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arXiv · 1905.11877

Chasing Convex Bodies with Linear Competitive Ratio

C. J. Argue·Anupam Gupta·Guru Guruganesh·Ziye Tang
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Abstract

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 sequence of length $T$.

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C. J. Argue, Anupam Gupta, Guru Guruganesh, Ziye Tang. 2019-05-28. Chasing Convex Bodies with Linear Competitive Ratio. https://arxiv.org/abs/1905.11877

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