Search Results for author: Xufeng Cai

Found 5 papers, 1 papers with code

Last Iterate Convergence of Incremental Methods and Applications in Continual Learning

no code implementations11 Mar 2024 Xufeng Cai, Jelena Diakonikolas

We further obtain generalizations of our results to weighted averaging of the iterates with increasing weights, which can be seen as interpolating between the last iterate and the average iterate guarantees.

Continual Learning

Variance Reduced Halpern Iteration for Finite-Sum Monotone Inclusions

no code implementations4 Oct 2023 Xufeng Cai, Ahmet Alacaoglu, Jelena Diakonikolas

Our main contributions are variants of the classical Halpern iteration that employ variance reduction to obtain improved complexity guarantees in which $n$ component operators in the finite sum are ``on average'' either cocoercive or Lipschitz continuous and monotone, with parameter $L$.

Adversarial Robustness

Empirical Risk Minimization with Shuffled SGD: A Primal-Dual Perspective and Improved Bounds

no code implementations21 Jun 2023 Xufeng Cai, Cheuk Yin Lin, Jelena Diakonikolas

Contrary to the empirical practice of sampling from the datasets without replacement and with (possible) reshuffling at each epoch, the theoretical counterpart of SGD usually relies on the assumption of sampling with replacement.

Cyclic Block Coordinate Descent With Variance Reduction for Composite Nonconvex Optimization

no code implementations9 Dec 2022 Xufeng Cai, Chaobing Song, Stephen J. Wright, Jelena Diakonikolas

Our convergence analysis is based on a gradient Lipschitz condition with respect to a Mahalanobis norm, inspired by a recent progress on cyclic block coordinate methods.

Stochastic Halpern Iteration with Variance Reduction for Stochastic Monotone Inclusions

1 code implementation17 Mar 2022 Xufeng Cai, Chaobing Song, Cristóbal Guzmán, Jelena Diakonikolas

We study stochastic monotone inclusion problems, which widely appear in machine learning applications, including robust regression and adversarial learning.

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