DECN: EVOLUTION INSPIRED DEEP CONVOLUTION NETWORK FOR BLACK-BOX OPTIMIZATION

Abstract

We design a deep evolution convolution network (DECN) to overcome the poor generalization of an evolutionary algorithm in handling continuous black-box optimization. DECN is composed of two modules: convolution-based reasoning module (CRM) and selection module (SM), to move from hand-designed optimization strategies to learned optimization strategies. CRM produces a population closer to the optimal solution based on the convolution operators, and SM removes poor solutions. We also design a proper loss function to train DECN so as to force the random population to move near the optimal solution. The experimental results on one synthetic case and two real-world cases show the advantages of learned optimization strategies over human-designed black-box optimization baselines. DECN obtains good performance with deep structure but encounters difficulties in training. In addition, DECN is friendly to the acceleration with Graphics Processing Units (GPUs) and runs 102 times faster than unaccelerated EA when evolving 32 populations, each containing 6400 individuals.

1. INTRODUCTION

Optimization has been an old and essential research topic in history; Many tasks in computer vision, machine learning, and natural language processing can be abstracted as optimization problems. Moreover, many of these problems are black-box, such as neural architecture search (Elsken et al., 2019) and hyperparameter optimization (Hutter et al., 2019) . Various approaches, such as Bayesian optimization (Snoek et al., 2012) and evolutionary algorithms (EAs), including genetic algorithms (Jin et al., 2019; Khadka & Tumer, 2018; Zhang & Li, 2007; Such et al., 2017; Stanley et al., 2019) and evolution strategies (ES) (Wierstra et al., 2014; Vicol et al., 2021; Hansen & Ostermeier, 2001; Auger & Hansen, 2005; Salimans et al., 2017) , have been proposed to deal with these problems in the past. The generalization ability of EAs is poor. Faced with a new black-box optimization task, we need experts to redesign the EA's crossover, mutation, and selection operations to maximize its performance on the target task, resulting in a hand-designed EA with big application limitation. Most importantly, due to the limitation of expert knowledge, only little target function information is used to assist the design of EA, which makes it challenging to adapt to the target task. How to automatically design optimization strategies according to new tasks is crucial. EA is a generative optimization model that realizes the generation from a random population to an optimal solution by generating potential solutions and retaining good solutions. The task of automatically designing an optimization strategy is learning how to automatically generate and retain potential solutions. This paper first attempts to develop a deep evolution convolution network (DECN) to learn to exploit structure in the problem of interest so that DECN can automatically move a random population near the optimal solution for different black-box optimization tasks. DECN uses the process of EAs to guide the design of this new learning-to-optimize architecture. Like EAs, we propose two critical components of DECN to generate and select potential solutions: a convolution-based reasoning module (CRM) and a selection module (SM). For CRM, we need to ensure the exchange of information between individuals in the population to achieve the function of generating potential solutions. We design a lattice-like environment organizing the population into the modified convolution operators and then employ mirror padding (Goodfellow et al., 2016) to generate the potential offspring. SM need to update the population to survive the fittest solutions. We design SM based on a pairwise

