Portfolio optimization by means of a χ-armed bandit algorithm

Abstract

In this paper, we are interested in studying and solving the portfolio selection problem by means of a machine learning method. Particularly, we use a χ-armed bandit algorithm called Hierarchical Optimistic Optimization (HOO). HOO is an optimization approach that can be used for finding optima of box constrained nonlinear and nonconvex functions. Under some restrictions, such as locally Lipschitz condition, HOO can provide global solutions. Our idea consists in using HOO for solving some NP-hard variants of the portfolio selection problem. We test this approach on some data sets and report the results. In order to verify the quality of the solutions, we compare them with the best known solutions, provided by a derivative-free approach, called DIRECT. The preliminary numerical experiments give promising results.