Online Optimization with Memory and Competitive Control

This paper presents competitive algorithms for a novel class of online optimization problems with memory. We consider a setting where the learner seeks to minimize the sum of a hitting cost and a switching cost that depends on the previous p decisions. This setting generalizes Smoothed Online Convex Optimization. The proposed approach, Optimistic Regularized Online Balanced Descent, achieves a constant, dimension-free competitive ratio. Further, we show a connection between online optimization with memory and online control with adversarial disturbances. This connection, in turn, leads to a new constant-competitive policy for a rich class of online control problems

Online Algorithms for Geographical Load Balancing

It has recently been proposed that Internet energy costs, both monetary and environmental, can be reduced by exploiting temporal variations and shifting processing to data centers located in regions where energy currently has low cost. Lightly loaded data centers can then turn off surplus servers. This paper studies online algorithms for determining the number of servers to leave on in each data center, and then uses these algorithms to study the environmental potential of geographical load balancing (GLB). A commonly suggested algorithm for this setting is “receding horizon control” (RHC), which computes the provisioning for the current time by optimizing over a window of predicted future loads. We show that RHC performs well in a homogeneous setting, in which all servers can serve all jobs equally well; however, we also prove that differences in propagation delays, servers, and electricity prices can cause RHC perform badly, So, we introduce variants of RHC that are guaranteed to perform as well in the face of such heterogeneity. These algorithms are then used to study the feasibility of powering a continent-wide set of data centers mostly by renewable sources, and to understand what portfolio of renewable energy is most effective

Online optimization with switching cost

We consider algorithms for "smoothed online convex optimization (SOCO)" problems. SOCO is a variant of the class of "online convex optimization (OCO)" problems that is strongly related to the class of "metrical task systems", each of which have been studied extensively. Prior literature on these problems has focused on two performance metrics: regret and competitive ratio. There exist known algorithms with sublinear regret and known algorithms with constant competitive ratios; however no known algorithms achieve both. In this paper, we show that this is due to a fundamental incompatibility between regret and the competitive ratio -- no algorithm (deterministic or randomized) can achieve sublinear regret and a constant competitive ratio, even in the case when the objective functions are linear