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Gossip-based distributed stochastic mirror descent for constrained optimization.

Xianju Fang1, Baoyong Zhang1, Deming Yuan1

  • 1School of Automation, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, PR China.

Neural Networks : the Official Journal of the International Neural Network Society
|April 9, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces a gossip-based distributed stochastic mirror descent (GB-DSMD) algorithm for non-Euclidean optimization in multi-agent networks. The GB-DSMD algorithm effectively handles changing network topologies and converges to optimal solutions.

Keywords:
Distributed constrained optimizationDistributed convex optimizationGossip algorithmStochastic mirror descent

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Area of Science:

  • Distributed optimization
  • Networked systems
  • Algorithm analysis

Background:

  • Multi-agent systems face communication challenges in distributed optimization.
  • Dynamic network topologies complicate distributed learning.
  • Non-Euclidean optimization requires specialized algorithms.

Purpose of the Study:

  • To propose a novel gossip-based distributed stochastic mirror descent (GB-DSMD) algorithm.
  • To analyze the performance of GB-DSMD under different step-size strategies.
  • To demonstrate the algorithm's effectiveness on a distributed logistic regression problem.

Main Methods:

  • Gossip protocol for reduced communication burden and adaptability to network changes.
  • Development of the gossip-based distributed stochastic mirror descent (GB-DSMD) algorithm.
  • Theoretical analysis of GB-DSMD with constant and diminishing step sizes.

Main Results:

  • Derived an error bound for constant step sizes, linking optimal and average iteration values.
  • Proved that diminishing step sizes lead to uniform convergence to the optimal value with probability 1.
  • Validated the GB-DSMD algorithm's effectiveness through a distributed logistic regression simulation.

Conclusions:

  • The GB-DSMD algorithm offers an efficient approach for distributed constrained optimization in dynamic networks.
  • Both constant and diminishing step sizes provide convergence guarantees, with diminishing steps offering stronger probabilistic convergence.
  • The algorithm is effective for practical applications like distributed logistic regression.