Personalized Time-varying Optimization with User's Feedback

Abstract

We present and characterize an online algorithm to solve a time-varying optimization problem with an objective that comprises a known time-varying cost and an unknown function, based on Gaussian Processes and invex functions. This problem structure is key in the emerging field of cyberphysical and social systems, where the known function captures time-varying engineering costs, and the unknown function captures user's satisfaction; in this context, the objective is to strike a balance between given performance metrics and user's satisfaction, thereby incorporating humans in the decision making process.