A generalized Frank–Wolfe method with “dual averaging” for strongly convex composite optimization
Abstract
We propose a simple variant of the generalized Frank–Wolfe method for solving strongly convex composite optimization problems, by introducing an additional averaging step on the dual variables. We show that in this variant, one can choose a simple constant step-size and obtain a linear convergence rate on the duality gaps. By leveraging the convergence analysis of this variant, we then analyze the local convergence rate of the logistic fictitious play algorithm, which is well-established in game theory but lacks any form of convergence rate guarantees. We show that, with high probability, this algorithm converges locally at rate O(1/t), in terms of certain expected duality gap.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Nov 07, 2022
- Source ID
- 10.1007/s11590-022-01951-0
Entities
People
- Qiuyun Zhu
- Renbo Zhao
Organizations
- Massachusetts Institute of Technology
- United States Air Force