Group Relative Policy Optimization (GRPO) has shown strong effectiveness in reinforcement learning from verifiable feedback, where sampled rollouts can be compared within a group using task-provided correctness signals. However, extending group-relative optimization beyond verifiable settings is challenging because success in many tasks is not captured by a single correctness criterion. We propose \textbf{Reference-Relative Policy Optimization (RRPO)}, which generalizes GRPO by replacing direct correctness-based advantage construction with reference-relative contrastive comparisons. RRPO first uses \emph{stratified conditional rollouts} to construct positive and negative anchor sets, and then trains a metric projection head with a set-contrastive objective to compare candidate rollouts against these anchors. The resulting alignment scores directly define contrastive advantages: during policy optimization, the projection head is frozen, and the scores are centered within each rollout group in a standard group-relative objective. We evaluate RRPO using anchor-based contrastive advantages throughout policy optimization, without relying on task ground-truth verifiers. Across verifiable reasoning, open-ended generation, and post-SFT settings, RRPO remains competitive with verifier-based optimization, improves over weakly supervised baselines, and provides additional gains after supervised fine-tuning.
Group Relative Policy Optimization (GRPO) is one of the most widely adopted RLVR algorithms for post-training large language models on reasoning tasks. We first show that GRPO admits an equivalent discriminative reformulation, in which policy optimization maximizes the expected score gap between verified positive and negative rollouts. This reformulation reveals two objective-level limitations: likelihood-misaligned surrogate scores, in which clipped ratio-based scores are optimized rather than the sequence likelihoods that govern generation, and score-insensitive credit assignment, in which rollout-level credit does not reflect the current score gaps between positive and negative rollouts. To address these limitations, we propose ConSPO, a Contrastive Sequence-level Policy Optimization method that uses length-normalized sequence log-probabilities as rollout scores and contrasts verified positive rollouts against negative distractors within the same group. ConSPO optimizes a group-wise InfoNCE-style objective to adaptively strengthen updates for poorly separated positives and high-scoring negatives, together with a curriculum-scheduled margin that preserves separation pressure as training progresses. Experiments across diverse settings show that ConSPO outperforms strong baselines on challenging reasoning benchmarks. Code will be released upon paper acceptance.
Reinforcement Learning with Verifiable Rewards (RLVR) has advanced the reasoning capabilities of Large Language Models (LLMs) by leveraging direct outcome verification instead of learned reward models. Building on this paradigm, Group Relative Policy Optimization (GRPO) eliminates the need for critic models but suffers from indiscriminate credit assignment for intermediate steps, which limits its ability to identify effective reasoning strategies and incurs overthinking. In this work, we introduce a model-free and verifiable process supervision via probing the model's belief in the correct answer throughout its reasoning trajectory. By segmenting the generation into discrete steps and tracking the conditional probability of the correct answer appended at each segment boundary, we efficiently compute interpretable segment-wise progress measurements to refine GRPO's trajectory-level feedback. This approach enables more targeted and sample-efficient policy updates, while avoiding the need for intermediate supervision derived from costly Monte Carlo rollouts or auxiliary models. Experiments on mathematical and general-domain benchmarks show consistent gains over GRPO across diverse models: up to 2.6-point accuracy improvements and 13.7% reasoning-length reductions on math tasks, and up to 2.4 points and 4% on general-domain tasks, demonstrating strong generalization.
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.