We consider an in-network optimal resource allocation problem in which a group of agents interacting over a connected graph want to meet a demand while minimizing their collective cost. The contribution of this paper is to design a distributed continuous-time algorithm for this problem inspired by a recently developed first-order transformed primal-dual method. The solution applies to cluster-based setting where each agent may have a set of subagents, and its local cost is the sum of the cost of these subagents. The proposed algorithm guarantees an exponential convergence for strongly convex costs and asymptotic convergence for convex costs. Exponential convergence when the local cost functions are strongly convex is achieved even when the local gradients are only locally Lipschitz. For convex local cost functions, our algorithm guarantees asymptotic convergence to a point in the minimizer set. Through numerical examples, we show that our proposed algorithm delivers a faster convergence compared to existing distributed resource allocation algorithms.
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On Consensus-Optimality Trade-offs in Collaborative Deep Learning
In distributed machine learning, where agents collaboratively learn from diverse private data sets, there is a fundamental tension between consensus and optimality . In this paper, we build on recent algorithmic progresses in distributed deep learning to explore various consensus-optimality trade-offs over a fixed communication topology. First, we propose the incremental consensus -based distributed stochastic gradient descent (i-CDSGD) algorithm, which involves multiple consensus steps (where each agent communicates information with its neighbors) within each SGD iteration. Second, we propose the generalized consensus -based distributed SGD (g-CDSGD) algorithm that enables us to navigate the full spectrum from complete consensus (all agents agree) to complete disagreement (each agent converges to individual model parameters). We analytically establish convergence of the proposed algorithms for strongly convex and nonconvex objective functions; we also analyze the momentum variants of the algorithms for the strongly convex case. We support our algorithms via numerical experiments, and demonstrate significant improvements over existing methods for collaborative deep learning.
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- NSF-PAR ID:
- 10318055
- Date Published:
- Journal Name:
- Frontiers in Artificial Intelligence
- Volume:
- 4
- ISSN:
- 2624-8212
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3389/frai.2021.573731
