On multivariate randomized classification trees: $l_0$-based sparsity, VC~dimension and decomposition methods

Decision trees are widely-used classification and regression models because of their interpretability and good accuracy. Classical methods such as CART are based on greedy approaches but a growing attention has recently been devoted to optimal decision trees. We investigate the nonlinear continuous optimization formulation proposed in Blanquero et al. (EJOR, vol. 284, 2020; COR, vol. 132, 2021) for (sparse) optimal randomized classification trees. Sparsity is important not only for feature selection but also to improve interpretability. We first consider alternative methods to sparsify such trees based on concave approximations of the $l_{0}$ ``norm". Promising results are obtained on 24 datasets in comparison with $l_1$ and $l_{\infty}$ regularizations. Then, we derive bounds on the VC dimension of multivariate randomized classification trees. Finally, since training is computationally challenging for large datasets, we propose a general decomposition scheme and an efficient version of it. Experiments on larger datasets show that the proposed decomposition method is able to significantly reduce the training times without compromising the accuracy.

ANDREAS: Artificial intelligence traiNing scheDuler foR accElerAted resource clusterS

Artificial Intelligence (AI) and Deep Learning (DL) algorithms are currently applied to a wide range of products and solutions. DL training jobs are highly resource demanding and they experience great benefits when exploiting AI accelerators (e.g., GPUs). However, the effective management of GPU-powered clusters comes with great challenges. Among these, efficient scheduling and resource allocation solutions are crucial to maximize performance and minimize Data Centers operational costs. In this paper we propose ANDREAS, an advanced scheduling solution that tackles these problems jointly, aiming at optimizing DL training runtime workloads and their energy consumption in accelerated clusters. Experiments based on simulation demostrate that we can achieve a cost reduction between 30 and 62% on average with respect to first-principle methods while the validation on a real cluster shows a worst case deviation below 13% between actual and predicted costs, proving the effectiveness of ANDREAS solution in practical scenarios.