Joint Sampling and Optimisation for Inverse Rendering
Martin Balint Karol Myszkowski Hans-Peter Seidel Gurprit Singh
When dealing with difficult inverse problems such as inverse rendering, using
Monte Carlo estimated gradients to optimise parameters can slow down
convergence due to variance. Averaging many gradient samples in each iteration
reduces this variance trivially. However, for problems that require thousands
of optimisation iterations, the computational cost of this approach rises
quickly.
  We derive a theoretical framework for interleaving sampling and optimisation.
We update and reuse past samples with low-variance finite-difference estimators
that describe the change in the estimated gradients between each iteration. By
combining proportional and finite-difference samples, we continuously reduce
the variance of our novel gradient meta-estimators throughout the optimisation
process. We investigate how our estimator interlinks with Adam and derive a
stable combination.
  We implement our method for inverse path tracing and demonstrate how our
estimator speeds up convergence on difficult optimisation tasks.