# SAT: Sequential Agent Tuning for Coordinator Free Plug and Play Multi-LLM Training with Monotonic Improvement Guarantees

arXiv: https://arxiv.org/abs/2605.05216 · HTML: https://mlsanity.com/paper/2605.05216/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for LLM agents, one of 16 directions in LLM agents and tool use.
- Builds on 22 of its 35 references that are in the map.
- First posted on arXiv 17 Apr 2026.

## Placed in

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

## Builds on (most cited first, 22 of 22)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation](https://mlsanity.com/paper/2308.08155/) (2023)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [Carbon Emissions and Large Neural Network Training](https://mlsanity.com/paper/2104.10350/) (2021)
- [Mixture-of-Agents Enhances Large Language Model Capabilities](https://mlsanity.com/paper/2406.04692/) (2024)
- [PlanBench: An Extensible Benchmark for Evaluating Large Language Models on Planning and Reasoning about Change](https://mlsanity.com/paper/2206.10498/) (2022)
- [Alphazero-like Tree-Search can Guide Large Language Model Decoding and Training](https://mlsanity.com/paper/2309.17179/) (2023)
- [Safe and Efficient Off-Policy Reinforcement Learning](https://mlsanity.com/paper/1606.02647/) (2016)
- [ZebraLogic: On the Scaling Limits of LLMs for Logical Reasoning](https://mlsanity.com/paper/2502.01100/) (2025)
- [LLM in a flash: Efficient Large Language Model Inference with Limited Memory](https://mlsanity.com/paper/2312.11514/) (2023)
- [Mean-Variance Policy Iteration for Risk-Averse Reinforcement Learning](https://mlsanity.com/paper/2004.10888/) (2020)
- [From Debate to Equilibrium: Belief-Driven Multi-Agent LLM Reasoning via Bayesian Nash Equilibrium](https://mlsanity.com/paper/2506.08292/) (2025)
- [Improving Generalization in Visual Reinforcement Learning via Conflict-aware Gradient Agreement Augmentation](https://mlsanity.com/paper/2308.01194/) (2023)
- [A Block Coordinate Ascent Algorithm for Mean-Variance Optimization](https://mlsanity.com/paper/1809.02292/) (2018)

## Built on by (most cited first, 2 of 2)

- [TeamTR: Trust-Region Fine-Tuning for Multi-Agent LLM Coordination](https://mlsanity.com/paper/2605.15207/) (2026)
- [DICE: Entropy-Regularized Equilibrium Selection for Stable Multi-Agent LLM Coordination](https://mlsanity.com/paper/2606.08068/) (2026)

## Abstract (arXiv)

Large language models (LLMs) with a large number of parameters achieve strong performance but are often prohibitively expensive to deploy. Recent work explores using teams of smaller, more efficient LLMs that collectively match or even outperform a single large model. However, jointly updating multiple agents introduces compounding distribution shifts, making coordination and stability during training difficult. We address this by introducing Sequential Agent Tuning (SAT), a coordinator-free training paradigm. SAT represents the team as a factorized policy and employs block-coordinate updates over agents, enabling scalable, decentralized training without a central controller. Specifically, we develop a sequence-aware, on-policy advantage estimator that conditions on the evolving team policy, coupled with per-agent KL trust regions that isolate occupancy drift. Theoretically, this framework provides two critical guarantees. First, it ensures monotonic improvement, stabilizing the training process. Second, it establishes provable plug-and-play invariance: any agent can be upgraded to a stronger model without retraining the rest of the team, with a formal guarantee that the performance bound improves. Empirically, a team of three 4B agents (12B total) trained with SAT surpasses the much larger Qwen3-32B on AIME24/25 benchmarks by 3.9% on average. We validate our plug-and-play theory by swapping in two 8B agents, which boosts the composite score by 10.4%. We provide code and appendix of proof at https://github.com/Yydc/SAT-AAMAS