In this paper, we focus on the stochastic generalized Nash equilibrium problem (SGNEP) which is an important and widely-used model in many different fields. In this model, subject to certain global resource constraints, a set of self-interested players aim to optimize their local objectives that depend on their own decisions and the decisions of others and are influenced by some random factors. We propose a distributed stochastic generalized Nash equilibrium seeking algorithm in a partial-decision information setting based on the Douglas-Rachford operator splitting scheme, which relaxes assumptions in the existing literature. The proposed algorithm updates players' local decisions through augmented best-response schemes and subsequent projections onto the local feasible sets, which occupy most of the computational workload. The projected stochastic subgradient method is applied to provide approximate solutions to the augmented best-response subproblems for each player. The Robbins-Siegmund theorem is leveraged to establish the main convergence results to a true Nash equilibrium using the proposed inexact solver. Finally, we illustrate the validity of the proposed algorithm via two numerical examples, i.e., a stochastic Nash-Cournot distribution game and a multi-product assembly problem with the two-stage model.
A distributed primal-dual algorithm for computation of generalized Nash equilibria with shared affine coupling constraints via operator splitting methods
We consider the problem of computing a mixed-strategy generalized Nash equilibrium (MS-GNE) for a class of games where each agent has both continuous and integer decision variables. Specifically, we propose a novel Bregman forward-reflected-backward splitting and design distributed algorithms that exploit the problem structure. Technically, we prove convergence to a variational MS-GNE under mere monotonicity and Lipschitz continuity assumptions, which are typical of continuous GNE problems. Finally, we show the performance of our algorithms via numerical experiments.
A fundamental open problem in monotone game theory is the computation of a specific generalized Nash equilibrium (GNE) among all the available ones, e.g. the optimal equilibrium with respect to a system-level objective. The existing GNE seeking algorithms have in fact convergence guarantees toward an arbitrary, possibly inefficient, equilibrium. In this paper, we solve this open problem by leveraging results from fixed-point selection theory and in turn derive distributed algorithms for the computation of an optimal GNE in monotone games. We then extend the technical results to the time-varyin…
We consider a network of autonomous agents whose outputs are actions in a game with coupled constraints. In such network scenarios, agents seeking to minimize coupled cost functions using distributed information while satisfying the coupled constraints. Current methods consider the small class of multi-integrator agents using primal-dual methods. These methods can only ensure constraint satisfaction in steady-state. In contrast, we propose an inexact penalty method using a barrier function for nonlinear agents with equilibrium-independent passive dynamics. We show that these dynamics converge …
Volt-VAR and Volt-Watt control functions are mechanisms that are included in distributed energy resource (DER) power electronic inverters to mitigate excessively high or low voltages in distribution systems. In the event that a subset of DER have had their Volt-VAR and Volt-Watt settings compromised as part of a cyber-attack, we propose a mechanism to control the remaining set of non-compromised DER to ameliorate large oscillations in system voltages and large voltage imbalances in real time. To do so, we construct control policies for individual non-compromised DER, directly searching the pol…
In this paper, we consider the problem of learning a generalized Nash equilibrium (GNE) in strongly monotone games. First, we propose a novel continuous-time solution algorithm that uses regular projections and first-order information. As second main contribution, we design a data-driven variant of the former algorithm where each agent estimates their individual pseudo-gradient via zero-order information, namely, measurements of their individual cost function values, as typical of extremum seeking control. Third, we generalize our setup and results for multi-agent systems with nonlinear dynami…
Latency is inherent in almost all real-world networked applications. In this paper, we propose a distributed allocation strategy over multi-agent networks with delayed communications. The state of each agent (or node) represents its share of assigned resources out of a fixed amount (equal to overall demand). Every node locally updates its state toward optimizing a global allocation cost function via received information of its neighbouring nodes even when the data exchange over the network is heterogeneously delayed at different links. The update is based on the alternating direction method of…
Mix-CALADIN: A Distributed Algorithm for Consensus Mixed-Integer Optimization
The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；KTH Royal Institute of Technology（瑞典皇家理工学院）；The Hong Kong University of Science and Technology（香港科技大学）
In this paper, we consider distributed simultaneous state and parameter estimation for a class of nonlinear systems, for which the augmented model comprising both the states and the parameters is only partially observable. Specifically, we first illustrate how the sensitivity analysis (SA) can select variables for simultaneous state and parameter estimation. Then, a community structure detection (CSD) based process decomposition method is proposed for dividing the entire system into interconnected subsystems as the basis of distributed estimation. Next, we develop local moving horizon estimato…
This paper presents a distributed optimization algorithm tailored for solving optimal control problems arising in multi-building coordination. The buildings coordinated by a grid operator, join a demand response program to balance the voltage surge by using an energy cost defined criterion. In order to model the hierarchical structure of the building network, we formulate a distributed convex optimization problem with separable objectives and coupled affine equality constraints. A variant of the Augmented Lagrangian based Alternating Direction Inexact Newton (ALADIN) method for solving the con…
In this paper, we propose a distributed stochastic second-order proximal method that enables agents in a network to cooperatively minimize the sum of their local loss functions without any centralized coordination. The proposed algorithm, referred to as St-SoPro, incorporates a decentralized second-order approximation into an augmented Lagrangian function, and then randomly samples the local gradients and Hessian matrices of the agents, so that it is computationally and memory-wise efficient, particularly for large-scale optimization problems. We show that for globally restricted strongly conv…
This paper introduces an open-source software for distributed and decentralized non-convex optimization named ALADIN-$α$. ALADIN-$α$ is a MATLAB implementation of tailored variants of the Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) algorithm. Its user interface is convenient for rapid prototyping of non-convex distributed optimization algorithms. An improved version of the recently proposed bi-level variant of ALADIN is included enabling decentralized non-convex optimization with reduced information exchange. A collection of examples from different applications fields in…
This research addresses distributed proportional power sharing of inverter-based Distributed Generators (DGs) in microgrids under variations in maximum power capacity of DGs. A microgrid can include renewable energy resources such as wind turbines, solar panels, fuel cells, etc. The intermittent nature of such energy resources causes variations in their maximum power capacities. Since DGs in microgrids can be regarded as Multi-Agent-Systems (MASs), a consensus algorithm is designed to have the DGs generate their output power in proportion to their maximum capacities under capacity fluctuations…
Learning the relationships between various entities from time-series data is essential in many applications. Gaussian graphical models have been studied to infer these relationships. However, existing algorithms process data in a batch at a central location, limiting their applications in scenarios where data is gathered by different agents. In this paper, we propose a distributed sparse inverse covariance algorithm to learn the network structure (i.e., dependencies among observed entities) in real-time from data collected by distributed agents. Our approach is built on an online graphical alt…
