Data-Driven Nonparametric Robust Control under Dependence Uncertainty

TL;DR

This paper develops a nonparametric robust control method for multi-period stochastic systems with known marginals but uncertain dependence, using adaptive optimization and data-driven shrinking uncertainty sets.

Contribution

It introduces a novel adaptive robust control framework that handles dependence uncertainty via worst-case copulas and employs stochastic gradient methods for high-dimensional optimization.

Findings

Controller improves performance with more dependence information

Method effectively manages dependence uncertainty in stochastic control

Numerical results demonstrate robustness and adaptability

Abstract

We consider a multi-period stochastic control problem where the multivariate driving stochastic factor of the system has known marginal distributions but uncertain dependence structure. To solve the problem, we propose to implement the nonparametric adaptive robust control framework. We aim to find the optimal control against the worst-case copulae in a sequence of shrinking uncertainty sets which are generated from continuously observing the data. Then, we use a stochastic gradient descent ascent algorithm to numerically handle the corresponding high dimensional dynamic inf-sup optimization problem. We present the numerical results in the context of utility maximization and show that the controller benefits from knowing more information about the uncertain model.