Multi-agent systems are characterized by environmental uncertainty, varying policies of agents, and partial observability, which result in significant risks.

The factorization of state-action value functions for Multi-Agent Reinforcement Learning (MARL) is important. Existing studies are limited by their representation capability, sample efficiency, and approximation error. To address these challenges, we propose, ResQ, a MARL value function factorization method, which can find the optimal joint policy for any state-action value function through residual functions. ResQ masks some state-action value pairs from a joint state-action value function, which is transformed as the sum of a main function and a residual function. ResQ can be used with mean-value and stochastic-value RL. We theoretically show that ResQ can satisfy both the individual global max (IGM) and the distributional IGM principle without representation limitations. Through experiments on matrix games, the predator-prey, and StarCraft benchmarks, we show that ResQ can obtain better results than multiple expected/stochastic value factorization methods.

Multi-agent systems are characterized by environmental uncertainty, varying policies of agents, and partial observability, which result in significant risks.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The paper develops lower and upper bounds on the required rank of adjacency tensor factorizations to recover the adjacency tensor. This is, it investigates the problem of the minimal rank required to express the true underlying data via factorizations. These bounds are shown to of practical use by scaling RESCAL up. The paper is extremely well written and makes several interesting and important contributions.

We extensively validate our method on both label-and domain-heterogeneous settings, on which it outperforms the state-of-the-art personalized federated learning methods.

Discrete diffusion models represent a significant advance in generative modeling, demonstrating remarkable success in synthesizing complex, high-quality discrete data. However, to avoid exponential computational costs, they typically rely on calculating per-dimension transition probabilities when learning high-dimensional distributions. In this study, we rigorously prove that this approach leads to a worst-case linear scaling of Kullback-Leibler (KL) divergence with data dimension. To address this, we propose a Quantum Discrete Denoising Diffusion Probabilistic Model (QD3PM), which enables joint probability learning through diffusion and denoising in exponentially large Hilbert spaces, offering a theoretical pathway to faithfully capture the true joint distribution. By deriving posterior states through quantum Bayes' theorem, similar to the crucial role of posterior probabilities in classical diffusion models, and by learning the joint probability, we establish a solid theoretical foundation for quantum-enhanced diffusion models. For denoising, we design a quantum circuit that utilizes temporal information for parameter sharing and incorporates learnable classical-data-controlled rotations for encoding. Exploiting joint distribution learning, our approach enables single-step sampling from pure noise, eliminating iterative requirements of existing models. Simulations demonstrate the proposed model's superior accuracy in modeling complex distributions compared to factorization methods. Hence, this paper establishes a new theoretical paradigm in generative models by leveraging the quantum advantage in joint distribution learning.

The factorization of state-action value functions for Multi-Agent Reinforcement Learning (MARL) is important. Existing studies are limited by their representation capability, sample efficiency, and approximation error. To address these challenges, we propose, ResQ, a MARL value function factorization method, which can find the optimal joint policy for any state-action value function through residual functions. ResQ masks some state-action value pairs from a joint state-action value function, which is transformed as the sum of a main function and a residual function. ResQ can be used with mean-value and stochastic-value RL.