# Follow the Winners: Conservative Policy Improvement with the Cross-Entropy Method for Critic-Free RFT

arXiv: https://arxiv.org/abs/2610.03361 · HTML: https://mlsanity.com/paper/2610.03361/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 62 of its 116 references that are in the map.
- First posted on arXiv 2 Oct 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)
- LLM agents and tool use / [Reinforcement learning for LLM agents](https://mlsanity.com/agents/reinforcement-learning-for-llm-agents/)

## Builds on (most cited first, 30 of 62)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning](https://mlsanity.com/paper/2503.09516/) (2025)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models](https://mlsanity.com/paper/1805.12114/) (2018)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [Reinforced Self-Training (ReST) for Language Modeling](https://mlsanity.com/paper/2308.08998/) (2023)
- [Group-in-Group Policy Optimization for LLM Agent Training](https://mlsanity.com/paper/2505.10978/) (2025)
- [Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review](https://mlsanity.com/paper/1805.00909/) (2018)
- [Brax -- A Differentiable Physics Engine for Large Scale Rigid Body Simulation](https://mlsanity.com/paper/2106.13281/) (2021)
- [RAGEN: Understanding Self-Evolution in LLM Agents via Multi-Turn Reinforcement Learning](https://mlsanity.com/paper/2504.20073/) (2025)
- [Beyond Human Data: Scaling Self-Training for Problem-Solving with Language Models](https://mlsanity.com/paper/2312.06585/) (2023)
- [Maximum a Posteriori Policy Optimisation](https://mlsanity.com/paper/1806.06920/) (2018)
- [Statistical Rejection Sampling Improves Preference Optimization](https://mlsanity.com/paper/2309.06657/) (2023)

## Abstract (arXiv)

Critic-free reinforcement fine-tuning (RFT) for agentic large language models is often done through GRPO-style methods, which compute a group baseline over repeated rollouts to reduce target variance. However, this setup is ill-suited to agents acting in stateful environments such as live services or security sandboxes, where repeated rollouts are impractical to obtain and aggressive updates entrench the noise of long, sparsely verified trajectories. We propose textitFollow the Winners (FTW), a critic-free policy-learning algorithm that adapts the cross-entropy method to RFT, replacing group rollouts with an ordinal filter on replay-buffer samples that yields polynomial concentration in the order statistic of returns. We derive FTW through a control-as-inference lens, which also recovers GRPO and DPO as specific modelling choices, identifying GRPO as risk-neutral while DPO and FTW share a bounded risk-seeking offset that FTW controls. We identify this offset as an inherent trade-off of variance reduction through ordinal filters on samples, whereas a critic model induces a different trade-off between bias and variance. Scaled to agentic LLM post-training, FTW matches GRPO and PPO on Sokoban and Search-R1 baselines, showing a viable trade-off from a value model or group rollouts to CPU memory.