Unleashing Implicit Rewards: Prefix-Value Learning for Distribution-Level Optimization
For researchers and practitioners using reinforcement learning for reasoning tasks, this work addresses a fundamental limitation of implicit PRMs, enabling more reliable and efficient reward signal extraction without expensive annotations.
The paper tackles the train-inference mismatch in implicit process reward models (PRMs) that leads to unreliable token-level credit assignment. The proposed IPVRM learns a prefix-conditioned value function and uses temporal-difference differences to derive step signals, improving step-verification F1 on ProcessBench. Combined with Distribution-Level RL (DistRL), it further enhances downstream reasoning.
Process reward models (PRMs) provide fine-grained reward signals along the reasoning process, but training reliable PRMs often requires step annotations or heavy verification pipelines, making them expensive to scale and refresh during online RL. Implicit PRMs mitigate this cost by learning decomposable token- or step-level rewards from trajectory-level outcome labels. However, they suffer from a train-inference mismatch: training only constrains a sequence-level aggregate, whereas inference requires token-level scores to reflect local step quality. As a result, token-level credits are weakly identified and may fail to faithfully reflect which reasoning steps are actually correct. This unreliability undermines a key promise of implicit PRMs: scoring many candidate tokens. In practice, noisy per-token advantages may systematically reinforce incorrect continuations. We address this problem with a novel Implicit Prefix-Value Reward Model (IPVRM), which directly learns a prefix-conditioned value function estimating the probability of eventual correctness, and derives step signals via temporal-difference (TD) differences. IPVRM substantially improves step-verification F1 on ProcessBench. Building on these calibrated prefix values, we further propose Distribution-Level RL (DistRL), which computes TD advantages for both sampled tokens and high-probability candidate tokens, enabling dense counterfactual updates without additional rollouts. While DistRL offers limited gains when powered by miscalibrated implicit rewards, it consistently improves downstream reasoning once paired with IPVRM.