Reformulate LLM Reinforcement Learning for Efficient Training under Black-box Discrepancy

Reinforcement Learning (RL) has emerged as a pivotal post-training paradigm, yet it frequently suffers from unpredictable sub-optimum performance or even training collapses. Recent findings attribute these failures to a hidden train-inference discrepancy (or mismatch), stemming from the disparate underlying engines and architecture. We find that the training policy can actively self-correct such a discrepancy when provided with an appropriate learning signal. Then, we further empirically identify a discrepancy tolerance region: within this region, aggressively narrowing the discrepancy can suppress policy exploration and reduce learning efficiency, whereas outside this region, reducing excessive discrepancy improves optimization consistency and raises the achievable local performance ceiling. According to such findings, we formulate this problem as a Discrepancy-Constrained Markov Decision Process (DCMDP), where reward maximization is coupled with a constraint that aligns training-Inference behavior, achieving stable dual-objective optimization. To adaptively balance performance improvement and discrepancy control, we introduce a Lagrangian relaxation mechanism that dynamically adjusts the relative weight of the two objectives according to the current degree of discrepancy violation. This enables stable dual-objective optimization: the policy is allowed to explore freely within the tolerance region, while being guided back when the discrepancy exceeds the safe boundary. Empirically, DCMDP significantly improves the performance of 8B dense model (Qwen-3-8b) and 30B Mixture-of-Expert model (Qwen-3-30bA3b), and enables a heterogeneous training paradigm, where LLMs can be optimized in high-fidelity training setup while being explicitly aligned for low-cost, resource-constrained inference deployment.