A Unified Approach for Maximizing Continuous DR-submodular Functions
This work addresses optimization challenges in machine learning and AI for researchers and practitioners dealing with submodular functions, though it is incremental in building on existing methods.
The paper tackles the problem of maximizing continuous DR-submodular functions by developing a unified approach that handles various settings and oracle types, achieving new or improved results in 9 out of 16 cases and enabling the first regret bounds with bandit feedback for stochastic functions.
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 two cases, with the proposed framework matching performance of state-of-the-art approaches in the remaining five cases. Notably, our approach for the stochastic function value-based oracle enables the first regret bounds with bandit feedback for stochastic DR-submodular functions.