Generalizing Stochastic Smoothing for Differentiation and Gradient Estimation
<|reference_start|>Generalizing Stochastic Smoothing for Differentiation and Gradient Estimation: We deal with the problem of gradient estimation for stochastic differentiable relaxations of algorithms, operators, simulators, and other non-differentiable functions. Stochastic smoothing conventionally perturbs the input of a non-differentiable function with a differentiable density distribution with full support, smoothing it and enabling gradient estimation. Our theory starts at first principles to derive stochastic smoothing with reduced assumptions, without requiring a differentiable density nor full support, and we present a general framework for relaxation and gradient estimation of non-differentiable black-box functions $f:\mathbb{R}^n\to\mathbb{R}^m$. We develop variance reduction for gradient estimation from 3 orthogonal perspectives. Empirically, we benchmark 6 distributions and up to 24 variance reduction strategies for differentiable sorting and ranking, differentiable shortest-paths on graphs, differentiable rendering for pose estimation, as well as differentiable cryo-ET simulations.<|reference_end|>
@article{petersen2024generalizing,
    title={Generalizing Stochastic Smoothing for Differentiation and Gradient
  Estimation},
    author={Felix Petersen, Christian Borgelt, Aashwin Mishra, Stefano Ermon},
    journal={arXiv preprint arXiv:2410.08125},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.08125},
    primaryClass={cs.LG stat.ML}
}