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• W2889776021 abstract "Anderson mixing (or Anderson acceleration) is an efficient acceleration method for fixed point iterations $x_{t+1}=G(x_t)$, e.g., gradient descent can be viewed as iteratively applying the operation $G(x) = x-alphanabla f(x)$. It is known that Anderson mixing is quite efficient in practice and can be viewed as an extension of Krylov subspace methods for nonlinear problems. In this paper, we show that Anderson mixing with Chebyshev polynomial parameters can achieve the optimal convergence rate $O(sqrt{kappa}lnfrac{1}{epsilon})$, which improves the previous result $O(kappalnfrac{1}{epsilon})$ provided by [Toth and Kelley, 2015] for quadratic functions. Then, we provide a convergence analysis for minimizing general nonlinear problems. Besides, if the hyperparameters (e.g., the Lipschitz smooth parameter $L$) are not available, we propose a guessing algorithm for guessing them dynamically and also prove a similar convergence rate. Finally, the experimental results demonstrate that the proposed Anderson-Chebyshev mixing method converges significantly faster than other algorithms, e.g., vanilla gradient descent (GD), Nesterov's Accelerated GD. Also, these algorithms combined with the proposed guessing algorithm (guessing the hyperparameters dynamically) achieve much better performance." @default.
• W2889776021 created "2018-09-27" @default.
• W2889776021 creator A5052883326 @default.
• W2889776021 creator A5060340617 @default.
• W2889776021 date "2018-09-07" @default.
• W2889776021 modified "2023-09-23" @default.
• W2889776021 title "An Anderson-Chebyshev Mixing Method for Nonlinear Optimization." @default.
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