Linear Submodular Maximization with Bandit Feedback
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866911942374850560 |
|---|---|
| author | Chen, Wenjing Crawford, Victoria G. |
| author_facet | Chen, Wenjing Crawford, Victoria G. |
| contents | Submodular optimization with bandit feedback has recently been studied in a variety of contexts. In a number of real-world applications such as diversified recommender systems and data summarization, the submodular function exhibits additional linear structure. We consider developing approximation algorithms for the maximization of a submodular objective function $f:2^U\to\mathbb{R}_{\geq 0}$, where $f=\sum_{i=1}^dw_iF_{i}$. It is assumed that we have value oracle access to the functions $F_i$, but the coefficients $w_i$ are unknown, and $f$ can only be accessed via noisy queries. We develop algorithms for this setting inspired by adaptive allocation algorithms in the best-arm identification for linear bandit, with approximation guarantees arbitrarily close to the setting where we have value oracle access to $f$. Finally, we empirically demonstrate that our algorithms make vast improvements in terms of sample efficiency compared to algorithms that do not exploit the linear structure of $f$ on instances of move recommendation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_02601 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Linear Submodular Maximization with Bandit Feedback Chen, Wenjing Crawford, Victoria G. Machine Learning Data Structures and Algorithms Submodular optimization with bandit feedback has recently been studied in a variety of contexts. In a number of real-world applications such as diversified recommender systems and data summarization, the submodular function exhibits additional linear structure. We consider developing approximation algorithms for the maximization of a submodular objective function $f:2^U\to\mathbb{R}_{\geq 0}$, where $f=\sum_{i=1}^dw_iF_{i}$. It is assumed that we have value oracle access to the functions $F_i$, but the coefficients $w_i$ are unknown, and $f$ can only be accessed via noisy queries. We develop algorithms for this setting inspired by adaptive allocation algorithms in the best-arm identification for linear bandit, with approximation guarantees arbitrarily close to the setting where we have value oracle access to $f$. Finally, we empirically demonstrate that our algorithms make vast improvements in terms of sample efficiency compared to algorithms that do not exploit the linear structure of $f$ on instances of move recommendation. |
| title | Linear Submodular Maximization with Bandit Feedback |
| topic | Machine Learning Data Structures and Algorithms |
| url | https://arxiv.org/abs/2407.02601 |