Aleksandr M. Kazachkov
Abstract: Better and Fairer Decisions: New Frontiers in Cutting Planes and Mechanism Design
My work involves designing methods for improving discrete decision-making, particularly combining traditional optimization objectives and contextual fairness considerations.
We first discuss fairness in sports in the form of leagues promoting competitive balance among teams. We show that this pursuit inherently creates perverse incentives for teams to “tank”, or purposefully lose, and that this inhibits the league from effectively improving equality of opportunity. We propose and analyze a new mechanism for ranking teams that can simultaneously reduce tanking and increase competitive balance.
We then present a new framework for cutting planes, a critical component of optimization solvers. Our procedure enables us to efficiently generate deeper cuts than those implemented in practice. Our theoretical and computational results indicate the cuts can substantially improve the performance of a commercial optimization solver. This lays the groundwork for extensions such as improving cuts in nonlinear settings and employing machine learning tools for cut generation.