### Jorge Cortés

#### Professor

Cooperative data-driven distributionally robust optimization

A. Cherukuri, J. Cortés

IEEE Transactions on Automatic Control 65 (10) (2020), 4400-4407

### Abstract

This paper studies a class of multiagent stochastic
optimization problems where the objective is to
minimize the expected value of a function which
depends on a random variable. The probability
distribution of the random variable is unknown to
the agents, so each one gathers samples of it. The
agents aim to cooperatively find, using their data,
a solution to the optimization problem with
guaranteed out-of-sample performance. The approach
is to formulate a data-driven distributionally
robust optimization problem using Wasserstein
ambiguity sets, which turns out to be equivalent to
a convex program. We reformulate the latter as a
distributed optimization problem and identify a
convex-concave augmented Lagrangian function whose
saddle points are in correspondence with the
optimizers provided a min-max interchangeability
criteria is met. Our distributed algorithm design
then consists of the saddle-point dynamics
associated to the augmented Lagrangian. We formally
establish that the trajectories of the dynamics
converge asymptotically to a saddle point and hence
an optimizer of the problem. Finally, we provide a
class of functions that meet the min-max
interchangeability criteria. Simulations illustrate
our results.

pdf

Mechanical and Aerospace Engineering,
University of California, San Diego

9500 Gilman Dr,
La Jolla, California, 92093-0411

Ph: 1-858-822-7930

Fax: 1-858-822-3107

cortes at ucsd.edu

Skype id:
jorgilliyo