6 papers · 1 filter
Gradient Descent's Last Iterate is Often (slightly) Suboptimal
Guy Kornowski, Ohad Shamir
We consider the well-studied setting of minimizing a convex Lipschitz function using either gradient descent (GD) or its stochastic variant (SGD), and examine the last iterate conv…
On the Complexity of Finding Small Subgradients in Nonsmooth Optimization
Guy Kornowski, Ohad Shamir
We study the oracle complexity of producing -stationary points of Lipschitz functions, in the sense proposed by Zhang et al. [2020]. While there exist dimension-free rando…
First-Order Methods for Linearly Constrained Bilevel Optimization
Guy Kornowski, Swati Padmanabhan, Kai Wang +2
Algorithms for bilevel optimization often encounter Hessian computations, which are prohibitive in high dimensions. While recent works offer first-order methods for unconstrained b…
On the Hardness of Meaningful Local Guarantees in Nonsmooth Nonconvex Optimization
Guy Kornowski, Swati Padmanabhan, Ohad Shamir
We study the oracle complexity of nonsmooth nonconvex optimization, with the algorithm assumed to have access only to local function information. It has been shown by Davis, Drusvy…
Open Problem: Anytime Convergence Rate of Gradient Descent
Guy Kornowski, Ohad Shamir
Recent results show that vanilla gradient descent can be accelerated for smooth convex objectives, merely by changing the stepsize sequence. We show that this can lead to surprisin…
An Algorithm with Optimal Dimension-Dependence for Zero-Order Nonsmooth Nonconvex Stochastic Optimization
Guy Kornowski, Ohad Shamir
We study the complexity of producing -stationary points of Lipschitz objectives which are possibly neither smooth nor convex, using only noisy function evaluations. Recent…