Max Out GRPO Signal: Adaptive Trace Prefix Control for Hard Reasoning Problems

Group Relative Policy Optimization (GRPO) is widely used for training reasoning models, but updating all sampled completions in each group incurs substantial cost and can reinforce verbose reasoning trajectories. In this paper, we study whether all completions provide equally useful update signals in GRPO-style reasoning RL. Our gradient-similarity analysis shows that, within the same prompt group, same-class completions often induce highly similar update directions, whereas correct-incorrect pairs provide more distinct contrastive signals. Motivated by this observation, we propose Binary Prefix Policy Optimization (BPPO), which uses the shortest correct completion and the shortest incorrect completion as a compact update unit while preserving full-group advantage normalization. BPPO further improves efficiency with adaptive completion scheduling and prefix-focused optimization; by updating only response prefixes, it avoids reinforcing redundant suffixes and encourages more concise responses. Experiments on GSM8K, MATH, and Geo3K show that BPPO achieves up to 6.08x speedup over GRPO while maintaining competitive accuracy, and reduces mean response length by approximately 30-50% without modifying the reward with an explicit length penalty.

Group Relative Policy Optimization (GRPO) is an effective recipe for training reasoning models with verifier-based outcome rewards, but its supervision is sparse: when all sampled trajectories for a prompt receive the same verifier reward, the group-relative advantage collapses to zero and learning stalls. Outcome-only rewards also provide no step-level credit assignment, limiting exploration and making it harder to learn robust reasoning. We present VeriGate (Verifier-Gated Step-Level GRPO), a verifier-gated extension of GRPO that addresses these limitations with three design choices. First, VeriGate keeps the verifier in charge whenever verifier rewards induce a meaningful preference among sampled trajectories, and uses process supervision only when verifier rewards are degenerate. Second, instead of collapsing Process Reward Model (PRM) step scores into a single trajectory reward, VeriGate converts them into future-cumulated rewards to assign continuation-aware credit. Third, VeriGate transforms these rewards into group-normalized token-level advantages, restoring informative gradients and fine-grained credit assignment while remaining less susceptible to reward hacking than methods that optimize aggregated PRM scores. Empirically, training on MATH with 1.5B and 7B Qwen2.5-Instruct models and evaluating on six reasoning benchmarks, VeriGate improves average accuracy by about 20% and 12% for 1.5B and 7B models respectively, substantially reduces zero-gradient failures, decreases reward-hacking behavior, and improves reasoning quality relative to outcome-only GRPO and PRM-as-outcome baselines.

Group Relative Policy Optimization (GRPO) has become a standard reinforcement learning method for post-training language models. Recent work shows that GRPO can reduce the base model's reasoning capacity and underperform it in Pass@k when k is large, indicating reduced coverage of reasoning paths. We find that this reduction is associated with GRPO concentrating on responses that the base model already generates with high probability. We trace this concentration to two mechanisms in the GRPO update. At the response level, high-probability responses dominate the group gradient through repeated occurrence. At the token level, GRPO's importance ratio scales gradients, further reinforcing tokens that become more likely under the current policy. We propose ReCo, a reweighting method that addresses both effects. Response contributions are normalized by their expected occurrence within the rollout group, and the token-level importance ratio is replaced with a variance-based ratio that gives larger update scale to non-saturated decision points where alternative token choices remain plausible. Across Qwen2.5-Math-1.5B/7B and Llama-3.1-8B-Instruct on five mathematical reasoning benchmarks, ReCo improves Pass@k for large values of k and is comparable to GRPO for small values of k.