A Unified Approach for Maximizing Continuous DR-submodular Functions

Published: 21 Sept 2023, Last Modified: 12 Jan 2024NeurIPS 2023 posterEveryoneRevisionsBibTeX
Keywords: Stochastic optimization, submodular maximization, Frank-Wolfe algorithm
Abstract: This paper presents a unified approach for maximizing continuous DR-submodular functions that encompasses a range of settings and oracle access types. Our approach includes a Frank-Wolfe type offline algorithm for both monotone and non-monotone functions, with different restrictions on the general convex set. We consider settings where the oracle provides access to either the gradient of the function or only the function value, and where the oracle access is either deterministic or stochastic. We determine the number of required oracle accesses in all cases. Our approach gives new/improved results for nine out of the sixteen considered cases, avoids computationally expensive projections in three cases, with the proposed framework matching performance of state-of-the-art approaches in the remaining four cases. Notably, our approach for the stochastic function value-based oracle enables the first regret bounds with bandit feedback for stochastic DR-submodular functions.
Supplementary Material: pdf
Submission Number: 13788