Asynchronous Saddle Point Algorithm for Stochastic Optimization in Heterogeneous Networks

We consider expected risk minimization in multi-agent systems comprised of distinct subsets of agents operating without a common time scale. Each individual in the network is charged with minimizing the global objective function, which is an average of sum of the statistical average loss function of...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 67; no. 7; pp. 1742 - 1757
Main Authors: Bedi, Amrit Singh, Koppel, Alec, Rajawat, Ketan
Format: Journal Article
Language:English
Published: New York IEEE 01.04.2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Convex functions
gradient descent
Hypotheses
interference management
Lagrange multiplier
Linear programming
Message passing
multi-agent systems
Multiagent systems
Optimization
Robot sensing systems
Saddle points
Signal processing algorithms
Stochastic optimizatiokn
Stochastic processes
Wireless communications
Wireless networks
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Summary:We consider expected risk minimization in multi-agent systems comprised of distinct subsets of agents operating without a common time scale. Each individual in the network is charged with minimizing the global objective function, which is an average of sum of the statistical average loss function of each agent in the network. Since agents are not assumed to observe data from identical distributions, the hypothesis that all agents seek a common action is violated, and thus the hypothesis upon that consensus constraints are formulated is violated. Thus, we consider nonlinear network proximity constraints, which incentivize nearby nodes to make decisions that are close to one another but do not necessarily coincide. Moreover, agents are not assumed to receive their sequentially arriving observations on a common time index, and thus seek to learn in an asynchronous manner. An asynchronous stochastic variant of the Arrow-Hurwicz saddle point method is proposed to solve this problem that operates by alternating primal stochastic descent steps and Lagrange multiplier updates that penalize the discrepancies between agents. This tool leads to an implementation that allows for each agent to operate asynchronously with local information only and message passing with neighbors. Our main result establishes that the proposed method yields convergence in expectation both in terms of the primal sub-optimality and constraint violation to radii of sizes <inline-formula><tex-math notation="LaTeX">{\mathcal O}(\sqrt{T})</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">{\mathcal O}(T^{3/4})</tex-math></inline-formula>, respectively. Empirical evaluation on an asynchronously operating wireless network that manages user channel interference through an adaptive communications pricing mechanism demonstrates that our theoretical results translates well to practice.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2019.2894803