Constrained Optimization framework for reinforcing LRMs, grounded in the principle of discriminative learning.
• Score: 55.06360285372418
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The recent success and openness of DeepSeek-R1 have brought widespread attention to Group Relative Policy Optimization (GRPO) as a reinforcement learning method for large reasoning models (LRMs). In this work, we analyze the GRPO objective under a binary reward setting and reveal an inherent limitation of question-level difficulty bias. We also identify a connection between GRPO and traditional discriminative methods in supervised learning. Motivated by these insights, we introduce a new Discriminative Constrained Optimization (DisCO) framework for reinforcing LRMs, grounded in the principle of discriminative learning. The main differences between DisCO and GRPO and its recent variants are: (1) it replaces the group relative objective with a discriminative objective defined by a scoring function; (2) it abandons clipping-based surrogates in favor of non-clipping RL surrogate objectives used as scoring functions; (3) it employs a simple yet effective constrained optimization approach to enforce the KL divergence constraint, ensuring stable training. As a result, DisCO offers notable advantages over GRPO and its variants: (i) it completely eliminates difficulty bias by adopting discriminative objectives; (ii) it addresses the entropy instability in GRPO and its variants through the use of non-clipping scoring functions and a constrained optimization approach; (iii) it allows the incorporation of advanced discriminative learning techniques to address data imbalance, where a significant number of questions have more negative than positive generated answers during training. Our experiments on enhancing the mathematical reasoning capabilities of SFT-finetuned models show that DisCO significantly outperforms GRPO and its improved variants such as DAPO, achieving average gains of 7\% over GRPO and 6\% over DAPO across six benchmark tasks for an 1.5B model.

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