  The solution set of a system of polynomial equations typically contains
ill-behaved, singular points. Resolution is a fundamental process in geometry
in which we replace singular points with smooth points, while keeping the rest
of the solution set unchanged. Resolutions are not unique: the usual way to
describe them involves repeatedly performing a fundamental operation known as
"blowing-up", and the complexity of the resolution highly depends on certain
choices. The process can be translated into various versions of a 2-player
game, the so-called Hironaka game, and a winning strategy for the first player
provides a solution to the resolution problem. In this paper we introduce a new
approach to the Hironaka game that uses reinforcement learning agents to find
optimal resolutions of singularities. In certain domains, the trained model
outperforms state-of-the-art selection heuristics in total number of polynomial
additions performed, which provides a proof-of-concept that recent developments
in machine learning have the potential to improve performance of algorithms in
symbolic computation.
