System Intelligence: 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 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 Learning-aided Budget-limited Intelligent System Control (\mtt{LBISC}). We show that \lbisc{} achieves an intelligence level that is within $O(N(T)^{-\frac{1}{2}}+\epsilon)$ 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 in the system, while guaranteeing an $O(\max( N(T)^{-\frac{1}{2}}/\epsilon, \log(1/\epsilon)^2))$ average resource deficit. Moreover, we show that \lbisc{} possesses an $O(\max( N(T)^{-\frac{1}{2}}/\epsilon$, $ \log(1/\epsilon)^2)+T)$ convergence time, which is much smaller compared to the $\Theta(1/\epsilon)$ time required for non-learning based algorithms. The analysis of \lbisc{} rigorously quantifies the impacts of data and user population (captured by $N(T)$), learning (captured by our learning method), and control (captured by \lbisc) on achievable system intelligence, and provides novel insight and guideline into designing future smart systems. 
Longbo Huang
math.OC