Distributed Stochastic Constrained Composite Optimization Over Time-Varying Network With a Class of Communication...

Area of Science:

• Optimization Theory
• Distributed Systems
• Network Science

Background:

• Addresses the challenge of distributed stochastic multiagent-constrained optimization in time-varying networks with communication noise.
• Highlights the limitations of existing Euclidean projection-based methods in noisy network optimization.
• Positions the study within the more general composite optimization framework.

Purpose of the Study:

• To develop a novel non-Euclidean optimization method for noisy distributed networks.
• To analyze the convergence behavior and derive error bounds for the proposed method.
• To establish new convergence rates for optimization algorithms in noisy network settings.

Main Methods:

• Introduces a Bregman projection-based mirror descent scheme.
• Proposes the Distributed Stochastic Composite Mirror Descent type method (DSCMD-N).
• Investigates the convergence properties of DSCMD-N in expectation, high probability, and almost surely senses.

Main Results:

• Obtains new error bounds for the DSCMD-N algorithm.
• Demonstrates the ability to achieve an optimal convergence rate of O(1/√T) for nonsmooth convex optimization under specific noise conditions.
• Provides the first analysis and derivation of convergence rates for optimization algorithms in noisy network optimization.

Conclusions:

• The proposed DSCMD-N offers a more general algorithmic framework for noisy network optimization.
• The study establishes novel convergence results, advancing the understanding of optimization in complex network environments.
• The findings pave the way for more robust and efficient distributed optimization solutions in the presence of communication noise.