Extending Pathwise Gradients to Discrete Random Variables via Finite-Order Relaxation

Key points

• Pathwise gradients are preferred for continuous random variables because they are unbiased, low variance, and work with a single sample.1
• For discrete variables, however, the pathwise identity cannot generally be exact for every differentiable function.1
• Against other admissible solutions, our estimator is unique and minimizes weight variance; in contrast, prior works use categorical variables or augmented representations to approximate non-categorical variables that induces excess variance and computations.1
• To understand approximation bias for functions beyond the prescribed class, we also derive a non-asymptotic bias bound.1

Sources (1)

• [1]Extending Pathwise Gradients to Discrete Random Variables via Finite-Order Relaxation
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 6, 05:30 AM

  We propose a general framework to construct finite-order exact pathwise gradient estimators for a range of common discrete variables such as Poisson.

  Pathwise gradients are preferred for continuous random variables because they are unbiased, low variance, and work with a single sample.

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