4 citations · 7 across the 9 of their papers we have counts for
7 papers · 1 filter
Natural Riemannian gradient for learning functional tensor networks
Nikolas Klug, Michael Ulbrich, André Uschmajew +1
We consider machine learning tasks with low-rank functional tree tensor networks (TTN) as the learning model. While in the case of least-squares regression, low-rank functional TTN…
Enclosing minima in nonsmooth optimization via trust regions of higher-order cutting-plane models
Bennet Gebken, Michael Ulbrich
We propose a globally convergent trust-region bundle method for minimizing lower- functions using higher-order cutting-plane models. Under certain growth assumptions on the ob…
Superlinear convergence in nonsmooth optimization via higher-order cutting-plane models
Bennet Gebken, Michael Ulbrich
A cutting-plane model for a nonsmooth function is the maximum of several first-order expansions centered at different points. Using such a model in a bundle method leads to linear…
A Stochastic Proximal Polyak Step Size
Fabian Schaipp, Robert M. Gower, Michael Ulbrich
Recently, the stochastic Polyak step size (SPS) has emerged as a competitive adaptive step size scheme for stochastic gradient descent. Here we develop ProxSPS, a proximal variant…
Sample Size Estimates for Risk-Neutral Semilinear PDE-Constrained Optimization
Johannes Milz, Michael Ulbrich
The sample average approximation (SAA) approach is applied to risk-neutral optimization problems governed by semilinear elliptic partial differential equations with random inputs.…
A Semismooth Newton Stochastic Proximal Point Algorithm with Variance Reduction
Andre Milzarek, Fabian Schaipp, Michael Ulbrich
We develop an implementable stochastic proximal point (SPP) method for a class of weakly convex, composite optimization problems. The proposed stochastic proximal point algorithm i…
A Stochastic Semismooth Newton Method for Nonsmooth Nonconvex Optimization
Andre Milzarek, Xiantao Xiao, Shicong Cen +2
In this work, we present a globalized stochastic semismooth Newton method for solving stochastic optimization problems involving smooth nonconvex and nonsmooth convex terms in the…