A GPU-Accelerated Moving-Horizon Algorithm for Training Deep Classification Trees on Large Datasets

Decision trees are essential yet NP-complete to train, prompting the widespread use of heuristic methods such as CART, which suffers from sub-optimal performance due to its greedy nature. Recently, breakthroughs in finding optimal decision trees have emerged; however, these methods still face significant computational costs and struggle with continuous features in large-scale datasets and deep trees. To address these limitations, we introduce a moving-horizon differential evolution algorithm for classification trees with continuous features (MH-DEOCT). Our approach consists of a discrete tree decoding method that eliminates duplicated searches between adjacent samples, a GPU-accelerated implementation that significantly reduces running time, and a moving-horizon strategy that iteratively trains shallow subtrees at each node to balance the vision and optimizer capability. Comprehensive studies on 68 UCI datasets demonstrate that our approach outperforms the heuristic method CART on training and testing accuracy by an average of 3.44% and 1.71%, respectively. Moreover, these numerical studies empirically demonstrate that MH-DEOCT achieves near-optimal performance (only 0.38% and 0.06% worse than the global optimal method on training and testing, respectively), while it offers remarkable scalability for deep trees (e.g., depth=8) and large-scale datasets (e.g., ten million samples).

A Global Optimization Algorithm for K-Center Clustering of One Billion Samples

This paper presents a practical global optimization algorithm for the K-center clustering problem, which aims to select K samples as the cluster centers to minimize the maximum within-cluster distance. This algorithm is based on a reduced-space branch and bound scheme and guarantees convergence to the global optimum in a finite number of steps by only branching on the regions of centers. To improve efficiency, we have designed a two-stage decomposable lower bound, the solution of which can be derived in a closed form. In addition, we also propose several acceleration techniques to narrow down the region of centers, including bounds tightening, sample reduction, and parallelization. Extensive studies on synthetic and real-world datasets have demonstrated that our algorithm can solve the K-center problems to global optimal within 4 hours for ten million samples in the serial mode and one billion samples in the parallel mode. Moreover, compared with the state-of-the-art heuristic methods, the global optimum obtained by our algorithm can averagely reduce the objective function by 25.8% on all the synthetic and real-world datasets.