Recent advances in artificial intelligence have expanded the focus from classical optimization to include equilibrium analysis in noncooperative games. Many such games involve shared constraints, leading to Generalized Nash Equilibrium Problems (GNEPs). Existing distributed algorithms typically require agents to exchange Lagrange multipliers to enforce consensus and compute variational-GNEs (v-GNEs). This work introduces fully distributed continuous-time algorithms and establishes convergence without requiring multiplier exchange, thereby reducing information exchange per iteration while improving privacy preservation. The analysis focuses on strongly monotone games with convex individual constraints and linear shared constraints. I also propose several discretization schemes for the continuous-time algorithms. The proposed approach converges to general GNEs, rather than being restricted to v-GNEs, with the attained equilibrium depending on the initialization. The effectiveness of the proposed method is demonstrated through applications in multi-robot coordination and placement. In the second part, this work includes research conducted in collaboration with Amazon scientists. One of the most challenging problems in real-world machine learning is labeled data collection, which typically requires substantial human effort and cost. Active learning aims to reduce this labeling requirement. Existing handcrafted active learning strategies, however, generally perform well only on specific types of datasets, which are often unknown in advance. In this work, I propose using contextual bandits to adaptively select the most suitable active learning strategy. The effectiveness of the proposed approach is demonstrated on publicly available external datasets.
Generalized Nash Equilibrium Problems (GNEPs) often arise in multi-agent engineering applications that require distributed algorithms. Unlike traditional approaches that enforce consensus on multipliers, our method removes the need to share multipliers, reducing communication and improving privacy. As a result, different initializations can lead to different GNEs, including non-variational ones. We establish convergence under sufficient conditions using an input-to-state stability (ISS) framework.
We propose and study distributionally robust Markov games (DR-MGs) with the average-reward criterion as a crucial framework for multi-agent decision-making under model mismatches and over extended horizons. Under a standard irreducible assumption, we first derive a correspondence between the optimal policies and the solutions of the robust Bellman equation, based on which we further show the existence of a stationary Nash Equilibrium (NE) of the game. We further study DR-MGs under a more general weakly communicating setting. We construct a set-valued map based on the constant-gain optimal robust Bellman operator and show that its value is a subset of the best-response policies. We further prove that this map admits a fixed point, which implies the existence of NE. We then design two algorithms, Robust Nash-Iteration and robust TD Descent, with provably convergent guarantees. Finally, we show that the NE under average-reward can be approximated by the ones for the discounted DR-MGs as the discount factor approaches one. Our studies provide a comprehensive theoretical and algorithmic foundation for decision-making in complex, uncertain, and long-running multi-player environments.
We study multi-objective multi-agent multi-armed bandits (MO-MA-MAB) under stochastic rewards, where agents observe heterogeneous reward vectors and communicate over time-varying graphs. We formulate this emerging problem setting to address \emph{efficient learning}, measured by Pareto regret, and incorporate \emph{fair learning} as an additional goal, captured via social welfare. To measure efficiency, we formulate Pareto regret and develop \textsc{Pareto UCB1 Gossip}, whose novel exploration radius explicitly separates statistical uncertainty in Pareto-based inference from consensus error. To express the fairness constraint, we formulate a Nash Social Welfare objective over preference-scalarized rewards and propose \textsc{Simulated NSW UCB Gossip}, which integrates preference-based reward simulation, gossip-based utility estimation, and UCB-style exploration. We prove that \textsc{Pareto UCB1 Gossip} achieves O(logT) regret and an instance-independent rate of O(T), while \textsc{Simulated NSW UCB Gossip} achieves an instance-independent regret bound of O(T3/4). This separation reveals the cost of imposing the fairness constraint to our efficiency objective: fairness limits information aggregation and slows convergence. Experiments show that our methods consistently outperform baselines, improving performance by approximately 100% and 50% in the efficiency and fairness settings, respectively.