Hybrid Decentralized Optimization: First- and Zeroth-Order Optimizers Can Be Jointly Leveraged For Faster Convergence

• URL: http://arxiv.org/abs/2210.07703v1
• Date: Fri, 14 Oct 2022 10:54:11 GMT
• Title: Hybrid Decentralized Optimization: First- and Zeroth-Order Optimizers Can Be Jointly Leveraged For Faster Convergence
• Authors: Shayan Talaei, Giorgi Nadiradze, Dan Alistarh
• Abstract summary: We study settings where nodes with zeroth-order and first-order optimization capabilities co-exist in a distributed system. We show that such a system can not only withstand noisier zeroth-order agents but can even benefit from integrating such agents into the optimization process.
• Score: 25.211914690635183
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Distributed optimization has become one of the standard ways of speeding up machine learning training, and most of the research in the area focuses on distributed first-order, gradient-based methods. Yet, there are settings where some computationally-bounded nodes may not be able to implement first-order, gradient-based optimization, while they could still contribute to joint optimization tasks. In this paper, we initiate the study of hybrid decentralized optimization, studying settings where nodes with zeroth-order and first-order optimization capabilities co-exist in a distributed system, and attempt to jointly solve an optimization task over some data distribution. We essentially show that, under reasonable parameter settings, such a system can not only withstand noisier zeroth-order agents but can even benefit from integrating such agents into the optimization process, rather than ignoring their information. At the core of our approach is a new analysis of distributed optimization with noisy and possibly-biased gradient estimators, which may be of independent interest. Experimental results on standard optimization tasks confirm our analysis, showing that hybrid first-zeroth order optimization can be practical.

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