FUSE: First-Order and Second-Order Unified SynthEsis in Stochastic Optimization

• URL: http://arxiv.org/abs/2503.04204v1
• Date: Thu, 06 Mar 2025 08:30:18 GMT
• Title: FUSE: First-Order and Second-Order Unified SynthEsis in Stochastic Optimization
• Authors: Zhanhong Jiang, Md Zahid Hasan, Aditya Balu, Joshua R. Waite, Genyi Huang, Soumik Sarkar,
• Abstract summary: First-order and second-order methods are in entirely different situations.<n>This paper presents a novel method that leverages both the first-order and second-order methods in a unified algorithmic framework.<n>FUSE-PV stands as a simple yet efficient optimization method involving a switch-over between first and second orders.
• Score: 9.909119107223265
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Stochastic optimization methods have actively been playing a critical role in modern machine learning algorithms to deliver decent performance. While numerous works have proposed and developed diverse approaches, first-order and second-order methods are in entirely different situations. The former is significantly pivotal and dominating in emerging deep learning but only leads convergence to a stationary point. However, second-order methods are less popular due to their computational intensity in large-dimensional problems. This paper presents a novel method that leverages both the first-order and second-order methods in a unified algorithmic framework, termed FUSE, from which a practical version (PV) is derived accordingly. FUSE-PV stands as a simple yet efficient optimization method involving a switch-over between first and second orders. Additionally, we develop different criteria that determine when to switch. FUSE-PV has provably shown a smaller computational complexity than SGD and Adam. To validate our proposed scheme, we present an ablation study on several simple test functions and show a comparison with baselines for benchmark datasets.

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