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.

翻译：在处理如逆向渲染等难度较大的逆问题时，使用蒙特卡洛估计梯度进行参数优化会因方差而降低收敛速度。简单地在每次迭代中对多个梯度样本求平均可降低这种方差，但对于需要数千次优化迭代的问题，该方法的计算成本会迅速增加。本文推导出了一种交织采样与优化的理论框架。我们利用描述每次迭代间估计梯度变化的低方差有限差分估计器来更新和复用历史样本。通过结合比例样本与有限差分样本，我们在整个优化过程中持续降低新型梯度元估计器的方差。我们探究了该估计器如何与Adam优化器联动，并推导出稳定结合方案。我们将该方法应用于逆向路径追踪，并通过实验证明该估计器能加速复杂优化任务的收敛过程。