Statistics Seminar - Jonathan Niles-Weed (NYU) "The Mean-Field Limit of Online Stochastic Vector Balancing"

Title: The Mean-Field Limit of Online Stochastic Vector Balancing

Abstract: We study an online "vector balancing" (or "discrepancy") problem with random inputs. Our main contribution is to study a continuum limit for this problem, which takes the form of a nonstandard stochastic control problem of mean-field type: find the narrowest terminal interval into which a Brownian motion can be adaptively steered under a uniform-in-time L^2 constraint on the drift. We prove a rigorous limiting result for Gaussian inputs, and provide some analysis and asymptotics for the limiting mean-field control problem. Joint work with C. Fiedler, J. Jackson, and D. Lacker.