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- W4379539289 abstract "In this paper, we propose an accelerated quasi-Newton proximal extragradient (A-QPNE) method for solving unconstrained smooth convex optimization problems. With access only to the gradients of the objective, we prove that our method can achieve a convergence rate of ${O}bigl(min{frac{1}{k^2}, frac{sqrt{dlog k}}{k^{2.5}}}bigr)$, where $d$ is the problem dimension and $k$ is the number of iterations. In particular, in the regime where $k = {O}(d)$, our method matches the optimal rate of ${O}(frac{1}{k^2})$ by Nesterov's accelerated gradient (NAG). Moreover, in the the regime where $k = Omega(d log d)$, it outperforms NAG and converges at a faster rate of ${O}bigl(frac{sqrt{dlog k}}{k^{2.5}}bigr)$. To the best of our knowledge, this result is the first to demonstrate a provable gain of a quasi-Newton-type method over NAG in the convex setting. To achieve such results, we build our method on a recent variant of the Monteiro-Svaiter acceleration framework and adopt an online learning perspective to update the Hessian approximation matrices, in which we relate the convergence rate of our method to the dynamic regret of a specific online convex optimization problem in the space of matrices." @default.
- W4379539289 created "2023-06-07" @default.
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- W4379539289 date "2023-06-03" @default.
- W4379539289 modified "2023-10-16" @default.
- W4379539289 title "Accelerated Quasi-Newton Proximal Extragradient: Faster Rate for Smooth Convex Optimization" @default.
- W4379539289 doi "https://doi.org/10.48550/arxiv.2306.02212" @default.
- W4379539289 hasPublicationYear "2023" @default.
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