This paper develops a continuous-time primal-dual accelerated method with an increasing damping coefficient for a class of convex optimization problems with affine equality constraints. We then analyze critical values for parameters in the proposed method and prove that the rate of convergence is $O(\frac{1}{t^2})$ with properly chosen parameters. As far as we know, this is the first continuous-time primal-dual accelerated method that can obtain the optimal rate. In addition, we apply the proposed method to two network optimization problems, a distributed optimization problem with consensus constraints and a distributed extended monotropic optimization problem, and obtain two variant distributed algorithms. Finally, numerical simulations are given to demonstrate the efficacy of the proposed method.

This paper considers distributed Nash equilibrium (NE) seeking of strongly monotone aggregative games over a multiagent network. Each player can only observe its own strategy while can exchange information with its neighbors via a communication graph. To solve the problem, we propose a distributed algorithm with multiple rounds of communication, where the players need constant rounds of communication with their neighbors at each iteration. Moreover, we prove that our algorithm converges to the (unique) NE with a linear convergence rate. We further study a single-round communication version of our algorithm, which can also achieve linear convergence rate with an additional condition related to the structure of the graph and the properties of the aggregative game. Finally, we provide numerical simulations to verify our results.

The work gives a review on the distributed Nash equilibrium seeking of noncooperative games in multi-agent networks, which emerges as one of the frontier research topics in the area of systems and control community. Firstly, we give the basic formulation and analysis of noncooperative games with continuous action spaces, and provide the motivation and basic setting for distributed Nash equilibrium seeking. Then we introduce both the gradient-based algorithms and best-response based algorithms for various type of games, including zero-sum games, aggregative games, potential games, monotone games, and multi-cluster games. In addition, we provide some applications of noncooperative games.

In this article, we consider distributed stochastic optimization over randomly switching networks, where agents collaboratively minimize the average of all agents’ local expectation-valued convex cost functions. Due to the stochasticity in gradient observations, distributedness of local functions, and randomness of communication topologies, distributed algorithms with an exact convergence guarantee under fixed step-sizes have not been achieved yet. This work incorporates variance reduction scheme into the distributed stochastic gradient tracking algorithm, where local gradients are estimated by averaging across a variable number of sampled gradients. With an identically and independently distributed random network, we show that all agents’ iterates converge almost surely to the same optimal solution under fixed step-sizes. When the global cost function is strongly convex and the sample size increases at a geometric rate, we prove that the iterates geometrically converge to the unique optimal solution, and establish the iteration, oracle, and communication complexity. The algorithm performance, including rate and complexity analysis, are further investigated with constant step-sizes and a polynomially increasing sample size. Finally, the empirical algorithm performance are illustrated with numerical examples.

In this article, we explore how to optimize task allocation for robot swarms in dynamic environments, emphasizing the necessity of formulating robust, flexible, and scalable strategies for robot cooperation. We introduce a novel framework using a decentralized partially observable Markov decision process (Dec-POMDP), specifically designed for distributed robot swarm networks. At the core of our methodology is the local information aggregation multiagent deep deterministic policy gradient (LIA-MADDPG) algorithm, which merges centralized training with distributed execution. During the centralized training phase, a local information aggregation (LIA) module is meticulously designed to gather critical data from neighboring robots, enhancing decision-making efficiency. In the distributed execution phase, a strategy improvement method is proposed to dynamically adjust task allocation based on changing and partially observable environmental conditions. Our empirical evaluations show that the LIA module can be seamlessly integrated into various centralized training and decentralized execution (CTDE)-based multiagent reinforcement learning (MARL) methods, significantly enhancing their performance. Additionally, by comparing LIA-MADDPG with six conventional reinforcement learning algorithms and a heuristic algorithm, we demonstrate its superior scalability, rapid adaptation to environmental changes, and ability to maintain both stability and convergence speed. These results underscore LIA-MADDPG’s outstanding performance and its potential to significantly improve dynamic task allocation in robot swarms through enhanced local collaboration and adaptive strategy execution.

This work considers an aggregative game over time-varying graphs, where each player's cost function depends on its own strategy and the aggregate of its competitors' strategies. Though the aggregate is unknown to any given player, each player may interact with its neighbors to construct an estimate of the aggregate. We design a distributed iterative Tikhonov regularization method in which each player may independently choose its steplengths and regularization parameters while meeting some overall coordination requirements. Under a monotonicity assumption on the concatenated player-specific gradient map, we prove that the generated sequence converges to the least-norm Nash equilibrium (i.e., a Nash equilibrium with the smallest two-norm) and validate the proposed method on a networked Nash-Cournot equilibrium problem.