Year: 2019
Type: preprint
Abstract: In this paper, we consider the problem of black box continuous submodular maximization where we only have access to the function values and no information about the derivatives is provided. For a monotone and continuous DR-submodular function, and subject to a bounded convex body constraint, we propose Black-box Continuous Greedy, a derivative-free algorithm that provably achieves the tight $[(1-1/e)OPT-ε]$ approximation guarantee with $O(d/ε^3)$ function evaluations. We then extend our result to the stochastic setting where function values are subject to stochastic zero-mean noise. It is through this stochastic generalization that we revisit the discrete submodular maximization problem and use the multi-linear extension as a bridge between discrete and continuous settings. Finally, we extensively evaluate the performance of our algorithm on continuous and discrete submodular objective functions using both synthetic and real data.
Source: arXiv (Cornell University)
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G1523888516, CAREER: Leveraging Combinatorial Structures for Robust and Scalable Learning, HDR TRIPODS: Penn Institute for Foundations of Data Science, CIF: Small: Collaborative Research: Communications in Ultra-Low-Rate Regime: Fundamental Limits, Code Constructions, and Applications, CPS: Medium: Rethinking Communication and Control for Low-Latency, High Reliability loT Devices, G5972442391, G6098521345, CAREER: Submodular Optimization in Complex Environments: Theory, Algorithms, and Applications, G6671297155, G8876996369
OpenAlex ID: W2912940760