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Random extrapolation for primal-dual coordinate descent
Ahmet Alacaoglu, Olivier Fercoq, Volkan Cevher
We introduce a randomly extrapolated primal-dual coordinate descent method that adapts to sparsity of the data matrix and the favorable structures of the objective function. Our me…
On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problems
Panayotis Mertikopoulos, Nadav Hallak, Ali Kavis +1
This paper analyzes the trajectories of stochastic gradient descent (SGD) to help understand the algorithm's convergence properties in non-convex problems. We first show that the s…
The limits of min-max optimization algorithms: convergence to spurious non-critical sets
Ya-Ping Hsieh, Panayotis Mertikopoulos, Volkan Cevher
Compared to ordinary function minimization problems, min-max optimization algorithms encounter far greater challenges because of the existence of periodic cycles and similar phenom…
A Newton Frank-Wolfe Method for Constrained Self-Concordant Minimization
Deyi Liu, Volkan Cevher, Quoc Tran-Dinh
We demonstrate how to scalably solve a class of constrained self-concordant minimization problems using linear minimization oracles (LMO) over the constraint set. We prove that the…