Neural Control Variates
- URL: http://arxiv.org/abs/2006.01524v2
- Date: Fri, 4 Sep 2020 06:47:36 GMT
- Title: Neural Control Variates
- Authors: Thomas M\"uller, Fabrice Rousselle, Jan Nov\'ak, Alexander Keller
- Abstract summary: We show that a set of neural networks can face the challenge of finding a good approximation of the integrand.
We derive a theoretically optimal, variance-minimizing loss function, and propose an alternative, composite loss for stable online training in practice.
Specifically, we show that the learned light-field approximation is of sufficient quality for high-order bounces, allowing us to omit the error correction and thereby dramatically reduce the noise at the cost of negligible visible bias.
- Score: 71.42768823631918
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We propose neural control variates (NCV) for unbiased variance reduction in
parametric Monte Carlo integration. So far, the core challenge of applying the
method of control variates has been finding a good approximation of the
integrand that is cheap to integrate. We show that a set of neural networks can
face that challenge: a normalizing flow that approximates the shape of the
integrand and another neural network that infers the solution of the integral
equation. We also propose to leverage a neural importance sampler to estimate
the difference between the original integrand and the learned control variate.
To optimize the resulting parametric estimator, we derive a theoretically
optimal, variance-minimizing loss function, and propose an alternative,
composite loss for stable online training in practice. When applied to light
transport simulation, neural control variates are capable of matching the
state-of-the-art performance of other unbiased approaches, while providing
means to develop more performant, practical solutions. Specifically, we show
that the learned light-field approximation is of sufficient quality for
high-order bounces, allowing us to omit the error correction and thereby
dramatically reduce the noise at the cost of negligible visible bias.
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