A Tight Lower Bound for Online Convex Optimization with Switching Costs

  • Antonios Antoniadis
  • Kevin SchewiorEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10787)


We investigate online convex optimization with switching costs (OCO; Lin et al., INFOCOM 2011), a natural online problem arising when rightsizing data centers: A server initially located at \(p_0\) on the real line is presented with an online sequence of non-negative convex functions \(f_1,f_2,\dots ,f_n: \mathbb {R}\rightarrow \mathbb {R}_+\). In response to each function \(f_i\), the server moves to a new position \(p_i\) on the real line, resulting in cost \(|p_i-p_{i-1}|+f_i(p_i)\). The total cost is the sum of costs of all steps. One is interested in designing competitive algorithms.

In this paper, we solve the problem in the classical sense: We give a lower bound of 2 on the competitive ratio of any possibly randomized online algorithm, matching the competitive ratio of previously known deterministic online algorithms (Andrew et al., COLT 2013/arXiv 2015; Bansal et al., APPROX 2015). It has been previously conjectured that \((2-\epsilon )\)-competitive algorithms exist for some \(\epsilon >0\) (Bansal et al., APPROX 2015).


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany
  2. 2.Universidad de ChileSantiagoChile

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