Integral Equations and Machine Learning

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.

Learning Light Transport the Reinforced Way

We show that the equations of reinforcement learning and light transport simulation are related integral equations. Based on this correspondence, a scheme to learn importance while sampling path space is derived. The new approach is demonstrated in a consistent light transport simulation algorithm that uses reinforcement learning to progressively learn where light comes from. As using this information for importance sampling includes information about visibility, too, the number of light transport paths with zero contribution is dramatically reduced, resulting in much less noisy images within a fixed time budget.