On Wasserstein Distributionally Robust Mean Semi-Absolute Deviation Portfolio Model: Robust Selection and Efficient Computation

This paper focuses on the Wasserstein distributionally robust mean-lower semi-absolute deviation (DR-MLSAD) model, where the ambiguity set is a Wasserstein ball centered on the empirical distribution of the training sample. This model can be equivalently transformed into a convex problem. We develop a robust Wasserstein profile inference (RWPI) approach to determine the size of the Wasserstein radius for DR-MLSAD model. We also design an efficient proximal point dual semismooth Newton (PpdSsn) algorithm for the reformulated equivalent model. In numerical experiments, we compare the DR-MLSAD model with the radius selected by the RWPI approach to the DR-MLSAD model with the radius selected by cross-validation, the sample average approximation (SAA) of the MLSAD model, and the 1/N strategy on the real market datasets. Numerical results show that our model has better out-of-sample performance in most cases. Furthermore, we compare PpdSsn algorithm with first-order algorithms and Gurobi solver on random data. Numerical results verify the effectiveness of PpdSsn in solving large-scale DR-MLSAD problems

Dual Newton Proximal Point Algorithm for Solution Paths of the L1-Regularized Logistic Regression

The l1-regularized logistic regression is a widely used statistical model in data classification. This paper proposes a dual Newton method based proximal point algorithm (PPDNA) to solve the l1-regularized logistic regression problem with bias term. The global and local convergence of PPDNA hold under mild conditions. The computational cost of a semismooth Newton (Ssn) algoithm for solving subproblems in the PPDNA can be effectively reduced by fully exploiting the second-order sparsity of the problem. We also design an adaptive sieving (AS) strategy to generate solution paths for the l1-regularized logistic regression problem, where each subproblem in the AS strategy is solved by the PPDNA. This strategy exploits active set constraints to reduce the number of variables in the problem, thereby speeding up the PPDNA for solving a series of problems. Numerical experiments demonstrate the superior performance of the PPDNA in comparison with some state-of-the-art second-order algorithms and the efficiency of the AS strategy combined with the PPDNA for generating solution paths