# Test-time Multi-agent Coordination by Decomposed Value Gradient Flow

arXiv: https://arxiv.org/abs/2610.02554 · HTML: https://mlsanity.com/paper/2610.02554/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for LLM agents, one of 16 directions in LLM agents and tool use.
- Builds on 49 of its 59 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Placed in

- LLM agents and tool use / [Reinforcement learning for LLM agents](https://mlsanity.com/agents/reinforcement-learning-for-llm-agents/)
- Offline RL and imitation learning from data / [Offline multi-agent RL](https://mlsanity.com/offlinerl/offline-multi-agent-rl/)

## Builds on (most cited first, 30 of 49)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems](https://mlsanity.com/paper/2005.01643/) (2020)
- [Conservative Q-Learning for Offline Reinforcement Learning](https://mlsanity.com/paper/2006.04779/) (2020)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Offline Reinforcement Learning with Implicit Q-Learning](https://mlsanity.com/paper/2110.06169/) (2021)
- [Off-Policy Deep Reinforcement Learning without Exploration](https://mlsanity.com/paper/1812.02900/) (2018)
- [A Minimalist Approach to Offline Reinforcement Learning](https://mlsanity.com/paper/2106.06860/) (2021)
- [Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning](https://mlsanity.com/paper/1910.00177/) (2019)
- [Diffusion Policies as an Expressive Policy Class for Offline Reinforcement Learning](https://mlsanity.com/paper/2208.06193/) (2022)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Monotonic Value Function Factorisation for Deep Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2003.08839/) (2020)
- [Distributional Reinforcement Learning with Quantile Regression](https://mlsanity.com/paper/1710.10044/) (2017)
- [QTRAN: Learning to Factorize with Transformation for Cooperative Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1905.05408/) (2019)
- [IDQL: Implicit Q-Learning as an Actor-Critic Method with Diffusion Policies](https://mlsanity.com/paper/2304.10573/) (2023)
- [Safe, Multi-Agent, Reinforcement Learning for Autonomous Driving](https://mlsanity.com/paper/1610.03295/) (2016)
- [Flow Matching Guide and Code](https://mlsanity.com/paper/2412.06264/) (2024)
- [Diffusion Policy Policy Optimization](https://mlsanity.com/paper/2409.00588/) (2024)
- [Flow Q-Learning](https://mlsanity.com/paper/2502.02538/) (2025)
- [Maximum Entropy RL (Provably) Solves Some Robust RL Problems](https://mlsanity.com/paper/2103.06257/) (2021)
- [Steering Your Diffusion Policy with Latent Space Reinforcement Learning](https://mlsanity.com/paper/2506.15799/) (2025)
- [Stein Variational Gradient Descent as Gradient Flow](https://mlsanity.com/paper/1704.07520/) (2017)
- [Parrot: Data-Driven Behavioral Priors for Reinforcement Learning](https://mlsanity.com/paper/2011.10024/) (2020)
- [Revisiting the Minimalist Approach to Offline Reinforcement Learning](https://mlsanity.com/paper/2305.09836/) (2023)
- [Theoretical guarantees on the best-of-n alignment policy](https://mlsanity.com/paper/2401.01879/) (2024)
- [Primal Wasserstein Imitation Learning](https://mlsanity.com/paper/2006.04678/) (2020)
- [Offline RL with No OOD Actions: In-Sample Learning via Implicit Value Regularization](https://mlsanity.com/paper/2303.15810/) (2023)
- [EMaQ: Expected-Max Q-Learning Operator for Simple Yet Effective Offline and Online RL](https://mlsanity.com/paper/2007.11091/) (2020)
- [Reinforcement Learning with Action Chunking](https://mlsanity.com/paper/2507.07969/) (2025)
- [Flow Matching for Scalable Simulation-Based Inference](https://mlsanity.com/paper/2305.17161/) (2023)

## Abstract (arXiv)

Offline multi-agent reinforcement learning (MARL) faces a persistent trade-off. Expressive generative policies can represent multi-modal coordination in the data, but cannot distinguish high-value regions, while value-optimized policies exploit the learned Q-function but collapse the multi-modal into a single dominant mode. A single agent's mode collapse can break joint coordination, and simultaneous drift across agents can push the joint policy into unseen regions of the action space. We propose scalable coordination via optimal unified transport (SCOUT), the first offline MARL framework to combine a generative foundation model with a learned value function through test-time action refinement. SCOUT trains two decoupled components: a flow-matching behavioral prior and a decomposed value function. At test-time, it transports behavioral samples toward high-value regions via Stein variational gradient descent. The number of transport steps controls adaptive test-time scaling, replacing a fixed regularization coefficient. Under the individual-global-max (IGM) principle, we prove a single-term KL bound on the joint soft-value gap that vanishes as transport converges, with an irreducible additive residual proportional to the IGM violation. Empirically, SCOUT achieves the best average performance across discrete and continuous offline MARL benchmarks and yields performance improvements in all offline-to-online configurations.