Intelligence of Smart Systems: Model, Bounds, and Algorithms

We present a general framework for understanding system intelligence, i. e., the level of system smartness perceived by users, and propose a novel metric for measuring the intelligence levels of dynamical human-in-the-loop systems, defined to be the maximum average reward obtained by proactively serving user demands, subject to a resource constraint. Our metric captures two important elements of smartness, i. e., being able to know what users want and pre-serve them, and achieving good resource management while doing so. We provide an explicit characterization of the system intelligence, and show that it is jointly determined by user demand volume (opportunity to impress), demand correlation (user predictability), and system resource and action costs (flexibility to pre-serve). We then propose an online learning-aided control algorithm called learningaided budget-limited intelligent system control (LBISC), and show that LBISC achieves an intelligence level that is within O(N(T)(-1/2) + epsilon) of the highest level, where N(T) represents the number of data samples collected within a learning period T and is proportional to the user population size, while guaranteeing an O(max(N(T)(-1/2)/epsilon, log(1/epsilon)(2))) average resource deficit. Moreover, we show that LBISC possesses an O(max(N(T)(-1/2)/epsilon, log(1/epsilon)(2)) + T) convergence time, which is smaller compared with the T(1/epsilon) time required for existing non-learning-based algorithms. Our analysis rigorously quantifies the impact of data and user population (captured by N(T)), learning (captured by our learning method), and control (captured by LBISC) on the achievable system intelligence, and provides novel insight and guideline into designing future smart systems.