Timezone: »

 
Poster
Self-Concordant Analysis of Frank-Wolfe Algorithms
Pavel Dvurechenskii · Petr Ostroukhov · Kamil Safin · Shimrit Shtern · Mathias Staudigl

Tue Jul 14 07:00 AM -- 07:45 AM & Tue Jul 14 08:00 PM -- 08:45 PM (PDT) @ Virtual #None

Projection-free optimization via different variants of the Frank-Wolfe (FW), a.k.a. Conditional Gradient method has become one of the cornerstones in optimization for machine learning since in many cases the linear minimization oracle is much cheaper to implement than projections and some sparsity needs to be preserved. In a number of applications, e.g. Poisson inverse problems or quantum state tomography, the loss is given by a self-concordant (SC) function having unbounded curvature, implying absence of theoretical guarantees for the existing FW methods. We use the theory of SC functions to provide a new adaptive step size for FW methods and prove global convergence rate O(1/k) after k iterations. If the problem admits a stronger local linear minimization oracle, we construct a novel FW method with linear convergence rate for SC functions.

Author Information

Pavel Dvurechenskii (Weierstrass Institute)

Graduated with honors from Moscow Institute of Physics and Technology. PhD on differential games in the same university. At the moment research associate in the area of optimization under inexact information in Berlin. Research interest include - algorithms for convex and non-convex large-scale optimization problems; - optimization under deterministic and stochastic inexact information; - randomized algorithms: random coordinate descent, random (derivative-free) directional search; - numerical aspects of Optimal Transport - Algorithms for saddle-point problems and variational inequalities

Petr Ostroukhov (Moscow Institute of Physics and Technology)
Kamil Safin (Moscow Institute of Physics and Technology)
Shimrit Shtern (Technion - Israel Institute of Technology)
Mathias Staudigl (Maastricht University)

More from the Same Authors