CEPO: RLVR Self-Distillation using Contrastive Evidence Policy Optimization
Authors: Ahmed Heakl, Abdelrahman M. Shaker, Youssef Mohamed, Rania Elbadry, Omar Fetouh, Fahad Shahbaz Khan, Salman Khan
Organizations: MBZUAI · Linköping University · Australian National University
Abstract
When a model produces a correct solution under reinforcement learning with verifiable rewards (RLVR), every token receives the same reward signal regardless of whether it was a decisive reasoning step or a grammatical filler. A natural fix is to condition the model on the correct answer as a teacher, identifying tokens it would have generated differently had it known the answer. Prior work shows this either corrupts training by leaking the answer into the gradient, or produces a weak signal that cannot distinguish decisive steps from filler, since both look equally surprising relative to the model's baseline. We propose Contrastive Evidence Policy Optimization (CEPO), which asks a sharper question at every token: not just "does the correct answer favor this token?" but "does the correct answer favor it while the wrong answer disfavors it?" A token satisfying both is a genuine reasoning step; one satisfying neither is filler. The wrong-answer teacher is constructed from rejected rollouts already in the training batch, incurring no additional sampling cost. We prove CEPO inherits all structural safety guarantees of the prior state of the art while strictly sharpening credit at decisive tokens, with the improvement vanishing exactly at filler positions. Empirically, CEPO achieves 43.43% and 60.56% average accuracy across five multimodal mathematical reasoning benchmarks at 2B and 4B scale, respectively, versus 41.17% and 57.43% for GRPO under identical training budgets. Distribution-matching self-distillation methods (OPSD, SDPO) fall below the untrained baseline, empirically confirming the information leakage our theory predicts. Our code is available at https://github.com/ahmedheakl/CEPO.
Verifiable rewards improve language models through reliable task-level feedback, but methods based on Group Relative Policy Optimization (GRPO) apply a sequence-level advantage uniformly across all tokens. This coarse credit assignment reinforces or penalizes entire responses without identifying which local decisions to preserve, reinforce, or revise. Conversely, evidence-conditioned self-distillation provides denser token-level supervision, yet teacher imitation can transfer stylistic artifacts and miscalibrated confidence that destabilize training when misaligned with task success. We introduce VERPO, which converts evidence-conditioned guidance into reward-aligned token-level credit assignment while retaining the outcome objective. VERPO decomposes teacher guidance into an evidence-free reference term and signed, evidence-induced corrections at each token. A stopped controller combines selective acceptance, token-wise localization, and cost-aware scaling by balancing alignment with the local GRPO update direction against Fisher movement cost. Furthermore, we introduce Fisher Evidence Contrast (FEC), which attenuates nuisance shifts along an estimated evidence-presence direction through a regularized projection. Across five scientific reasoning and tool-use tasks, VERPO prevents optimization collapse and consistently achieves the highest multi-task average across model backbones, yielding marked improvements particularly on smaller models over strong baselines. Qualitative diagnostics confirm that token acceptance selectively targets reasoning bottlenecks consistent with local reward alignment and Fisher movement cost.
On-policy self-distillation (OPSD) provides dense, token-level supervision for reasoning models by aligning a model's own distribution with that under privileged context, typically a verified solution. However, we show that the resulting distributional gap concentrates on style tokens rather than task-bearing ones, as the hinted model tends to produce shorter, more direct outputs. We term this pathology \emph{privilege-induced style drift}, which can destabilize training and shorten responses. To address this, we propose \textbf{RLCSD} (Reinforcement Learning with Contrastive on-policy Self-Distillation), which mitigates this drift by contrasting the teacher-student gap under a correct hint against that under a wrong hint, suppressing style shifts induced by hints regardless of correctness and yielding a signal more concentrated on task-bearing tokens. Experiments on Qwen3 (1.7B/4B/8B) and Olmo-3-7B-Think across mathematical and logical reasoning show that RLCSD consistently outperforms GRPO and prior OPSD methods, with additional results on agentic tasks supporting broader applicability. We further show that the contrastive principle is general: it plugs into existing OPSD methods to improve them, and its underlying insight extends to broader cross-model on-policy distillation.
Reinforcement learning with verifiable rewards (RLVR) has driven substantial progress in training LLMs for reasoning tasks, but representative methods such as GRPO assign uniform credit across all tokens, wasting gradient on routine tokens while under-crediting pivotal reasoning steps. Existing token-level credit assignment methods require resources beyond the model's own rollouts. GRPO variants rely on process reward models or ground-truth answers. Knowledge distillation assigns credit through per-token divergence but requires external teachers (On-Policy Distillation) or privileged information (On-Policy Self Distillation). However, these dependencies limit applicability in the pure RLVR setting. We observe that conditioning the model on its own verified trajectories induces a measurable per-token KL divergence between the original and conditioned distributions, and prove that distilling from a self-teacher constructed by verified trajectories leads to infeasible weighted-average solutions when multiple verified trajectories exist. We propose SC-GRPO (Self-Conditioned GRPO), which uses KL divergence mentioned before as a multiplicative weight on GRPO gradients. Across five benchmarks spanning math, code, and agentic tasks, SC-GRPO consistently outperforms 8.1% over GRPO and 5.9% over DAPO with stronger OOD performance. Moreover, SC-GRPO achieves higher performance than OPD.