Optimal choice problem and its solutions

The article introduces the Optimal Choice problem. The problem emerges quite often in various practical applications, but it was not formalized as a machine learning problem to the best of author's knowledge. The problem may seem perplexing because the most common assumptions of statistical learning theory are violated here, as we discuss. Yet, the Optimal Choice problem may be solved successfully, as we demonstrate on an example of a real life dataset from a signal processing application. We propose two approaches to solve the problem. Both of them reach good solutions, at least on the data at hand.