A Tight Lower Bound for Online Convex Optimization with Switching Costs.

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.