arXiv subjects

Jan Zimmermann

Publications and source records attributed to Jan Zimmermann.

24 records · Page 2Linked to original sources

arXiv2021

Gradient Play in $n$-Cluster Games with Zero-Order Information

We study a distributed approach for seeking a Nash equilibrium in $n$-cluster games with strictly monotone mappings. Each player within each cluster has access to the current value of her own smooth local cost function estimated by a zero-order oracle at some query point. We assume the agents to be able to communicate with their neighbors in the same cluster over some undirected graph. The goal of the agents in the cluster is to minimize their collective cost. This cost depends, however, on actions of agents from other clusters. Thus, a game between the clusters is to be solved. We present a distributed gradient play algorithm for determining a Nash equilibrium in this game. The algorithm takes into account the communication settings and zero-order information under consideration. We prove almost sure convergence of this algorithm to a Nash equilibrium given appropriate estimations of the local cost functions' gradients.

cs.GT↗

arXiv2021

Gradient-Tracking over Directed Graphs for solving Leaderless Multi-Cluster Games

We are concerned with finding Nash Equilibria in agent-based multi-cluster games, where agents are separated into distinct clusters. While the agents inside each cluster collaborate to achieve a common goal, the clusters are considered to be virtual players that compete against each other in a non-cooperative game with respect to a coupled cost function. In such scenarios, the inner-cluster problem and the game between the clusters need to be solved simultaneously. Therefore, the resulting inter-cluster Nash Equilibrium should also be a minimizer of the social welfare problem inside the clusters. In this work, this setup is cast as a distributed optimization problem with sparse state information. Hence, critical information, such as the agent's cost functions, remain private. We present a distributed algorithm that converges with a linear rate to the optimal solution. Furthermore, we apply our algorithm to an extended cournot game to verify our theoretical results.

eess.SY↗

arXiv2020

Minimal Specifications for Non-Human Primate MRI: Challenges in Standardizing and Harmonizing Data Collection

Recent methodological advances in MRI have enabled substantial growth in neuroimaging studies of non-human primates (NHPs), while open data-sharing through the PRIME-DE initiative has increased the availability of NHP MRI data and the need for robust multi-subject multi-center analyses. Streamlined acquisition and analysis protocols would accelerate and improve these efforts. However, consensus on minimal standards for data acquisition protocols and analysis pipelines for NHP imaging remains to be established, particularly for multi-center studies. Here, we draw parallels between NHP and human neuroimaging and provide minimal guidelines for harmonizing and standardizing data acquisition. We advocate robust translation of widely used open-access toolkits that are well established for analyzing human data. We also encourage the use of validated, automated pre-processing tools for analyzing NHP data sets. These guidelines aim to refine methodological and analytical strategies for small and large-scale NHP neuroimaging data. This will improve reproducibility of results, and accelerate the convergence between NHP and human neuroimaging strategies which will ultimately benefit fundamental and translational brain science.

q-bio.NC↗

arXiv2020

Revisiting Consensus-Based Energy-Management in Smart Grid with Transmission Losses and Directed Communication

We discovered a deficiency in Algorithm 1 and Theorem 3 of [1]. The algorithm called CEMA aims to solve an energy management problem distributively. However, by means of a counter example, we show that Theorem 2 and 3 of [1] contradict each other in the case of a valid scenario, proving that the suggested algorithm does not always find the optimum. Furthermore, we provide theoretic results, showing that Theorem 3 of [1] does not hold generally. At last, we provide a rectification by adjusting the algorithm and the corresponding proof of Theorem 3.

eess.SY↗

arXiv2020

Projected Push-Sum Gradient Descent-Ascent for Convex Optimizationwith Application to Economic Dispatch Problems

We propose a novel algorithm for solving convex, constrained and distributed optimization problems defined on multi-agent-networks, where each agent has exclusive access to a part of the global objective function. The agents are able to exchange information over a directed, weighted communication graph, which can be represented as a column-stochastic matrix. The algorithm combines an adjusted push-sum consensus protocol for information diffusion and a gradient descent-ascent on the local cost functions, providing convergence to the optimum of their sum. We provide results on a reformulation of the push-sum into single matrix-updates and prove convergence of the proposed algorithm to an optimal solution, given standard assumptions in distributed optimization. The algorithm is applied to a distributed economic dispatch problem, in which the constraints can be expressed in local and global subsets.

eess.SY↗

arXiv2019

Penalized Push-Sum Algorithm for Constrained Distributed Optimization with Application to Energy Management in Smart Grid

We study distributed convex constrained optimization on a time-varying multi-agent network. Each agent has access to its own local cost function, its local constraints, and its instant number of out-neighbors. The collective goal is to minimize the sum of the cost functions over the set of all constraints. We utilize the push-sum protocol to be able to solve this distributed optimization problem. We adapt the push-sum optimization algorithm, which has been studied in context of unconstrained optimization so far, to convex constrained optimization by introducing an appropriate choice of penalty functions and penalty parameters. Under some additional technical assumptions on the gradients we prove convergence of the distributed penalty-based push-sum algorithm to the optimal value of the global objective function. We apply the proposed penalty-based push-sum algorithm to the problem of distributed energy management in smart grid and discuss the advantages of this novel procedure in comparison with existing ones.

eess.SP↗