  Several strategies have been recently proposed in order to improve Monte
Carlo sampling efficiency using machine learning tools. Here, we challenge
these methods by considering a class of problems that are known to be
exponentially hard to sample using conventional local Monte Carlo at low enough
temperatures. In particular, we study the antiferromagnetic Potts model on a
random graph, which reduces to the coloring of random graphs at zero
temperature. We test several machine-learning-assisted Monte Carlo approaches,
and we find that they all fail. Our work thus provides good benchmarks for
future proposals for smart sampling algorithms.
