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-ofthe-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.

Pre-training a diverse set of neural network controllers in simulation has enabled robots to adapt online to damage in robot locomotion tasks. However, finding diverse, high-performing controllers requires expensive network training and extensive tuning of a large number of hyperparameters. On the other hand, Covariance Matrix Adaptation MAP-Annealing (CMA-MAE), an evolution strategies (ES)-based quality diversity algorithm, does not have these limitations and has achieved state-of-the-art performance on standard QD benchmarks. However, CMA-MAE cannot scale to modern neural network controllers due to its quadratic complexity. We leverage efficient approximation methods in ES to propose three new CMA-MAE variants that scale to high dimensions. Our experiments show that the variants outperform ES-based baselines in benchmark robotic locomotion tasks, while being comparable with or exceeding state-of-the-art deep reinforcement learning-based quality diversity algorithms.

Consider a walking agent that must adapt to damage. To approach this task, we can train a collection of policies and have the agent select a suitable policy when damaged. Training this collection may be viewed as a quality diversity (QD) optimization problem, where we search for solutions (policies) which maximize an objective (walking forward) while spanning a set of measures (measurable characteristics). Recent work shows that differentiable quality diversity (DQD) algorithms greatly accelerate QD optimization when exact gradients are available for the objective and measures. However, such gradients are typically unavailable in RL settings due to non-differentiable environments. To apply DQD in RL settings, we propose to approximate objective and measure gradients with evolution strategies and actor-critic methods. We develop two variants of the DQD algorithm CMA-MEGA, each with different gradient approximations, and evaluate them on four simulated walking tasks. One variant achieves comparable performance (QD score) with the state-of-the-art PGA-MAP-Elites in two tasks. The other variant performs comparably in all tasks but is less efficient than PGA-MAP-Elites in two tasks. These results provide insight into the limitations of CMA-MEGA in domains that require rigorous optimization of the objective and where exact gradients are unavailable.

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 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.