Optimization of random polynomials on the sphere in the full-RSB regime

Abstract:
The talk will focus on optimization on the high-dimensional sphere when the objective function is a linear combination of homogeneous polynomials with standard Gaussian coefficients. Such random processes are called spherical spin glasses in physics, and have been extensively studied since the 80s. I will describe certain geometric properties of spherical spin glasses unique to the full-RSB case, and explain how they can be used to design a polynomial time algorithm that finds points within small multiplicative error from the global minimum.

Biography:
Eliran Subag is a Junior Fellow in the Simons Society of Fellows, at the Courant Institute, NYU.