# BRACE: Anchored Bellman-Residual Correction for Stale Critics in Asynchronous RL

arXiv: https://arxiv.org/abs/2609.09783 · HTML: https://mlsanity.com/paper/2609.09783/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 37 of its 50 references that are in the map.
- First posted on arXiv 9 Sep 2026.

## Builds on (most cited first, 30 of 37)

- [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)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Megatron-LM: Training Multi-Billion Parameter Language Models Using Model Parallelism](https://mlsanity.com/paper/1909.08053/) (2019)
- [Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning](https://mlsanity.com/paper/2503.09516/) (2025)
- [DeepSeek-V4: Towards Highly Efficient Million-Token Context Intelligence](https://mlsanity.com/paper/2606.19348/) (2026)
- [IMPALA: Scalable Distributed Deep-RL with Importance Weighted Actor-Learner Architectures](https://mlsanity.com/paper/1802.01561/) (2018)
- [Group-in-Group Policy Optimization for LLM Agent Training](https://mlsanity.com/paper/2505.10978/) (2025)
- [AReaL: A Large-Scale Asynchronous Reinforcement Learning System for Language Reasoning](https://mlsanity.com/paper/2505.24298/) (2025)
- [BrowseComp-Plus: A More Fair and Transparent Evaluation Benchmark of Deep-Research Agent](https://mlsanity.com/paper/2508.06600/) (2025)
- [Stabilizing MoE Reinforcement Learning by Aligning Training and Inference Routers](https://mlsanity.com/paper/2510.11370/) (2025)
- [Defeating the Training-Inference Mismatch via FP16](https://mlsanity.com/paper/2510.26788/) (2025)
- [Every Step Evolves: Scaling Reinforcement Learning for Trillion-Scale Thinking Model](https://mlsanity.com/paper/2510.18855/) (2025)
- [Prosperity before Collapse: How Far Can Off-Policy RL Reach with Stale Data on LLMs?](https://mlsanity.com/paper/2510.01161/) (2025)
- [LlamaRL: A Distributed Asynchronous Reinforcement Learning Framework for Efficient Large-scale LLM Training](https://mlsanity.com/paper/2505.24034/) (2025)
- [PipelineRL: Faster On-policy Reinforcement Learning for Long Sequence Generation](https://mlsanity.com/paper/2509.19128/) (2025)
- [Turn-PPO: Turn-Level Advantage Estimation with PPO for Improved Multi-Turn RL in Agentic LLMs](https://mlsanity.com/paper/2512.17008/) (2025)
- [From Reasoning to Agentic: Credit Assignment in Reinforcement Learning for Large Language Models](https://mlsanity.com/paper/2604.09459/) (2026)
- [Trust Region Masking for Long-Horizon LLM Reinforcement Learning](https://mlsanity.com/paper/2512.23075/) (2025)
- [DORA: A Scalable Asynchronous Reinforcement Learning System for Language Model Training](https://mlsanity.com/paper/2604.26256/) (2026)
- [Trajectory Bellman Residual Minimization: A Simple Value-Based Method for LLM Reasoning](https://mlsanity.com/paper/2505.15311/) (2025)
- [VESPO: Variational Sequence-Level Soft Policy Optimization for Stable Off-Policy LLM Training](https://mlsanity.com/paper/2602.10693/) (2026)
- [Stable Asynchrony: Variance-Controlled Off-Policy RL for LLMs](https://mlsanity.com/paper/2602.17616/) (2026)
- [LLMs Can Learn to Reason Via Off-Policy RL](https://mlsanity.com/paper/2602.19362/) (2026)
- [CAPO: Critic-Guided Action-Aligned Policy Optimization for Advancing LLM Agent Capabilities](https://mlsanity.com/paper/2604.18401/) (2026)
- [Ratio-Variance Regularized Policy Optimization for Efficient LLM Fine-tuning](https://mlsanity.com/paper/2601.03320/) (2026)
- [From log π to π: Taming Divergence in Soft Clipping via Bilateral Decoupled Decay of Probability Gradient Weight](https://mlsanity.com/paper/2603.14389/) (2026)
- [Bidirectional Resource Scheduling for Disaggregated and Asynchronous RL Post-Training](https://mlsanity.com/paper/2607.09207/) (2026)
- [Orchestrating Tokens and Sequences: Dynamic Hybrid Policy Optimization for RLVR](https://mlsanity.com/paper/2601.05607/) (2026)

## Abstract (arXiv)

Asynchronous reinforcement learning has become the standard way to scale training for large language models (LLM), but the resulting policy lag biases the critic toward the stale behavior policy. Existing work on asynchronous LLM training corrects the actor and leaves this bias unaddressed, while the off-policy value correction of classical RL does not carry over to long-horizon agentic tasks, since a short correction horizon leaves the regression target free of the reward and a long one lets the product of importance ratios drift exponentially with the trajectory length. We propose BRACE, an anchored Bellman-residual correction for stale value models. BRACE bounds the correction horizon to a prefix of policy tokens and anchors a constant-weight Monte-Carlo tail beyond it, which separates policy correction from reward propagation. BRACE delivers a 9.8% relative improvement in mean@1 on BrowseComp-Plus over the strongest baseline, runs 2.46× faster per step than synchronous training, and remains stable 50 updates off-policy.