AISTATS 2019poster42 citations
Projection-Free Bandit Convex Optimization
Lin Chen, Mingrui Zhang, Amin Karbasi
Abstract
In this paper, we propose the first computationally efficient projection-free algorithm for bandit convex optimization (BCO) with a general convex constraint. We show that our algorithm achieves a sublinear regret of $O(nT^{4/5})$ (where $T$ is the horizon and $n$ is the dimension) for any bounded convex functions with uniformly bounded gradients. We also evaluate the performance of our algorithm against baselines on both synthetic and real data sets for quadratic programming, portfolio selection and matrix completion problems.
BibTeX
@InProceedings{pmlr-v89-chen19f,
title = {Projection-Free Bandit Convex Optimization},
author = {Chen, Lin and Zhang, Mingrui and Karbasi, Amin},
booktitle = {Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics},
pages = {2047--2056},
year = {2019},
editor = {Chaudhuri, Kamalika and Sugiyama, Masashi},
volume = {89},
series = {Proceedings of Machine Learning Research},
month = {16--18 Apr},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v89/chen19f/chen19f.pdf},
url = {https://proceedings.mlr.press/v89/chen19f.html},
abstract = {In this paper, we propose the first computationally efficient projection-free algorithm for bandit convex optimization (BCO) with a general convex constraint. We show that our algorithm achieves a sublinear regret of $O(nT^{4/5})$ (where $T$ is the horizon and $n$ is the dimension) for any bounded convex functions with uniformly bounded gradients. We also evaluate the performance of our algorithm against baselines on both synthetic and real data sets for quadratic programming, portfolio selection and matrix completion problems.}
}