Tom94/practical-path-guiding

Question about the KL Divergence

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deadmarston commented

Hi Tom,

Thanks for your great work.
Regarding your gradient descent for KL Divergence, I wonder is there any possibility that your optimized bsdfSamplingFraction will fall into a local optimization because the whole sphere domain share a same bsdfSamplingFraction?

Tom94 commented

Hi deadmarston,

the solution is definitely suboptimal because of the lack of dependence on incident direction as well as the averaging within the spatial SD-tree cell.

Alleviating either of these two limitations would make the learned BSDF sampling fraction more accurate.

Regarding local minima: applying SGD on the spatio-directionally averaged gradients amounts to finding an optimum of the spatio-directionally averaged loss function... so I believe you may be right about the averaging introducing local optima. Averaging multiple loss functions with a single global optimum can absolutely lead to multiple local optima, but I'm not able to make a definitive statement whether this'll happen in the specific use of the KL divergence that we have here (and under which conditions).

Cheers!

deadmarston commented

Hi Tom,

Thank you for your valueable reply:)

Cheers!