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Distributed Optimization over Time-Varying Networks: Imperfect Information with Feedback is as Good as Perfect Information
The convergence of an error-feedback algorithm is studied for decentralized stochastic gradient descent (DSGD) algorithm with compressed information sharing over time-varying graphs. It is shown that for both strongly-convex and convex cost functions, despite of imperfect information sharing, the convergence rates match those with perfect information sharing. To do so, we show that for strongly-convex loss functions, with a proper choice of a step-size, the state of each node converges to the global optimizer at the rate of O(T^{−1}). Similarly, for general convex cost functions, with a proper choice of step-size, we show that the value of loss function at a temporal average of each node’s estimates converges to the optimal value at the rate of O(T^{−1/2+ϵ }) for any ϵ > 0.
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- Award ID(s):
- 1749981
- NSF-PAR ID:
- 10427582
- Date Published:
- Journal Name:
- 2022 American Control Conference (ACC)
- Page Range / eLocation ID:
- 2791 to 2796
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.23919/ACC53348.2022.9867680
