Distributed decision problems feature a group of agents that can only communicate over a peer-to-peer network, without a central memory. In applications such as network control and data ranking, each agent is only affected by a small portion of the decision vector: this sparsity is typically ignored in distributed algorithms, while it could be leveraged to improve efficiency and scalability. To address this issue, our recent paper [1] introduces Estimation Network Design (END), a graph theoretical language for analysis and design of distributed iterations. END methods can be tuned to exploit the sparsity of specific problem instances, reducing communication overhead and minimizing redundancy, yet without requiring case-by-case convergence analysis. In this paper, we showcase the flexibility of END in the context of distributed optimization. In particular, we study the sparsity-aware version of many established algorithms, including ADMM, AugDGM and PushSum DGD. Simulations on an estimation problem in sensor networks demonstrate that END algorithms can boost convergence speed and greatly reduce the communication cost.

Multiagent decision problems are typically solved via distributed iterative algorithms, where the agents only communicate among themselves on a peer-to-peer network. Each agent usually maintains a copy of each decision variable, while agreement among the local copies is enforced via consensus protocols. Yet, each agent is often directly influenced by a small portion of the decision variables only: neglecting this sparsity results in redundancy, poor scalability with the network size, and communication and memory overhead. To address these challenges, we develop Estimation Network Design (END), a framework for the design and analysis of distributed algorithms. END algorithms can be tuned to exploit problem-specific sparsity structures, by optimally allocating copies of each variable only to a subset of agents, to improve efficiency and minimize redundancy. We illustrate the END's potential on generalized Nash equilibrium seeking under partial-decision information by designing new algorithms that can leverage the sparsity in cost functions, constraints, and aggregation values, and by relaxing the assumptions on the (directed) communication network postulated in the literature. Finally, we numerically test our methods on a unicast rate allocation problem, revealing greatly reduced communication and memory costs.

We study generalized games with full row rank equality coupling constraints and we provide a strikingly simple proof of strong monotonicity of the associated KKT operator. This allows us to show linear convergence to a variational equilibrium of the resulting primal-dual pseudo-gradient dynamics. Then, we propose a fully-distributed algorithm with linear convergence guarantee for aggregative games under partial-decision information. Based on these results, we establish stability properties for online GNE seeking in games with time-varying cost functions and constraints. Finally, we illustrate our findings numerically on an economic dispatch problem for peer-to-peer energy markets.

The topic of this dissertation is the distributed computation of Generalized Nash Equilibria (GNEs) in multi-agent games with network structure. In particular, we design and analyze algorithms in the partial-decision information scenario (also named fully-distributed algorithms), where each agent can only rely on the information received by some neighbors over a communication graph, although its cost function depends on the actions of possibly all the competitors. This setup is motivated by engineering applications with no central system coordinator, for instance multi-agent autonomous driving or coverage control. While the agents can estimate the unknown variables via local data exchange and consensus protocols, the estimation error introduces critical challenges in the development of algorithms. In fact, the existing schemes for GNE seeking under partial-decision information suffer important limitations, as to performance and conditions to guarantee convergence. In this perspective, this thesis advances the theoretical understanding of games in the partial-decision information scenario, and provides a broad tool kit for designing efficient algorithmic solutions, suitable to cope with complex network interaction and dynamic coupling.

We consider Nash equilibrium problems in a partial-decision information scenario, where each agent can only exchange information with some neighbors, while its cost function possibly depends on the strategies of all agents. We characterize the relation between several monotonicity and smoothness assumptions postulated in the literature. Furthermore, we prove convergence of a preconditioned proximal-point algorithm, under a restricted monotonicity property that allows for a non-Lipschitz, non-continuous game mapping.

We address the generalized Nash equilibrium seeking problem in a partial-decision information scenario, where each agent can only exchange information with some neighbors, although its cost function possibly depends on the strategies of all agents. The few existing methods build on projected pseudo-gradient dynamics, and require either double-layer iterations or conservative conditions on the step sizes. To overcome both these flaws and improve efficiency, we design the first fully-distributed single-layer algorithms based on proximal best-response. Our schemes are fixed-step and allow for inexact updates, which is crucial for reducing the computational complexity. Under standard assumptions on the game primitives, we establish convergence to a variational equilibrium (with linear rate for games without coupling constraints) by recasting our algorithms as proximal-point methods, opportunely preconditioned to distribute the computation among the agents. Since our analysis hinges on a restricted monotonicity property, we also provide new general results that significantly extend the domain of applicability of proximal-point methods. Besides, our operator-theoretic approach favors the implementation of provably correct acceleration schemes that can further improve the convergence speed. Finally, the potential of our algorithms is demonstrated numerically, revealing much faster convergence with respect to projected pseudo-gradient methods and validating our theoretical findings.

