Abstract

This paper studies the effect of stochastic errors on two constrained incremental subgradient algorithms. The incremental subgradient algorithms are viewed as decentralized network optimization algorithms as applied to minimize a sum of functions, when each component function is known only to a particular agent of a distributed network. First, the standard cyclic incremental subgradient algorithm is studied. In this, the agents form a ring structure and pass the iterate in a cycle. When there are stochastic errors in the subgradient evaluations, sufficient conditions on the moments of the stochastic errors are obtained that guarantee almost sure convergence when a diminishing step-size is used. In addition, almost sure bounds on the algorithm's performance with a constant step-size are also obtained. Next, the Markov randomized incremental subgradient method is studied. This is a noncyclic version of the incremental algorithm where the sequence of computing agents is modeled as a time nonhomogeneous Markov chain. Such a model is appropriate for mobile networks, as the network topology changes across time in these networks. Convergence results and error bounds for the Markov randomized method in the presence of stochastic errors for diminishing and constant step-sizes are obtained.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.