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.

翻译：质量多样性（QD）算法旨在搜索大量兼具多样性与高性能的解决方案，而非单一局部最优解集合。早期QD算法将目标函数与描述函数视为黑箱函数，而新型工具已引入梯度信息来加速连续输入空间的搜索过程并提升算法整体性能。然而，药物发现或图像生成等众多应用场景涉及离散空间。这些空间因组合爆炸特性而难以探索，且梯度无法像在连续空间中那样直接使用。我们提出基于梯度引导离散发射器的地图精英算法（ME-GIDE），该方法将可微函数的质量多样性优化扩展到离散搜索空间。ME-GIDE利用目标函数与描述函数关于离散输入的梯度信息，提出梯度引导的更新策略，从而引导搜索过程朝向兼具多样性与高质量的解集合。我们在蛋白质设计与离散潜空间照明等具有挑战性的基准测试中评估该方法，结果表明其所有基准测试中均优于当前最先进的QD算法。