Abstract
We study optimal distributed first-order optimization algorithms when the network (i.e., communication constraints between the agents) changes with time. This problem is motivated by scenarios where agents experience network malfunctions. We provide a sufficient condition that guarantees a convergence rate with optimal (up to logarithmic terms) dependencies on the network and function parameters if the network changes are constrained to a small percentage α of the total number of iterations. We call such networks slowly time-varying networks. Moreover, we show that Nesterov's method has an iteration complexity of Ω (equation presented) for decentralized algorithms, where κΦ is the condition number of the objective function, and χ is a worst case bound on the condition number of the sequence of communication graphs. Additionally, we provide an explicit upper bound on α in terms of the condition number of the objective function and network topologies.
Original language | English (US) |
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Article number | 8882272 |
Pages (from-to) | 829-841 |
Number of pages | 13 |
Journal | IEEE Transactions on Control of Network Systems |
Volume | 7 |
Issue number | 2 |
DOIs | |
State | Published - Jun 2020 |
Keywords
- Accelerated method
- distributed optimization
- time-varying graph
ASJC Scopus subject areas
- Control and Systems Engineering
- Signal Processing
- Computer Networks and Communications
- Control and Optimization