Adaptive Maximization of Pointwise Submodular Functions With Budget Constraint

TL;DR

This paper analyzes the effectiveness of greedy algorithms for adaptive optimization of pointwise submodular functions under budget constraints, providing theoretical guarantees and empirical validation.

Contribution

It establishes near-optimality conditions for greedy algorithms in adaptive submodular optimization with budget constraints, introducing a combined approach.

Findings

Two simple greedy algorithms are not always near-optimal.

The best among the two greedy algorithms is near-optimal under certain submodularity conditions.

Experimental results demonstrate the practical effectiveness of the proposed algorithms.

Abstract

We study the worst-case adaptive optimization problem with budget constraint that is useful for modeling various practical applications in artificial intelligence and machine learning. We investigate the near-optimality of greedy algorithms for this problem with both modular and non-modular cost functions. In both cases, we prove that two simple greedy algorithms are not near-optimal but the best between them is near-optimal if the utility function satisfies pointwise submodularity and pointwise cost-sensitive submodularity respectively. This implies a combined algorithm that is near-optimal with respect to the optimal algorithm that uses half of the budget. We discuss applications of our theoretical results and also report experiments comparing the greedy algorithms on the active learning problem.