The Smart Home, as an intelligent agent, provides automation of repetitive tasks in order to maximize inhabitant comfort. Therefore, one of the tasks of the Smart Home is the prediction of device usage based on previous history. In this work, we present Active LeZi - an online, sequential prediction algorithm that is founded on an Information Theoretic approach, and based on the acclaimed LZ78 family of text compression algorithms. We demonstrate the performance of this algorithm on a synthetic data set that is representative of typical interactions of inhabitants with a smart home.