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The encoding of solutions in black-box optimization is a delicate, handcrafted balance between expressiveness and domain knowledge between exploring a wide variety of solutions, and ensuring that those solutions are useful. Our main insight is that this process can be automated by generating a dataset of high-performing solutions with a quality diversity algorithm (here, MAP-Elites), then learning a representation with a generative model (here, a Varia-tional Autoencoder) from that dataset. Our second insight is that this representation can be used to scale quality diversity optimization to higher dimensions-but only if we carefully mix solutions generated with the learned representation and those generated with traditional variation operators. We demonstrate these capabilities by learning an low-dimensional encoding for the inverse kinemat-ics of a thousand joint planar arm. The results show that learned representations make it possible to solve high-dimensional problems with orders of magnitude fewer evaluations than the standard MAP-Elites, and that, once solved, the produced encoding can be used for rapid optimization of novel, but similar, tasks. The presented techniques not only scale up quality diversity algorithms to high dimensions, but show that black-box optimization encodings can be automatically learned, rather than hand designed.
The way solutions are represented, or encoded, is usually the result of domain knowledge and experience. In this work, we combine MAP-Elites with Variational Autoencoders to learn a Data-Driven Encoding (DDE) that captures the essence of the highest-performing solutions while still able to encode a wide array of solutions. Our approach learns this data-driven encoding during optimization by balancing between exploiting the DDE to generalize the knowledge contained in the current archive of elites and exploring new representations that are not yet captured by the DDE. Learning representation during optimization allows the algorithm to solve high-dimensional problems, and provides a low-dimensional representation which can be then be re-used. We evaluate the DDE approach by evolving solutions for inverse kinematics of a planar arm (200 joint angles) and for gaits of a 6-legged robot in action space (a sequence of 60 positions for each of the 12 joints). We show that the DDE approach not only accelerates and improves optimization, but produces a powerful encoding that captures a bias for high performance while expressing a variety of solutions.