47-841 Topics in Optimization and Statistics

6 units, Carnegie Mellon University

This is a graduatelevel course covering current topics at the intersection of optimization and statistics. Typically, this intersection concerns optimization as an algorithmic toolkit for solving statistical problems estimation in low and high dimensions, inference, StatML, statistical physics, the list goes on. The theme for Spring 2023 is precisely the opposite direction, i.e. probability as a toolkit for solving optimization problems. At the highest level, we will be concerned with what probability can do for solving welldefined optimization problems. We will see that the probabilistic toolkit can help us answer questions such as a why algorithms with provably bad runtimes, such as the simplex method and basic branch and bound, work so well in practice, b why stochastic versions of gradient descent might be advantageous even when computation is not a bottleneck, and c what the theoretically fastest algorithms for linear programming look like.

Prerequisites: none listed

Offered: Spring 2027

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