Diffusion models have been widely adopted in image and language generation and are now being applied to reinforcement learning. However, the application of diffusion models in offline cooperative Multi-Agent Reinforcement Learning (MARL) remains limited. Although existing studies explore this direction, they suffer from scalability or poor cooperation issues due to the lack of design principles for diffusion-based MARL. The Individual-Global-Max (IGM) principle is a popular design principle for cooperative MARL. By satisfying this principle, MARL algorithms achieve remarkable performance with good scalability. In this work, we extend the IGM principle to the Individual-Global-identically-Distributed (IGD) principle. This principle stipulates that the generated outcome of a multi-agent diffusion model should be identically distributed as the collective outcomes from multiple individual-agent diffusion models. We propose DoF, a diffusion factorization framework for Offline MARL. It uses noise factorization function to factorize a centralized diffusion model into multiple diffusion models. We theoretically show that the noise factorization functions satisfy the IGD principle. Furthermore, DoF uses data factorization function to model the complex relationship among data generated by multiple diffusion models. Through extensive experiments, we demonstrate the effectiveness of DoF. The source code is available at [https://github.com/xmu-rl-3dv/DoF](https://github.com/xmu-rl-3dv/DoF).

Parameter-sharing (PS) techniques have been widely adopted in cooperative Multi-Agent Reinforcement Learning (MARL). In PS, all the agents share a policy network with identical parameters, which enjoys good sample efficiency. However, PS could lead to homogeneous policies that limit MARL performance. We tackle this problem from the angle of gradient conflict among agents. We find that the existence of futile neurons whose update is canceled out by gradient conflicts among agents leads to poor learning efficiency and diversity. To address this deficiency, we propose GradPS, a gradient-based PS method. It dynamically creates multiple clones for each futile neuron. For each clone, a group of agents with low gradient-conflict shares the neuron's parameters. Our method can enjoy good sample efficiency by sharing the gradients among agents of the same clone neuron. Moreover, it can encourage diverse behaviors through independently updating an exclusive clone neuron. Through extensive experiments, we show that GradPS can learn diverse policies with promising performance. The source code for GradPS is available in \url{https://github.com/xmu-rl-3dv/GradPS}.

Large Language Models (LLMs) are increasingly being explored across a range of reasoning tasks. However, LLMs sometimes struggle with reasoning tasks under uncertainty that are relatively easy for humans, such as planning actions in stochastic environments. The adoption of LLMs for reasoning is impeded by uncertainty challenges, such as LLM uncertainty and environmental uncertainty. LLM uncertainty arises from the stochastic sampling process inherent to LLMs. Most LLM-based Decision-Making (LDM) approaches address LLM uncertainty through multiple reasoning chains or search trees. However, these approaches overlook environmental uncertainty, which leads to poor performance in environments with stochastic state transitions. Some recent LDM approaches deal with uncertainty by forecasting the probability of unknown variables. However, they are not designed for multi-step reasoning tasks that require interaction with the environment. To address uncertainty in LLM decision-making, we introduce PlanU, an LLM-based planning method that captures uncertainty within Monte Carlo Tree Search (MCTS). PlanU models the return of each node in the MCTS as a quantile distribution, which uses a set of quantiles to represent the return distribution. To balance exploration and exploitation during tree search, PlanU introduces an Upper Confidence Bounds with Curiosity (UCC) score which estimates the uncertainty of MCTS nodes. Through extensive experiments, we demonstrate the effectiveness of PlanU in LLM-based reasoning tasks under uncertainty.