# Chasing Convex Bodies with Linear Competitive Ratio

@inproceedings{Argue2020ChasingCB,
title={Chasing Convex Bodies with Linear Competitive Ratio},
author={C. J. Argue and Anupam Gupta and Guru Guruganesh and Ziye Tang},
booktitle={SODA},
year={2020}
}
• Published in SODA 28 May 2019
• Mathematics, Computer Science
We study the problem of chasing convex bodies online: given a sequence of convex bodies $K_t\subseteq \mathbb{R}^d$ the algorithm must respond with points $x_t\in K_t$ in an online fashion (i.e., $x_t$ is chosen before $K_{t+1}$ is revealed). The objective is to minimize the sum of distances between successive points in this sequence. Bubeck et al. (STOC 2019) gave a $2^{O(d)}$-competitive algorithm for this problem. We give an algorithm that is $O(\min(d, \sqrt{d \log T}))$-competitive for any…

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