Core Concepts
Analyzing online non-convex optimization with memory and switching cost for capacity provisioning.
Abstract
The content discusses an online non-convex optimization problem for capacity provisioning, focusing on minimizing flow time with switching costs. It covers worst-case and stochastic inputs, competitive algorithms, and prior work on online convex optimization. The analysis includes linear and quadratic switching costs, memory features, and algorithmic approaches.
Introduction
Describes the capacity provisioning problem in data centers.
Discusses the objective function and penalty for changing active servers.
Prior Work
Explores online convex optimization without memory.
Discusses OCO-S and its variations with different switching costs.
Speed Scaling
Introduces speed scaling models for minimizing flow time and energy spent.
Studies multi-server cases with homogenous and heterogeneous servers.
Comparison with Prior Work
Compares the time scale considerations between different optimization problems.
Highlights the importance of memory features and non-convex cost functions.
Our Contributions
Presents algorithms for worst-case and stochastic models with small competitive ratios.
Discusses the impact of linear and quadratic switching costs on algorithm performance.
Stats
Compared to OCO-S, the competitive ratio of any algorithm for the considered problem grows linearly with memory length.
The competitive ratio of A𝐿𝐺 is at most 4𝛼1/4.
Algorithm A𝐿𝐺 has a competitive ratio of at most 4𝛼1/4.
Quotes
"An online non-convex optimization problem is considered where the goal is to minimize the flow time of a set of jobs by modulating the number of active servers." - Rahul Vaze, Jayakrishnan Nair