Title: Integral Equations and Machine Learning,
Abstract: As both light transport simulation and reinforcement learning are ruled by
the same Fredholm integral equation of the second kind, reinforcement learning
techniques may be used for photorealistic image synthesis: Efficiency may be
dramatically improved by guiding light transport paths by an approximate
solution of the integral equation that is learned during rendering. In the
light of the recent advances in reinforcement learning for playing games, we
investigate the representation of an approximate solution of an integral
equation by artificial neural networks and derive a loss function for that
purpose. The resulting Monte Carlo and quasi-Monte Carlo methods train neural
networks with standard information instead of linear information and naturally
are able to generate an arbitrary number of training samples. The methods are
demonstrated for applications in light transport simulation.