Title: Gradient-Informed Quality Diversity for the Illumination of Discrete Spaces. Abstract: Quality Diversity (QD) algorithms have been proposed to search for a large collection of both diverse and high-performing solutions instead of a single set of local optima. While early QD algorithms view the objective and descriptor functions as black-box functions, novel tools have been introduced to use gradient information to accelerate the search and improve overall performance of those algorithms over continuous input spaces. However a broad range of applications involve discrete spaces, such as drug discovery or image generation. Exploring those spaces is challenging as they are combinatorially large and gradients cannot be used in the same manner as in continuous spaces. We introduce MAP-Elites with a Gradient-Informed Discrete Emitter (ME-GIDE), which extends QD optimisation with differentiable functions over discrete search spaces. ME-GIDE leverages the gradient information of the objective and descriptor functions with respect to its discrete inputs to propose gradient-informed updates that guide the search towards a diverse set of high quality solutions. We evaluate our method on challenging benchmarks including protein design and discrete latent space illumination and find that our method outperforms state-of-the-art QD algorithms in all benchmarks.


