mlsanityData to 14 Oct 2026

OPPO: Bayesian Value Recursion for Token-Level Credit Assignment in LLM Reasoning

arXiv 2605.21851 ↗First posted 21 May 2026cs.LG cs.AIcited by 4

On the map: LLM reasoning → Reinforcement learning for reasoning

also in 1 more
Abstract (arXiv)

Reinforcement learning with verifiable rewards has become the standard recipe for improving LLM reasoning, but the dominant algorithm GRPO assigns a single trajectory-level advantage to every token, diluting the signal at pivotal reasoning steps and injecting noise at uninformative ones. Critic-free alternatives derived from on-policy distillation supply per-token signals through oracle-conditioned likelihood ratios, yet apply each signal in isolation from the trajectory-level evidence accumulated up to that position. We propose Oracle-Prompted Policy Optimization (OPPO), which rests on a single observation: the oracle signal used by prior distillation-style methods for local discrimination is also the natural Bayesian update of the model's belief about eventual success. Accumulating the signal along a trajectory yields, in closed form and at the cost of one extra forward pass, a running estimate of the success probability at every position, together with a token-level advantage that requires no learned value network and no additional rollouts. A first-order analysis factorizes the advantage into the per-token discrimination signal used by distillation methods modulated by a state weight that concentrates credit on genuinely pivotal tokens, with a directional variance-reduction guarantee. The framework admits two estimators differing only in which model scores the evidence: a textitself-oracle that reuses the student and recovers the on-policy distillation reward as a strict special case, and a textitteacher-oracle that delegates scoring to a stronger frozen model. On two base LLMs across seven mathematics, science, and code reasoning benchmarks, OPPO improves over GRPO, DAPO, and SDPO by up to +6.0 points on AMC'23 and +5.2 points on AIME'24, with gains that widen monotonically with response length.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning. Builds on 25 of its 39 references that are in the map. First posted on arXiv 21 May 2026.

Builds on

25 of 39 references.

Closest ancestors · 10

Same direction, newest first

  1. 2026Reason in Chains, Learn in Trees: Self-Rectification and Grafting for Multi-turn Agent Policy Optimization8 Apr
  2. 2025Learning to Reason with Mixture of Tokens25 Sep
  3. 2025Geometric-Mean Policy Optimization28 Jul
  4. 2025Segment Policy Optimization: Effective Segment-Level Credit Assignment in RL for Large Language Models29 May
  5. 2025Understanding R1-Zero-Like Training: A Critical Perspective26 Mar
  6. 2025DAPO: An Open-Source LLM Reinforcement Learning System at Scale18 Mar
  7. 2025Process Reinforcement through Implicit Rewards3 Feb
  8. 2025DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning22 Jan
  9. 2023Let's Verify Step by Step31 May
  10. 2017Proximal Policy Optimization Algorithms20 Jul

Other references · 15

  1. 2021Training Verifiers to Solve Math Word Problemscited by 10,109
  2. 2025Qwen3 Technical Reportcited by 8,820
  3. 2018Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challengecited by 4,886
  4. 2024LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Codecited by 2,004
  5. 2024OpenAI o1 System Cardcited by 1,244
  6. 2025Group Sequence Policy Optimizationcited by 835
  7. 2026Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Modelscited by 455
  8. 2026Reinforcement Learning via Self-Distillationcited by 332
  9. 2026A Survey of On-Policy Distillation for Large Language Modelscited by 163
  10. 2025Phi-4-reasoning Technical Reportcited by 151
  11. 2023MiniLLM: On-Policy Distillation of Large Language Modelscited by 139
  12. 2026Self-Distilled RLVRcited by 131
3 more
  1. 2024ARGS: Alignment as Reward-Guided Searchcited by 103
  2. 2025Advancing Reasoning in Large Language Models: Promising Methods and Approachescited by 43
  3. 2025Heterogeneous Adaptive Policy Optimization: Tailoring Optimization to Every Token's Naturecited by 11

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 4.

4 papers.

  1. 2026Localizing Credit at the Divergence: Path-Conditioned Self-Distillation for LLM Reasoningcited by 7
  2. 2026Privileged Likelihood Is Not Automatically Value: Three Checks for Token Credit in On-Policy Self-Distillationcited by 4
  3. 2026A Note on Stability for Orthogonalized Matrix Momentum with Client Samplingcited by 1
  4. 2026Surprising Success, Repeated Failure: Entropy-Guided Credit Assignment for Exploration in LLM Reasoningcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Exploiting Tree Structure for Credit Assignment in RL Training of LLMs
  2. 2026Learning from Own Solutions: Self-Conditioned Credit Assignment for Reinforcement Learning with Verifiable Rewards
  3. 2026Grad2Reward: From Sparse Judgment to Dense Rewards for Improving Open-Ended LLM Reasoning
  4. 2025Token-Efficient RL for LLM Reasoning
  5. 2026DelTA: Discriminative Token Credit Assignment for Reinforcement Learning from Verifiable Rewards
  6. 2025GRPO-λ: Credit Assignment improves LLM Reasoning
  7. 2026Discovering Process-Outcome Credit in Multi-Step LLM Reasoning
  8. 2026AMR-SD: Asymmetric Meta-Reflective Self-Distillation for Token-Level Credit Assignment