Summary of Bridging the Gap Between General and Down-closed Convex Sets in Submodular Maximization, by Loay Mualem et al.
Bridging the Gap Between General and Down-Closed Convex Sets in Submodular Maximization
by Loay Mualem, Murad Tukan, Moran Fledman
First submitted to arxiv on: 17 Jan 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Optimization and Control (math.OC)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper addresses a significant development in non-convex optimization, specifically optimizing DR-submodular functions over general convex set constraints. Recent works have focused on maximizing non-monotone DR-submodular functions, but a recent hardness result shows that the commonly used minimum _norm approach cannot yield a smooth interpolation between down-closed and non-down-closed constraints. The authors propose novel offline and online algorithms that provably provide such an interpolation by decomposing the convex body constraint into two distinct bodies: a down-closed convex body and a general convex body. These algorithms are demonstrated to be superior in three offline and two online applications. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper is about finding the best way to optimize certain functions, which is important for many real-world problems. The authors found that a common approach doesn’t work as well as it could, so they developed new methods that do better. These new methods can be used in different situations and are proven to be more effective. |
Keywords
* Artificial intelligence * Optimization
