Online Portfolio Selection with Group Sparsity

In portfolio selection, it often might be preferable to focus on a few top performing industries/sectors to beat the mar-ket. These top performing sectors however might change over time. In this paper, we propose an online portfolio selec-tion algorithm that can take advantage of sector informa-tion through the use of a group sparsity inducing regularizer while making lazy updates to the portfolio. The lazy updates prevent changing ones portfolio too often which otherwise might incur huge transaction costs. The proposed formula-tion leads to a non-smooth constrained optimization problem at every step, with the constraint that the solution has to lie in a probability simplex. We propose an efficient primal-dual based alternating direction method of multipliers algorithm and demonstrate its effectiveness for the problem of online portfolio selection with sector information. We show that our algorithm OLU-GS has sub-linear regret w.r.t. the best fixed and best shifting solution in hindsight. We successfully estab-lish the robustness and scalability of OLU-GS by performing extensive experiments on two real-world datasets.