Jun Maeda

Jun Maeda, Saul D. Jacka

Folklore says that Howard's Policy Improvement Algorithm converges extraordinarily fast, even for controlled diffusion settings. In a previous paper, we proved that approximations of the solution of a particular parabolic partial differential equation obtained via the policy improvement algorithm show a quadratic local convergence. In this paper, we show that we obtain the same rate of convergence of the algorithm in a more general setup. This provides some explanation as to why the algorithm converges fast. We provide an example by solving a semilinear elliptic partial differential equation numerically by applying the algorithm and check how the approximations converge to the analytic solution.

Koji Hashimoto, Yuji Hirono, Jun Maeda et al.

It has been proposed that random wide neural networks near Gaussian process are quantum field theories around Gaussian fixed points. In this paper, we provide a novel map with which a wide class of quantum mechanical systems can be cast into the form of a neural network with a statistical summation over network parameters. Our simple idea is to use the universal approximation theorem of neural networks to generate arbitrary paths in the Feynman's path integral. The map can be applied to interacting quantum systems / field theories, even away from the Gaussian limit. Our findings bring machine learning closer to the quantum world.