ES-ENAS: Blackbox Optimization over Hybrid Spaces via Combinatorial and Continuous Evolution

We consider the problem of efficient blackbox optimization over a large hybrid search space, consisting of a mixture of a high dimensional continuous space and a complex combinatorial space. Such examples arise commonly in evolutionary computation, but also more recently, neuroevolution and architecture search for Reinforcement Learning (RL) policies. In this paper, we introduce ES-ENAS, a simple joint optimization procedure by combining Evolutionary Strategies (ES) and combinatorial optimization techniques in a highly scalable and intuitive way, inspired by the \textit{one-shot} or \textit{supernet} paradigm introduced in Efficient Neural Architecture Search (ENAS). Our main insight is noticing that ES is already a highly distributed algorithm involving hundreds of blackbox evaluations which can not only be used for training neural network weights, but also for feedback to a combinatorial optimizer. Through this relatively simple marriage between two different lines of research, we are able to gain the best of both worlds, and empirically demonstrate our approach by optimizing BBOB functions over hybrid spaces as well as combinatorial neural network architectures via edge pruning and quantization on popular RL benchmarks. Due to the modularity of the algorithm, we also are able incorporate a wide variety of popular techniques ranging from use of different continuous and combinatorial optimizers, as well as constrained optimization.