Differentiable Quality Diversity
  Quality diversity (QD) is a growing branch of stochastic optimization
research that studies the problem of generating an archive of solutions that
maximize a given objective function but are also diverse with respect to a set
of specified measure functions. However, even when these functions are
differentiable, QD algorithms treat them as "black boxes", ignoring gradient
information. We present the differentiable quality diversity (DQD) problem, a
special case of QD, where both the objective and measure functions are first
order differentiable. We then present MAP-Elites via a Gradient Arborescence
(MEGA), a DQD algorithm that leverages gradient information to efficiently
explore the joint range of the objective and measure functions. Results in two
QD benchmark domains and in searching the latent space of a StyleGAN show that
MEGA significantly outperforms state-of-the-art QD algorithms, highlighting
DQD's promise for efficient quality diversity optimization when gradient
information is available. Source code is available at
https://github.com/icaros-usc/dqd.
