Adaptive Maximization of Pointwise Submodular Functions With Budget Constraint
This work addresses adaptive optimization problems in AI/ML, such as active learning, but is incremental as it builds on existing greedy algorithm analyses.
The paper tackles the worst-case adaptive optimization problem with budget constraints by analyzing greedy algorithms for both modular and non-modular cost functions, proving that a combined greedy algorithm achieves near-optimality relative to an optimal algorithm using half the budget.
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.