Verifier-Induced Support Reshaping in On-Policy Optimization

• URL: http://arxiv.org/abs/2608.00220v1
• Date: Fri, 31 Jul 2026 19:05:43 GMT
• Title: Verifier-Induced Support Reshaping in On-Policy Optimization
• Abstract summary: We show that on-policy reinforcement learning with verifiable rewards (RLVR) can improve the current objective while making successful behaviors for later objectives too rare to sample and reinforce.<n>We call this verifier-induced support reshaping and define effective rewardable support as successful trajectories reachable within a fixed rollout budget.
• Score: 27.782412748608255
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We show that on-policy reinforcement learning with verifiable rewards (RLVR) can improve the current objective while making successful behaviors for later objectives too rare to sample and reinforce. We call this verifier-induced support reshaping and define effective rewardable support as successful trajectories reachable within a fixed rollout budget. Across two model families, we study this effect through repeated verifier-scored sampling and bidirectional training on mathematical reasoning and constrained instruction following, including sequential training with the opposite verifier. Math-RLVR raises average instruction-following success but reduces the number of prompts with any successful response under repeated sampling. On IFEval with Qwen3-8B-Base, pass@1 rises by 6.5 percentage points while best@32 falls by 9.8 percentage points, and the same divergence appears across both models and IF benchmarks. Conversely, IF-RLVR shifts math responses from step-by-step openings toward direct answers, lowers best@k across sampling budgets, and reduces reward variation for later Math-RLVR. Token-distribution analyses and controlled opening interventions show that these changes concentrate in the first few response tokens. RLVR mainly reranks openings already available in the base policy, and the selected opening causally affects math searchability. The tested reference-policy constraints, routing priors, and on-policy distillation preserve cross-task support only partially; MathIF and ReasonIF show that marginal gains translate only partly into responses that are both correct and constraint-following. Therefore, endpoint improvements do not guarantee future trainability or joint capability under on-policy optimization. Code is available at https://github.com/sylvain-wei/verifier-induced-support-reshaping

