Rewarding the Unlikely: Lifting GRPO Beyond Distribution Sharpening

• URL: http://arxiv.org/abs/2506.02355v2
• Date: Fri, 20 Jun 2025 04:14:47 GMT
• Title: Rewarding the Unlikely: Lifting GRPO Beyond Distribution Sharpening
• Authors: Andre He, Daniel Fried, Sean Welleck,
• Abstract summary: Reinforcement learning is emerging as a primary driver for improving language model reasoning capabilities.<n>We investigate whether current reinforcement learning algorithms merely sharpen the base model's distribution around problems it can already solve.<n>We show that unlikeliness reward mitigates rank bias and improves pass@$N$ across a large range of $N$ in both synthetic and real theorem proving settings.
• Score: 36.81125165911328
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Reinforcement learning is emerging as a primary driver for improving language model reasoning capabilities. A fundamental question is whether current reinforcement learning algorithms -- such as Group Relative Policy Optimization (GRPO), the de facto standard algorithm used to improve language model reasoning -- merely sharpen the base model's distribution around problems it can already solve. We investigate this question in the context of formal theorem proving, which has access to a perfect verifier. We identify a degenerate rank bias in GRPO in which highly probable trajectories are reinforced and rare ones are neglected. This results in distribution sharpening: the model can solve some problems with fewer samples, but underperforms simply sampling more solutions from the original model. To overcome GRPO's rank bias we introduce unlikeliness reward, a simple method for explicitly up-weighting rare but correct solutions. We show that unlikeliness reward mitigates rank bias and improves pass@$N$ across a large range of $N$ in both synthetic and real theorem proving settings. We also uncover an unexpected link between rank bias and a seemingly mundane hyperparameter -- the number of updates per batch -- that leads to a second, complementary mitigation. We combine our insights into a revised GRPO training recipe for formal theorem proving, yielding an open pipeline that achieves competitive performance to DeepSeek-Prover-V1.5-RL on the miniF2F-test benchmark. We release our implementation at https://github.com/AndreHe02/rewarding-unlikely-release

Related papers

• ExPO: Unlocking Hard Reasoning with Self-Explanation-Guided Reinforcement Learning [12.83211408922535]
  Reinforcement learning-style post-training improves reasoning by optimizing model outputs based on reward or preference signals.<n> GRPO-style approaches implement this by using self-generated samples labeled by an outcome-based verifier.<n>We propose $textbfSelf-Explanation Policy Optimization (ExPO)$-a simple and modular framework that generates such samples by conditioning on the ground-truth answer.
  arXiv  Detail & Related papers  (2025-07-03T17:44:55Z)
• GRPO-CARE: Consistency-Aware Reinforcement Learning for Multimodal Reasoning [53.894789613838654]
  We introduce SEED-Bench-R1, a benchmark with complex real-world videos requiring balanced perception and reasoning.<n>Using SEED-Bench-R1, we find that standard GRPO, while improving answer accuracy, often reduces logical coherence between reasoning steps and answers, with only a 57.9% consistency rate.<n>We propose GRPO-CARE, a consistency-aware RL framework optimizing both answer correctness and reasoning coherence without explicit supervision.
  arXiv  Detail & Related papers  (2025-06-19T08:49:13Z)
• Response-Level Rewards Are All You Need for Online Reinforcement Learning in LLMs: A Mathematical Perspective [6.069069082518759]
  We study the Zero-Reward Assumption in reinforcement learning for large language models (LLMs)<n>We show that the policy gradient based on true, unknown token-level rewards can be unbiasedly estimated using only a response-level reward model.<n>We propose a new algorithm: Token-Reinforced Policy Optimization (TRePO)
  arXiv  Detail & Related papers  (2025-06-03T07:44:31Z)
• The Surprising Effectiveness of Negative Reinforcement in LLM Reasoning [43.310209758380886]
  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)
• Reinforcing Video Reasoning with Focused Thinking [65.85683941058916]
  Novel framework enhances visual reasoning with focused thinking and dense reward granularity.<n>We employ a token weighting mechanism that prioritizes tokens with high informational density.<n>We reformulate RL training by shifting from single-choice to multi-choice QA tasks.
  arXiv  Detail & Related papers  (2025-05-30T15:42:19Z)
• Accelerating RLHF Training with Reward Variance Increase [5.330219278966635]
  Reinforcement learning from human feedback (RLHF) is an essential technique for ensuring that large language models (LLMs) are aligned with human values and preferences during the post-training phase.<n>We propose a reward adjustment model to accelerate successHF training by provably increasing the reward variance and preserving the relative preferences reward expectation.
  arXiv  Detail & Related papers  (2025-05-29T08:54:06Z)
• Spectral Policy Optimization: Coloring your Incorrect Reasoning in GRPO [21.369307672809366]
  Group Relative Policy optimization ( GRPO) stalls when all sampled responses in a group are incorrect.<n>We propose a framework that introduces response diversity within all-negative-sample groups in GRPO using AI feedback.<n>We empirically validate our approach, showing the improved performance across various model sizes.
  arXiv  Detail & Related papers  (2025-05-16T18:02:05Z)
• A Minimalist Approach to LLM Reasoning: from Rejection Sampling to Reinforce [68.99924691391048]
  We revisit GRPO from a reinforce-like algorithm perspective and analyze its core components.<n>We find that a simple rejection sampling baseline, RAFT, yields competitive performance than GRPO and PPO.<n>Motivated by this insight, we propose Reinforce-Rej, a minimal extension of policy gradient that filters both entirely incorrect and entirely correct samples.
  arXiv  Detail & Related papers  (2025-04-15T16:15:02Z)
• VinePPO: Unlocking RL Potential For LLM Reasoning Through Refined Credit Assignment [66.80143024475635]
  We propose VinePPO, a straightforward approach to compute unbiased Monte Carlo-based estimates. We show that VinePPO consistently outperforms PPO and other RL-free baselines across MATH and GSM8K datasets.
  arXiv  Detail & Related papers  (2024-10-02T15:49:30Z)
• From $r$ to $Q^*$: Your Language Model is Secretly a Q-Function [50.812404038684505]
  We show that we can derive DPO in the token-level MDP as a general inverse Q-learning algorithm, which satisfies the Bellman equation. We discuss applications of our work, including information elicitation in multi-turn dialogue, reasoning, agentic applications and end-to-end training of multi-model systems.
  arXiv  Detail & Related papers  (2024-04-18T17:37:02Z)
• PRDP: Proximal Reward Difference Prediction for Large-Scale Reward Finetuning of Diffusion Models [13.313186665410486]
  Reward finetuning has emerged as a promising approach to aligning foundation models with downstream objectives. Existing reward finetuning methods are limited by their instability in large-scale prompt datasets. We propose Proximal Reward Difference Prediction (PRDP) to enable stable black-box reward finetuning for diffusion models.
  arXiv  Detail & Related papers  (2024-02-13T18:58:16Z)
• Distributionally Robust Models with Parametric Likelihood Ratios [123.05074253513935]
  Three simple ideas allow us to train models with DRO using a broader class of parametric likelihood ratios. We find that models trained with the resulting parametric adversaries are consistently more robust to subpopulation shifts when compared to other DRO approaches.
  arXiv  Detail & Related papers  (2022-04-13T12:43:12Z)

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.