  The Variational Monte Carlo method has recently seen important advances
through the use of neural network quantum states. While more and more
sophisticated ans\"atze have been designed to tackle a wide variety of quantum
many-body problems, modest progress has been made on the associated
optimisation algorithms. In this work, we revisit the Kronecker Factored
Approximate Curvature, an optimiser that has been used extensively in a variety
of simulations. We suggest improvements on the scaling and the direction of
this optimiser, and find that they substantially increase its performance at a
negligible additional cost. We also reformulate the Variational Monte Carlo
approach in a game theory framework, to propose a novel optimiser based on
decision geometry. We find that, on a practical test case for continuous
systems, this new optimiser consistently outperforms any of the KFAC
improvements in terms of stability, accuracy and speed of convergence. Beyond
Variational Monte Carlo, the versatility of this approach suggests that
decision geometry could provide a solid foundation for accelerating a broad
class of machine learning algorithms.