Related papers

• When RLVR Shrinks the Reasoning Boundary: Diagnosing Pass@k Inversion [0.0]
  Reinforcement learning with verifiable rewards (RLVR) can improve one-sample accuracy while making a model worse under repeated sampling.<n>We study this pass@k inversion: after training, the policy may solve fewer distinct problems than its base model at large $k$.<n>The failure concentrates on boundary prompts, where the base model contains rare correct trajectories that are recoverable by sampling but too sparse to reliably appear in finite RLVR rollout groups.
  arXiv  Detail & Related papers  (2026-07-12T17:17:18Z)
• LatentRevise: Learning from Zero-Hit Reasoning [46.1536368072511]
  Reinforcement learning with verifiable rewards is bottlenecked by hard prompts on which correct trajectories have low probability.<n>We frame such zero-hit prompts as RLVR's sampling frontier, where new reasoning behavior is most valuable yet least likely to be sampled.<n>We introduce LatentRevise, a first-order latent revision method that recovers training signal for this zero-hit regime.
  arXiv  Detail & Related papers  (2026-06-29T08:14:47Z)
• REVES: REvision and VErification--Augmented Training for Test-Time Scaling [53.197756110943395]
  We propose a two-stage iterative framework that alternates between online data/prompt augmentation and policy optimization.<n>We observe gains of +6.5 points over the RL baseline and +4.0 points over standard multi-turn training.
  arXiv  Detail & Related papers  (2026-06-17T10:37:23Z)
• TRACE: A Unified Rollout Budget Allocation Framework for Efficient Agentic Reinforcement Learning [52.67756371231985]
  Reinforcement learning with verifiable rewards (RLVR) is a promising approach for enhancing reasoning and agentic behavior in large language models.<n>We introduce Tree Rollout Allocation for Contrastive Exploration (TRACE), a unified rollout allocation framework.<n>Technically, TRACE allocates rollout budget to both prompt roots and intermediate prefixes that are most likely to yield mixed terminal rewards.
  arXiv  Detail & Related papers  (2026-06-09T17:16:03Z)
• Learning to Solve, Forgetting to Retain: Correct-Set Turnover in RLVR [16.681943272535104]
  Reinforcement learning with verifiable rewards (RLVR) improves the ability of large language model, yet headline accuracy gains often conceal a hidden cost.<n>We propose textbfmethod, a retention-aware review mechanism that tracks mastered prompts and periodically reintroduces them to textbfremind the model of previous solutions.
  arXiv  Detail & Related papers  (2026-06-02T03:17:34Z)
• VeriGate: Verifier-Gated Step-Level Supervision for GRPO [51.26100506256885]
  Group Relative Policy Optimization is an effective recipe for training reasoning models with verifier-based outcome rewards.<n>We present VeriGate, a verifier-gated extension of GRPO that addresses these limitations with three design choices.<n>We show that VeriGate improves average accuracy by about 20% and 12% for 1.5B and 7B models respectively.
  arXiv  Detail & Related papers  (2026-05-28T18:20:32Z)
• SAGE: Shaping Anchors for Guided Exploration in RLVR of LLMs [55.46289074417954]
  reinforcement learning with verifiable rewards (RLVR) reliably improves pass@1 on reasoning tasks, yet often fails to yield comparable gains in pass@k.<n>We argue that a central structural constraint arises from reverse-KL regularization, which stabilizes training but inherently anchors the policy to the reference distribution.<n>We propose SAGE, a principled framework that enables controllable empirical support expansion by reshaping the reverse-KL anchor distribution itself.
  arXiv  Detail & Related papers  (2026-05-15T07:42:21Z)
• Learning from Failures: Correction-Oriented Policy Optimization with Verifiable Rewards [73.44333771806282]
  Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as an effective paradigm for improving the reasoning capabilities of large language models.<n>We propose Correction-Oriented Policy Optimization (CIPO), a simple and effective extension to RLVR that converts on-policy failed trajectories into correction-oriented supervision.<n>CIPO improves learning effectiveness while explicitly enhancing the model's ability to correct its own errors.
  arXiv  Detail & Related papers  (2026-05-14T08:22:21Z)
• CARE What Fails: Contrastive Anchored-REflection for Verifiable Multimodal [84.71254539482369]
  Group-relative reinforcement learning with verifiable rewards (RLVR) often wastes the most informative data it already has the failures.<n>We present CARE, a failure-centric post-training framework for multimodal reasoning that turns errors into supervision.<n> CARE improves accuracy and training smoothness while explicitly increasing the share of learning signal that comes from failures.
  arXiv  Detail & Related papers  (2025-12-22T16:34:21Z)
• Reinforcement Learning with Verifiable yet Noisy Rewards under Imperfect Verifiers [90.50039419576807]
  Reinforcement Learning with Verifiable Rewards (RLVR) trains policies against automated verifiers to avoid costly human labeling.<n>To reduce vulnerability to verifier hacking, many RLVR systems collapse rewards to binary $0,1$ during training.<n>This choice carries a cost: it introduces textitfalse negatives (rejecting correct answers, FNs) and textitfalse positives (accepting incorrect ones, FPs)
  arXiv  Detail & Related papers  (2025-10-01T13:56:44Z)
• The Surprising Effectiveness of Negative Reinforcement in LLM Reasoning [37.13807960501503]
  Reinforcement learning with verifiable rewards (RLVR) is a promising approach for training language models (LMs)<n>We decompose the learning signal into reinforcing correct responses and penalizing incorrect ones, referred to as Positive and Negative Sample Reinforcement (PSR and NSR)<n>We show that NSR works by suppressing incorrect generations and redistributing probability mass toward other plausible candidates, guided by the model's prior beliefs.
  arXiv  Detail & Related papers  (2025-06-02T06:10:54Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.