Chasing Convex Bodies Optimally

@inproceedings{Sellke2020ChasingCB,
  title={Chasing Convex Bodies Optimally},
  author={Mark Sellke},
  booktitle={SODA},
  year={2020}
}
In the chasing convex bodies problem, an online player receives a request sequence of $N$ convex sets $K_1,\dots, K_N$ contained in a normed space $\mathbb R^d$. The player starts at $x_0\in \mathbb R^d$, and after observing each $K_n$ picks a new point $x_n\in K_n$. At each step the player pays a movement cost of $||x_n-x_{n-1}||$. The player aims to maintain a constant competitive ratio against the minimum cost possible in hindsight, i.e. knowing all requests in advance. The existence of a… 

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