# When Right Meets Wrong: Bilateral Context Conditioning with Reward-Confidence Correction for GRPO

arXiv: https://arxiv.org/abs/2603.13134 · HTML: https://mlsanity.com/paper/2603.13134/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 24 of its 39 references that are in the map.
- First posted on arXiv 13 Mar 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 24 of 24)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [VAPO: Efficient and Reliable Reinforcement Learning for Advanced Reasoning Tasks](https://mlsanity.com/paper/2504.05118/) (2025)
- [KTO: Model Alignment as Prospect Theoretic Optimization](https://mlsanity.com/paper/2402.01306/) (2024)
- [Unifying distillation and privileged information](https://mlsanity.com/paper/1511.03643/) (2015)
- [Geometric-Mean Policy Optimization](https://mlsanity.com/paper/2507.20673/) (2025)
- [Reinforcement Learning with Verifiable Rewards: GRPO's Effective Loss, Dynamics, and Success Amplification](https://mlsanity.com/paper/2503.06639/) (2025)
- [Back to Basics: Revisiting REINFORCE Style Optimization for Learning from Human Feedback in LLMs](https://mlsanity.com/paper/2402.14740/) (2024)
- [The Optimal Reward Baseline for Gradient-Based Reinforcement Learning](https://mlsanity.com/paper/1301.2315/) (2013)
- [Revisiting Group Relative Policy Optimization: Insights into On-Policy and Off-Policy Training](https://mlsanity.com/paper/2505.22257/) (2025)
- [On-Policy RL with Optimal Reward Baseline](https://mlsanity.com/paper/2505.23585/) (2025)
- [Single-stream Policy Optimization](https://mlsanity.com/paper/2509.13232/) (2025)
- [When Importance Sampling Misallocates Credit: Asymmetric Ratios for Outcome-Supervised RL](https://mlsanity.com/paper/2510.06062/) (2025)
- [InSPO: Unlocking Intrinsic Self-Reflection for LLM Preference Optimization](https://mlsanity.com/paper/2512.23126/) (2025)

## Built on by (most cited first, 10 of 10)

- [Reason in Chains, Learn in Trees: Self-Rectification and Grafting for Multi-turn Agent Policy Optimization](https://mlsanity.com/paper/2604.07165/) (2026)
- [Localizing Credit at the Divergence: Path-Conditioned Self-Distillation for LLM Reasoning](https://mlsanity.com/paper/2606.15576/) (2026)
- [Recursive Self-Evolving Agents via Held-Out Selection](https://mlsanity.com/paper/2606.28374/) (2026)
- [MomentKV: Closing the Directional Gap in KV Cache Eviction for Long-Context Inference](https://mlsanity.com/paper/2606.01563/) (2026)
- [Kernelized Advantage Estimation: From Nonparametric Statistics to LLM Reasoning](https://mlsanity.com/paper/2604.28005/) (2026)
- [Zone of Proximal Policy Optimization: Teacher in Prompts, Not Gradients](https://mlsanity.com/paper/2606.18216/) (2026)
- [IntentScore: Intent-Conditioned Action Evaluation for Computer-Use Agents](https://mlsanity.com/paper/2604.05157/) (2026)
- [CAP-CoT: Cycle Adversarial Prompt for Improving Chain of Thoughts in LLM Reasoning](https://mlsanity.com/paper/2604.23270/) (2026)
- [Small Language Model Helps Resolve Semantic Ambiguity of LLM Prompt](https://mlsanity.com/paper/2604.23263/) (2026)
- [VAA-CSEC: Vote-guided Advantage Allocation for Chinese Semantic Error Correction](https://mlsanity.com/paper/2609.36804/) (2026)

## Abstract (arXiv)

Group Relative Policy Optimization (GRPO) has emerged as an effective method for training reasoning models. While it computes advantages based on group mean, GRPO treats each output as an independent sample during the optimization and overlooks a vital structural signal: the natural contrast between correct and incorrect solutions within the same group, thus ignoring the rich, comparative data that could be leveraged by explicitly pitting successful reasoning traces against failed ones. To capitalize on this, we present a contrastive reformulation of GRPO, showing that the GRPO objective implicitly maximizes the margin between the policy ratios of correct and incorrect samples. Building on this insight, we propose Bilateral Context Conditioning (BICC), a mechanism that allows the model to cross-reference successful and failed reasoning traces during the optimization, enabling a direct information flow across samples. We further introduce Reward-Confidence Correction (RCC) to stabilize training by dynamically adjusts the advantage baseline in GRPO using reward-confidence covariance derived from the first-order approximation of the variance-minimizing estimator. Both mechanisms require no additional sampling or auxiliary models and can be adapted to all GRPO variants. Experiments on mathematical reasoning benchmarks demonstrate consistent improvements across comprehensive models and algorithms. Code is available at hrefhttps://github.com/Skylanding/BiCChttps://github.com/Skylanding/BiCC.