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• W3209201550 abstract "Optimization is important in machine learning problems, and quasi-Newton methods have a reputation as the most efficient numerical schemes for smooth unconstrained optimization. In this paper, we consider the explicit superlinear convergence rates of quasi-Newton methods and address two open problems mentioned by Rodomanov and Nesterov. First, we extend Rodomanov and Nesterov's results to random quasi-Newton methods, which include common DFP, BFGS, SR1 methods. Such random methods adopt a random direction for updating the approximate Hessian matrix in each iteration. Second, we focus on the specific quasi-Newton methods: SR1 and BFGS methods. We provide improved versions of greedy and random methods with provable better explicit (local) superlinear convergence rates. Our analysis is closely related to the approximation of a given Hessian matrix, unconstrained quadratic objective, as well as the general strongly convex, smooth, and strongly self-concordant functions." @default.
• W3209201550 created "2021-11-08" @default.
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• W3209201550 date "2021-04-18" @default.
• W3209201550 modified "2023-10-18" @default.
• W3209201550 title "Explicit Convergence Rates of Greedy and Random Quasi-Newton Methods" @default.
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• W3209201550 doi "https://doi.org/10.48550/arxiv.2104.08764" @default.
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