Control Oriented Learning in the Era of Big Data

Recent advances in control, coupled with an exponential growth in data gathering capabilities, have made feasible a wide range of applications that can profoundly impact society. Yet, achieving this vision requires addressing the challenge of extracting control relevant information from large amounts of data, a problem that has proven to be surprisingly difficult. While modern machine learning techniques can handle very large data sets, most control oriented learning algorithms struggle with a few thousand points. The goal of this letter is to point out the reason why dynamic data is challenging and to indicate strategies to overcome this challenge. The main message is twofold (i) computational complexity in control oriented learning is driven both by system order and the presence of uncertainty, rather than the dimension of the data, and (ii) exploiting the underlying sparsity provides a way around the "curse of dimensionality".