GPU-Accelerated Branch-and-Bound and Conditional Screening for Sparse Logistic Regression

Sparse logistic regression selects a small set of predictors, but optimizing over feature subsets requires many closely related continuous solves. We develop a branch-and-bound framework that batches ridge-logistic subproblems on a GPU and uses gradient residuals to obtain valid lower bounds from inexact solves. A complementary analysis of conditional greedy screening gives a finite-sample support-containment guarantee with a controlled number of competitive irrelevant selections. The analysis accommodates signals that become detectable only after conditioning and separates the statistical screening guarantee from the deterministic pruning bounds. Synthetic experiments show faster support recovery for conditional screening than for marginal screening in a correlated suppressor design. On two classification datasets, the GPU implementation attains smaller terminal optimality gaps than the tested CPU baselines and lower batch runtimes for moderate and large batch sizes. These results support batched GPU computation for exact sparse classification.