Title:
Convergence in min-max optimization
Convergence in min-max optimization
| dc.contributor.advisor | Abernethy, Jacob | |
| dc.contributor.author | Lai, Kevin A. | |
| dc.contributor.committeeMember | Cummings, Rachel | |
| dc.contributor.committeeMember | Morgenstern, Jamie | |
| dc.contributor.committeeMember | Pokutta, Sebastian | |
| dc.contributor.committeeMember | Singh, Mohit | |
| dc.contributor.department | Computer Science | |
| dc.date.accessioned | 2020-05-20T17:01:29Z | |
| dc.date.available | 2020-05-20T17:01:29Z | |
| dc.date.created | 2020-05 | |
| dc.date.issued | 2020-04-20 | |
| dc.date.submitted | May 2020 | |
| dc.date.updated | 2020-05-20T17:01:30Z | |
| dc.description.abstract | Min-max optimization is a classic problem with applications in constrained optimization, robust optimization, and game theory. This dissertation covers new convergence rate results in min-max optimization. We show that the classic fictitious play dynamic with lexicographic tiebreaking converges quickly for diagonal payoff matrices, partly answering a conjecture by Karlin from 1959. We also show that linear last-iterate convergence rates are possible for the Hamiltonian Gradient Descent algorithm for the class of “sufficiently bilinear” min-max problems. Finally, we explore higher-order methods for min-max optimization and monotone variational inequalities, showing improved iteration complexity compared to first-order methods such as Mirror Prox. | |
| dc.description.degree | Ph.D. | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | http://hdl.handle.net/1853/62809 | |
| dc.language.iso | en_US | |
| dc.publisher | Georgia Institute of Technology | |
| dc.subject | Optimization | |
| dc.subject | Zero-sum game | |
| dc.subject | Game theory | |
| dc.subject | Fictitious play | |
| dc.subject | Generative adversarial networks | |
| dc.subject | Last-iterate | |
| dc.subject | Min-max | |
| dc.subject | Saddle point | |
| dc.title | Convergence in min-max optimization | |
| dc.type | Text | |
| dc.type.genre | Dissertation | |
| dspace.entity.type | Publication | |
| local.contributor.corporatename | College of Computing | |
| local.contributor.corporatename | School of Computer Science | |
| relation.isOrgUnitOfPublication | c8892b3c-8db6-4b7b-a33a-1b67f7db2021 | |
| relation.isOrgUnitOfPublication | 6b42174a-e0e1-40e3-a581-47bed0470a1e | |
| thesis.degree.level | Doctoral |