DISH: A Distributed Hybrid Optimization Method Leveraging System Heterogeneity

Xiaochun Niu; Ermin Wei

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arXiv · 2212.02638

DISH: A Distributed Hybrid Optimization Method Leveraging System Heterogeneity

Xiaochun Niu·Ermin Wei

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Abstract

We study distributed optimization problems over multi-agent networks, including consensus and network flow problems. Existing distributed methods neglect the heterogeneity among agents' computational capabilities, limiting their effectiveness. To address this, we propose DISH, a distributed hybrid method that leverages system heterogeneity. DISH allows agents with higher computational capabilities or lower computational costs to perform local Newton-type updates while others adopt simpler gradient-type updates. Notably, DISH covers existing methods like EXTRA, DIGing, and ESOM-0 as special cases. To analyze DISH's performance with general update directions, we formulate distributed problems as minimax problems and introduce GRAND (gradient-related ascent and descent) and its alternating version, Alt-GRAND, for solving these problems. GRAND generalizes DISH to centralized minimax settings, accommodating various descent ascent update directions, including gradient-type, Newton-type, scaled gradient, and other general directions, within acute angles to the partial gradients. Theoretical analysis establishes global sublinear and linear convergence rates for GRAND and Alt-GRAND in strongly-convex-nonconcave and strongly-convex-PL settings, providing linear rates for DISH. In addition, we derive the local superlinear convergence of Newton-based variations of GRAND in centralized settings. Numerical experiments validate the effectiveness of our methods.

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BibTeX RIS

Xiaochun Niu, Ermin Wei. 2023-08-01. DISH: A Distributed Hybrid Optimization Method Leveraging System Heterogeneity. https://arxiv.org/abs/2212.02638

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