A Hyper-Transformer model for Controllable Pareto Front Learning with Split Feasibility Constraints

Controllable Pareto front learning (CPFL) approximates the Pareto solution set and then locates a Pareto optimal solution with respect to a given reference vector. However, decision-maker objectives were limited to a constraint region in practice, so instead of training on the entire decision space, we only trained on the constraint region. Controllable Pareto front learning with Split Feasibility Constraints (SFC) is a way to find the best Pareto solutions to a split multi-objective optimization problem that meets certain constraints. In the previous study, CPFL used a Hypernetwork model comprising multi-layer perceptron (Hyper-MLP) blocks. With the substantial advancement of transformer architecture in deep learning, transformers can outperform other architectures in various tasks. Therefore, we have developed a hyper-transformer (Hyper-Trans) model for CPFL with SFC. We use the theory of universal approximation for the sequence-to-sequence function to show that the Hyper-Trans model makes MED errors smaller in computational experiments than the Hyper-MLP model.

A Novel Approach in Solving Stochastic Generalized Linear Regression via Nonconvex Programming

Generalized linear regressions, such as logistic regressions or Poisson regressions, are long-studied regression analysis approaches, and their applications are widely employed in various classification problems. Our study considers a stochastic generalized linear regression model as a stochastic problem with chance constraints and tackles it using nonconvex programming techniques. Clustering techniques and quantile estimation are also used to estimate random data's mean and variance-covariance matrix. Metrics for measuring the performance of logistic regression are used to assess the model's efficacy, including the F1 score, precision score, and recall score. The results of the proposed algorithm were over 1 to 2 percent better than the ordinary logistic regression model on the same dataset with the above assessment criteria.