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Non-convex constrained optimization problems have become a powerful framework for modeling a wide range of machine learning problems, with applications in k-means clustering, large- scale semidefinite programs (SDPs), and various other tasks. As the perfor ...
In this article, we propose a dynamical system to avoid obstacles which are star shaped and simultaneously converge to a goal. The convergence is almost-global in a domain and the stationary points are identified explicitly. Our approach is based on the id ...
We consider the problem of provably finding a stationary point of a smooth function to be minimized on the variety of bounded-rank matrices. This turns out to be unexpectedly delicate. We trace the difficulty back to a geometric obstacle: On a nonsmooth se ...
We study the performance of Stochastic Cubic Regularized Newton (SCRN) on a class of functions satisfying gradient dominance property with 1≤α≤2 which holds in a wide range of applications in machine learning and signal processing. This conditio ...
Control systems operating in real-world environments often face disturbances arising from measurement noise and model mismatch. These factors can significantly impact the perfor- mance and safety of the system. In this thesis, we aim to leverage data to de ...
Le nomadisme, mode de vie séculaire des minorités yéniches et sintés en Suisse, est mis en péril par une politique de zonage soutenue par la LAT de 1979 qui inscrit chaque parcelle de territoire et son usage dans un cadre juridique. Pour les nomades, la re ...
Under appropriate cooperation protocols and parameter choices, fully decentralized solutions for stochastic optimization have been shown to match the performance of centralized solutions and result in linear speedup (in the number of agents) relative to no ...
We describe the first gradient methods on Riemannian manifolds to achieve accelerated rates in the non-convex case. Under Lipschitz assumptions on the Riemannian gradient and Hessian of the cost function, these methods find approximate first-order critical ...
SPRINGER2022
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In this work we investigate stochastic non-convex optimization problems wherethe objective is an expectation over smooth loss functions, and the goal is to find an approximate stationary point. The most popular approach to handling such problems is varianc ...
2021
We introduce a generic \emph{two-loop} scheme for smooth minimax optimization with strongly-convex-concave objectives. Our approach applies the accelerated proximal point framework (or Catalyst) to the associated \emph{dual problem} and takes full advantag ...
