A Unified Perspective on Regularization and Perturbation in Differentiable Subset Selection

Subset selection, i.e., finding a bunch of items from a collection to achieve specific goals, has wide applications in information retrieval, statistics, and machine learning. To implement an endto-end learning framework, different relaxed differentiable operators of subset selection are proposed. Most existing work relies on either regularization method or perturbation method. In this work, we provide a probabilistic interpretation for regularization relaxation and unify two schemes. Besides, we build some concrete examples to show the generic connection between these two relaxations. Finally, we evaluate the perturbed selector as well as the regularized selector on two tasks: the maximum entropy sampling problem and the feature selection problem. The experimental results show that these two methods can achieve competitive performance against other benchmarks.