Optimal choice: new machine learning problem and its solution

The task of learning to pick a single preferred example out a finite set of examples, an "optimal choice problem", is a supervised machine learning problem with complex, structured input. Problems of optimal choice emerge often in various practical applications. We formalize the problem, show that it does not satisfy the assumptions of statistical learning theory, yet it can be solved efficiently in some cases. We propose two approaches to solve the problem. Both of them reach good solutions on real life data from a signal processing application.