Differentiable Greedy Networks

Abstract

Optimal selection of a subset of items from a given set is a hard problem that requires combinatorial optimization. In this paper, we propose a subset selection algorithm that is trainable with gradient based methods yet achieves near optimal performance via submodular optimization. We focus on the task of identifying a relevant set of sentences for claim verification in the context of the FEVER task. Conventional methods for this task look at sentences on their individual merit and thus do not optimize the informativeness of sentences as a set. We show that our proposed method which builds on the idea of unfolding a greedy algorithm into a computational graph allows both interpretability and gradient based training. The proposed differentiable greedy network (DGN) outperforms discrete optimization algorithms as well as other baseline methods in terms of precision and recall.

Differentiable Greedy Submodular Maximization: Guarantees, Gradient Estimators, and Applications

“…SMOOTHED GREEDY We develop SMOOTHED GREEDY by stochastically perturbing argmax; this generalizes the existing algorithms [52,46]. We prove that the perturbation does not spoil the original guarantees: almost (1 − 1/e)and 1 κ+1 -approximation guarantees are achieved in expectation for the cases of cardinality and κ-extensible system constraints, respectively, where a subtractive term depending on the perturbation strength affects the guarantees.…”

“…Differentiable greedy submodular maximization is studied in [52,46]. Our work is different from them in terms of theoretical guarantees, differentiation methods, and problem settings as explained above (see, also Appendix A).…”

“…another softmax-based algorithm that forms a neural network (NN) [46] and applications [32,44] have been studied. However, this field is still in its infancy and the following problems remain open:…”

“…The first problem is important since, without the guarantees, we cannot ensure that the differentiationbased methods work well. The existing studies [52,46] state that the (1 − 1/e)-approximation for the cardinality constrained case is obtained if the temperature of softmax is zero (i.e., equal to argmax). This, however, provides no theoretical guarantees for the smoothed differentiable algorithms.…”

“…As regards the second problem, the existing methods [52,46] focus on differentiating some functions defined with subsets X 1 , X 2 , . .…”