We propose a framework for the joint inference of network topology, multi-type interaction kernels, and latent type assignments in heterogeneous interacting particle systems from multi-trajectory data. This learning task is a challenging non-convex mixed-integer optimization problem, which we address through a novel three-stage approach. First, we leverage shared structure across agent interactions to recover a low-rank embedding of the system parameters via matrix sensing. Second, we identify discrete interaction types by clustering within the learned embedding. Third, we recover the network weight matrix and kernel coefficients through matrix factorization and a post-processing refinement. We provide theoretical guarantees with estimation error bounds under a Restricted Isometry Property (RIP) assumption and establish conditions for the exact recovery of interaction types based on cluster separability. Numerical experiments on synthetic datasets, including heterogeneous predator-prey systems, demonstrate that our method yields an accurate reconstruction of the underlying dynamics and is robust to noise.

Cooperative MARL often assumes frequent access to global information in a data buffer, such as team rewards or other agents' actions, which is typically unrealistic in decentralized MARL systems due to high communication costs. When communication is limited, agents must rely on outdated information to estimate gradients and update their policies. A common approach to handle missing data is called importance sampling, in which we reweigh old data from a base policy to estimate gradients for the current policy. However, it quickly becomes unstable when the communication is limited (i.e. missing data probability is high), so that the base policy in importance sampling is outdated. To address this issue, we propose a technique called base policy prediction, which utilizes old gradients to predict the policy update and collect samples for a sequence of base policies, which reduces the gap between the base policy and the current policy. This approach enables effective learning with significantly fewer communication rounds, since the samples of predicted base policies could be collected within one communication round. Theoretically, we show that our algorithm converges to an $\varepsilon$-Nash equilibrium in potential games with only $O(\varepsilon^{-3/4})$ communication rounds and $O(poly(\max_i |A_i|)\varepsilon^{-11/4})$ samples, improving existing state-of-the-art results in communication cost, as well as sample complexity without the exponential dependence on the joint action space size. We also extend these results to general Markov Cooperative Games to find an agent-wise local maximum. Empirically, we test the base policy prediction algorithm in both simulated games and MAPPO for complex environments.

Decentralized online convex optimization (D-OCO), where multiple agents within a network collaboratively learn optimal decisions in real-time, arises naturally in applications such as federated learning, sensor networks, and multi-agent control. In this paper, we study D-OCO under unknown, time-and agent-varying feedback delays. While recent work has addressed this problem (Nguyen et al., 2024), existing algorithms assume prior knowledge of the total delay over agents and still suffer from suboptimal dependence on both the delay and network parameters. To overcome these limitations, we propose a novel algorithm that achieves an improved regret bound of O N $\sqrt$ d tot + N $\sqrt$ T (1-$σ$2) 1/4 , where T is the total horizon, d tot denotes the average total delay across agents, N is the number of agents, and 1 -$σ$ 2 is the spectral gap of the network. Our approach builds upon recent advances in D-OCO (Wan et al., 2024a), but crucially incorporates an adaptive learning rate mechanism via a decentralized communication protocol. This enables each agent to estimate delays locally using a gossip-based strategy without the prior knowledge of the total delay. We further extend our framework to the strongly convex setting and derive a sharper regret bound of O N $δ$max ln T $α$ , where $α$ is the strong convexity parameter and $δ$ max is the maximum number of missing observations averaged over agents. We also show that our upper bounds for both settings are tight up to logarithmic factors. Experimental results validate the effectiveness of our approach, showing improvements over existing benchmark algorithms.

Grouping is ubiquitous in natural systems and is essential for promoting efficiency in team coordination. This paper proposes a novel formulation of Group-oriented Multi-Agent Reinforcement Learning (GoMARL), which learns automatic grouping without domain knowledge for efficient cooperation. In contrast to existing approaches that attempt to directly learn the complex relationship between the joint action-values and individual utilities, we empower subgroups as a bridge to model the connection between small sets of agents and encourage cooperation among them, thereby improving the learning efficiency of the whole team. In particular, we factorize the joint action-values as a combination of group-wise values, which guide agents to improve their policies in a fine-grained fashion. We present an automatic grouping mechanism to generate dynamic groups and group action-values. We further introduce a hierarchical control for policy learning that drives the agents in the same group to specialize in similar policies and possess diverse strategies for various groups. Experiments on the StarCraft II micromanagement tasks and Google Research Football scenarios verify our method's effectiveness. Extensive component studies show how grouping works and enhances performance.

The cooperative Multi-Agent Reinforcement Learning (MARL) with permutation invariant agents framework has achieved tremendous empirical successes in real-world applications. Unfortunately, the theoretical understanding of this MARL problem is lacking due to the curse of many agents and the limited exploration of the relational reasoning in existing works. In this paper, we verify that the transformer implements complex relational reasoning, and we propose and analyze model-free and model-based offline MARL algorithms with the transformer approximators. We prove that the suboptimality gaps of the model-free and model-based algorithms are independent of and logarithmic in the number of agents respectively, which mitigates the curse of many agents. These results are consequences of a novel generalization error bound of the transformer and a novel analysis of the Maximum Likelihood Estimate (MLE) of the system dynamics with the transformer. Our model-based algorithm is the first provably efficient MARL algorithm that explicitly exploits the permutation invariance of the agents. Our improved generalization bound may be of independent interest and is applicable to other regression problems related to the transformer beyond MARL.

Hedonic Games (HGs) are a classical framework modeling coalition formation of strategic agents guided by their individual preferences. According to these preferences, it is desirable that a coalition structure (i.e. a partition of agents into coalitions) satisfies some form of stability. The most well-known and natural of such notions is arguably core-stability. Informally, a partition is core-stable if no subset of agents would like to deviate by regrouping in a so-called core-blocking coalition. Unfortunately, core-stable partitions seldom exist and even when they do, it is often computationally intractable to find one. To circumvent these problems, we propose the notion of $\varepsilon$-fractional core-stability, where at most an $\varepsilon$-fraction of all possible coalitions is allowed to core-block. It turns out that such a relaxation may guarantee both existence and polynomial-time computation.