Submodular Learning and Covering with Response-Dependent Costs

TL;DR

This paper introduces a greedy algorithm for interactive learning and covering problems with response-dependent costs, providing bounds on its approximation factor and demonstrating its near-optimality and practical advantages.

Contribution

It proposes a natural greedy algorithm for response-dependent costs and analyzes its approximation bounds in active learning and general settings, showing near-optimal performance.

Findings

The greedy algorithm achieves near-optimal approximation bounds.

The approximation factor depends on specific properties of the cost function.

Experiments show the algorithm's effectiveness in response-dependent cost scenarios.

Abstract

We consider interactive learning and covering problems, in a setting where actions may incur different costs, depending on the response to the action. We propose a natural greedy algorithm for response-dependent costs. We bound the approximation factor of this greedy algorithm in active learning settings as well as in the general setting. We show that a different property of the cost function controls the approximation factor in each of these scenarios. We further show that in both settings, the approximation factor of this greedy algorithm is near-optimal among all greedy algorithms. Experiments demonstrate the advantages of the proposed algorithm in the response-dependent cost setting.