14 papers · 1 filter
Stochastic Dynamic Barrier Perturbed Gradient Methods for Nonconvex Simple Bilevel Optimization
Mohammad Mahdi Ahmadi, Jincheng Cao, Aryan Mokhtari +1
We study stochastic simple bilevel optimization with smooth, possibly nonconvex upper- and lower-level objectives accessed only through stochastic gradient oracles. A key challenge…
Adaptive Matrix Online Learning through Smoothing with Guarantees for Nonsmooth Nonconvex Optimization
Ruichen Jiang, Zakaria Mhammedi, Mehryar Mohri +1
We study online linear optimization with matrix variables constrained by the operator norm, a setting where the geometry renders designing data-dependent and efficient adaptive alg…
Improving Online-to-Nonconvex Conversion for Smooth Optimization via Double Optimism
Francisco Patitucci, Ruichen Jiang, Aryan Mokhtari
A recent breakthrough in nonconvex optimization is the online-to-nonconvex conversion framework of [Cutkosky et al., 2023], which reformulates the task of finding an -…
On the Complexity of Finding Stationary Points in Nonconvex Simple Bilevel Optimization
Jincheng Cao, Ruichen Jiang, Erfan Yazdandoost Hamedani +1
In this paper, we study the problem of solving a simple bilevel optimization problem, where the upper-level objective is minimized over the solution set of the lower-level problem.…
Affine-Invariant Global Non-Asymptotic Convergence Analysis of BFGS under Self-Concordance
Qiujiang Jin, Aryan Mokhtari
In this paper, we establish global non-asymptotic convergence guarantees for the BFGS quasi-Newton method without requiring strong convexity or the Lipschitz continuity of the grad…
Improved Complexity for Smooth Nonconvex Optimization: A Two-Level Online Learning Approach with Quasi-Newton Methods
Ruichen Jiang, Aryan Mokhtari, Francisco Patitucci
We study the problem of finding an -first-order stationary point (FOSP) of a smooth function, given access only to gradient information. The best-known gradient query complexity…