Learning in physical domains: Mating safety requirements and costly sampling

Agents learning in physical domains face two problems: they must meet safety requirements because their behaviour must not cause damage to the environment, and they should learn with as few samples as possible because acquiring new data requires costly interactions. Active learning strategies reduce sampling costs, as new data are requested only when and where they are deemed most useful to improve on agent's accuracy, but safety remains a standing challenge. In this paper we focus on active learning with support vector regression and introduce a methodology based on satisfiability modulo theory to prove that predictions are bounded as long as input patterns satisfy some preconditions. We present experimental results showing the feasibility of our approach, and compare our results with Gaussian processes, another class of kernel methods which natively provide bounds on predictions.