Covariance Matrix Adaptation MAP-Annealing

Single-objective optimization algorithms search for the single highest-quality solution with respect to an objective. In contrast, quality diversity (QD) optimization algorithms, such as Covariance Matrix Adaptation MAP-Elites (CMA-ME), search for a collection of solutions that are both high-quality with respect to an objective and diverse with respect to specified measure functions. We propose a new quality diversity algorithm, Covariance Matrix Adaptation MAP-Annealing (CMA-MAE), which bridges the gap between single-objective optimization and QD optimization. We prove that CMA-MAE smoothly blends between the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) single-objective optimizer and CMA-ME by gradually annealing a discount function with a scalar learning rate. We show that CMA-MAE has better performance than the current state-of-the-art QD algorithms on several benchmark domains and that its performance is empirically invariant to the archive resolution and robust to the discount function learning rate.