77 citations · 318 across the 57 of their papers we have counts for
7 papers · 1 filter
Proximal methods avoid active strict saddles of weakly convex functions
Damek Davis, Dmitriy Drusvyatskiy
We introduce a geometrically transparent strict saddle property for nonsmooth functions. This property guarantees that simple proximal algorithms on weakly convex problems converge…
Pathological subgradient dynamics
Aris Daniilidis, Dmitriy Drusvyatskiy
We construct examples of Lipschitz continuous functions, with pathological subgradient dynamics both in continuous and discrete time. In both settings, the iterates generate bounde…
Iterative Linearized Control: Stable Algorithms and Complexity Guarantees
Vincent Roulet, Siddhartha Srinivasa, Dmitriy Drusvyatskiy +1
We examine popular gradient-based algorithms for nonlinear control in the light of the modern complexity analysis of first-order optimization algorithms. The examination reveals th…
Stochastic algorithms with geometric step decay converge linearly on sharp functions
Damek Davis, Dmitriy Drusvyatskiy, Vasileios Charisopoulos
Stochastic (sub)gradient methods require step size schedule tuning to perform well in practice. Classical tuning strategies decay the step size polynomially and lead to optimal sub…
From low probability to high confidence in stochastic convex optimization
Damek Davis, Dmitriy Drusvyatskiy, Lin Xiao +1
Standard results in stochastic convex optimization bound the number of samples that an algorithm needs to generate a point with small function value in expectation. More nuanced hi…
Low-rank matrix recovery with composite optimization: good conditioning and rapid convergence
Vasileios Charisopoulos, Yudong Chen, Damek Davis +3
The task of recovering a low-rank matrix from its noisy linear measurements plays a central role in computational science. Smooth formulations of the problem often exhibit an undes…