The distributed dual ascent is an established algorithm to solve strongly convex multi-agent optimization problems with separable cost functions, in the presence of coupling constraints. In this letter, we study its asynchronous counterpart. Specifically, we assume that each agent only relies on the outdated information received from some neighbors. Differently from the existing randomized and dual block-coordinate schemes, we show convergence under heterogeneous delays, communication and update frequencies. Consequently, our asynchronous dual ascent algorithm can be implemented without requiring any coordination between the agents.

We design a distributed algorithm for learning Nash equilibria over time-varying communication networks in a partial-decision information scenario, where each agent can access its own cost function and local feasible set, but can only observe the actions of some neighbors. Our algorithm is based on projected pseudo-gradient dynamics, augmented with consensual terms. Under strong monotonicity and Lipschitz continuity of the game mapping, we provide a simple proof of linear convergence, based on a contractivity property of the iterates. Compared to similar solutions proposed in literature, we also allow for time-varying communication and derive tighter bounds on the step sizes that ensure convergence. In fact, in our numerical simulations, our algorithm outperforms the existing gradient-based methods, when the step sizes are set to their theoretical upper bounds. Finally, to relax the assumptions on the network structure, we propose a different pseudo-gradient algorithm, which is guaranteed to converge on time-varying balanced directed graphs.

We consider strongly monotone games with convex separable coupling constraints, played by dynamical agents, in a partial-decision information scenario. We start by designing continuous-time fully distributed feedback controllers, based on consensus and primal–dual gradient dynamics, to seek a generalized Nash equilibrium in networks of single-integrator agents. Our first solution adopts a fixed gain, whose choice requires the knowledge of some global parameters of the game. To relax this requirement, we conceive a controller that can be tuned in a completely decentralized fashion, thanks to the use of uncoordinated integral adaptive weights. We further introduce algorithms specifically devised for generalized aggregative games. Finally, we adapt all our control schemes to deal with heterogeneous multi-integrator agents and, in turn, with nonlinear feedback-linearizable dynamical systems. For all the proposed dynamics, we show convergence to a variational equilibrium, by leveraging monotonicity properties and stability theory for projected dynamical systems.

We address the Nash equilibrium problem in a partial-decision information scenario, where each agent can only observe the actions of some neighbors, while its cost possibly depends on the strategies of other agents. Our main contribution is the design of a fully-distributed, single-layer, fixed-step algorithm, based on a proximal best-response augmented with consensus terms. To derive our algorithm, we follow an operator-theoretic approach. First, we recast the Nash equilibrium problem as that of finding a zero of a monotone operator. Then, we demonstrate that the resulting inclusion can be solved in a fully-distributed way via a proximal-point method, thanks to the use of a novel preconditioning matrix. Under strong monotonicity and Lipschitz continuity of the game mapping, we prove linear convergence of our algorithm to a Nash equilibrium. Furthermore, we show that our method outperforms the fastest known gradient-based schemes, both in terms of guaranteed convergence rate, via theoretical analysis, and in practice, via numerical simulations.

We consider a system of single- or double-integrator agents playing a generalized Nash game over a network, in a partial-information scenario. We address the generalized Nash equilibrium seeking problem by designing a fully-distributed dynamic controller, based on continuous-time consensus and primal-dual gradient dynamics. Our main technical contribution is to show convergence of the closed-loop system to a variational equilibrium, under strong monotonicity and Lipschitz continuity of the game mapping, by leveraging monotonicity properties and stability theory for projected dynamical systems.

We consider the Nash equilibrium problem in a partial-decision information scenario. Specifically, each agent can only receive information from some neighbors via a communication network, while its cost function depends on the strategies of possibly all agents. In particular, while the existing methods assume undirected or balanced communication, in this paper we allow for non-balanced, directed graphs. We propose a fully-distributed pseudo-gradient scheme, which is guaranteed to converge with linear rate to a Nash equilibrium, under strong monotonicity and Lipschitz continuity of the game mapping. Our algorithm requires global knowledge of the communication structure, namely of the Perron-Frobenius eigenvector of the adjacency matrix and of a certain constant related to the graph connectivity. Therefore, we adapt the procedure to setups where the network is not known in advance, by computing the eigenvector online and by means of vanishing step sizes.