Elastic-Net Regularized Online Portfolio Selection with Transaction Costs

Online portfolio selection via machine learning systems attracts considerable amount of attentions recently. This paper focus on online portfolio optimization with transaction costs. The objective of the proposed minimization problem over the simplex contains three terms: negative expected return, transaction cost controlled term and regularization term for portfolio. Specifically, we use the elastic-net regularization of the difference between the portfolios of the next and the last periods to attack transaction costs. We additionally apply the elastic-net regularization to the portfolio variable, which due to the simplex constraint reduces to the square of the L2 norm of the variable, in order to improve the generalization of the model. We solve the proposed model by linearized augmented Lagrangian method, and its convergence is proved mathematically. Further, we obtain closed-form solutions of subproblem in each iteration, which increase the algorithm’s efficiency. Numerical experiments on four benchmark data-sets demonstrate that our algorithm outperforms the compared state-of-the-art algorithms in most case in a higher efficiency.