Multi-agent network systems have found applications in various societal infrastructures, such as power systems, traffic networks, and smart cities [McArthur et al., 2007, Burmeister et al., 1997, Roscia et al., 2013]. One particularly important class of such problems is the cooperative multi-agent network MDP setting, where agents are embedded in a graph, and each agent has its own local state [Qu et al., 2020b]. In network MDPs, the local state transition probabilities and rewards only depend on the states and actions of the agent's direct neighbors in the graph. Such a property has been observed in a great variety of cooperative network control problems, ranging from thermal control of multizone buildings [Zhang et al., 2016], wireless access control [Zocca, 2019] to phase synchronization in electrical grids [Blaabjerg et al., 2006], where agents typically only need to act and learn based on information within a local neighborhood due to constraints on the information and communication infrastructure.

In this paper, we formulate the multi-agent graph bandit problem as a multi-agent extension of the graph bandit problem introduced by Zhang, Johansson, and Li [CISS 57, 1-6 (2023)]. In our formulation, $N$ cooperative agents travel on a connected graph $G$ with $K$ nodes. Upon arrival at each node, agents observe a random reward drawn from a node-dependent probability distribution. The reward of the system is modeled as a weighted sum of the rewards the agents observe, where the weights capture the decreasing marginal reward associated with multiple agents sampling the same node at the same time. We propose an Upper Confidence Bound (UCB)-based learning algorithm, Multi-G-UCB, and prove that its expected regret over $T$ steps is bounded by $O(N\log(T)[\sqrt{KT} + DK])$, where $D$ is the diameter of graph $G$. Lastly, we numerically test our algorithm by comparing it to alternative methods.

We study the performance of the gradient play algorithm for stochastic games (SGs), where each agent tries to maximize its own total discounted reward by making decisions independently based on current state information which is shared between agents. Policies are directly parameterized by the probability of choosing a certain action at a given state. We show that Nash equilibria (NEs) and first-order stationary policies are equivalent in this setting, and give a local convergence rate around strict NEs. Further, for a subclass of SGs called Markov potential games (which includes the setting with identical rewards as an important special case), we design a sample-based reinforcement learning algorithm and give a non-asymptotic global convergence rate analysis for both exact gradient play and our sample-based learning algorithm. Our result shows that the number of iterations to reach an $\epsilon$-NE scales linearly, instead of exponentially, with the number of agents. Local geometry and local stability are also considered, where we prove that strict NEs are local maxima of the total potential function and fully-mixed NEs are saddle points.

Robust Markov Decision Processes (MDPs) and risk-sensitive MDPs are both powerful tools for making decisions in the presence of uncertainties. Previous efforts have aimed to establish their connections, revealing equivalences in specific formulations. This paper introduces a new formulation for risk-sensitive MDPs, which assesses risk in a slightly different manner compared to the classical Markov risk measure (Ruszczy\'nski 2010), and establishes its equivalence with a class of regularized robust MDP (RMDP) problems, including the standard RMDP as a special case. Leveraging this equivalence, we further derive the policy gradient theorem for both problems, proving gradient domination and global convergence of the exact policy gradient method under the tabular setting with direct parameterization. This forms a sharp contrast to the Markov risk measure, known to be potentially non-gradient-dominant (Huang et al. 2021). We also propose a sample-based offline learning algorithm, namely the robust fitted-Z iteration (RFZI), for a specific regularized RMDP problem with a KL-divergence regularization term (or equivalently the risk-sensitive MDP with an entropy risk measure). We showcase its streamlined design and less stringent assumptions due to the equivalence and analyze its sample complexity.

This paper considers multi-agent reinforcement learning (MARL) where the rewards are received after delays and the delay time varies across agents and across time steps. Based on the V-learning framework, this paper proposes MARL algorithms that efficiently deal with reward delays. When the delays are finite, our algorithm reaches a coarse correlated equilibrium (CCE) with rate $\tilde{\mathcal{O}}(\frac{H^3\sqrt{S\mathcal{T}_K}}{K}+\frac{H^3\sqrt{SA}}{\sqrt{K}})$ where $K$ is the number of episodes, $H$ is the planning horizon, $S$ is the size of the state space, $A$ is the size of the largest action space, and $\mathcal{T}_K$ is the measure of total delay formally defined in the paper. Moreover, our algorithm is extended to cases with infinite delays through a reward skipping scheme. It achieves convergence rate similar to the finite delay case.

We introduce a new method based on nonnegative matrix factorization, Neural NMF, for detecting latent hierarchical structure in data. Datasets with hierarchical structure arise in a wide variety of fields, such as document classification, image processing, and bioinformatics. Neural NMF recursively applies NMF in layers to discover overarching topics encompassing the lower-level features. We derive a backpropagation optimization scheme that allows us to frame hierarchical NMF as a neural network. We test Neural NMF on a synthetic hierarchical dataset, the 20 Newsgroups dataset, and the MyLymeData symptoms dataset. Numerical results demonstrate that Neural NMF outperforms other hierarchical NMF methods on these data sets and offers better learned hierarchical structure and interpretability of topics.

This paper studies policy optimization algorithms for multi-agent reinforcement learning. We begin by proposing an algorithm framework for two-player zero-sum Markov Games in the full-information setting, where each iteration consists of a policy update step at each state using a certain matrix game algorithm, and a value update step with a certain learning rate. This framework unifies many existing and new policy optimization algorithms. We show that the state-wise average policy of this algorithm converges to an approximate Nash equilibrium (NE) of the game, as long as the matrix game algorithms achieve low weighted regret at each state, with respect to weights determined by the speed of the value updates. Next, we show that this framework instantiated with the Optimistic Follow-The-Regularized-Leader (OFTRL) algorithm at each state (and smooth value updates) can find an $\mathcal{\widetilde{O}}(T^{-5/6})$ approximate NE in $T$ iterations, and a similar algorithm with slightly modified value update rule achieves a faster $\mathcal{\widetilde{O}}(T^{-1})$ convergence rate. These improve over the current best $\mathcal{\widetilde{O}}(T^{-1/2})$ rate of symmetric policy optimization type algorithms. We also extend this algorithm to multi-player general-sum Markov Games and show an $\mathcal{\widetilde{O}}(T^{-3/4})$ convergence rate to Coarse Correlated Equilibria (CCE). Finally, we provide a numerical example to verify our theory and investigate the importance of smooth value updates, and find that using "eager" value updates instead (equivalent to the independent natural policy gradient algorithm) may significantly slow down the convergence, even on a simple game with $H=2$ layers.