2018/06/22 by C. J. Argue, Sébastien Bubeck, Argue, C. J. +7
Computer Science · #Complexity and Algorithms in Graphs #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Optimization and Search Problems #Reinforcement Learning in Robotics
paper · pdf · doi:10.48550/arxiv.1806.08865
openalex publication_date 2018/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Friedman and Linial introduced the convex body chasing problem to explore the interplay between geometry and competitive ratio in metrical task systems. In convex body chasing, at each time step t ∈ ℕ, the online algorithm receives a request in the form of a convex body Kt ⊆ ℝd and must output a point xt ∈ Kt. The goal is to minimize the total movement between consecutive output points, where the distance is measured in some given norm. This problem is still far from being understood, and recently Bansal et al. gave an algorithm for the nested version, where each convex body is contained within the previous one. We propose a different strategy which is O(d log d)-competitive algorithm for this nested convex body chasing problem, improving substantially over previous work. Our algorithm works for any norm. This result is almost tight, given an Ω(d) lower bound for the ℓ∞.