Recognition of defects in concrete infrastructure, especially in bridges, is a costly and time consuming crucial first step in the assessment of the structural integrity. Large variation in appearance of the concrete material, changing illumination and weather conditions, a variety of possible surface markings as well as the possibility for different types of defects to overlap, make it a challenging real-world task. In this work we introduce the novel COncrete DEfect BRidge IMage dataset (CODEBRIM) for multi-target classification of five commonly appearing concrete defects. We investigate and compare two reinforcement learning based meta-learning approaches, MetaQNN and efficient neural architecture search, to find suitable convolutional neural network architectures for this challenging multi-class multi-target task. We show that learned architectures have fewer overall parameters in addition to yielding better multi-target accuracy in comparison to popular neural architectures from the literature evaluated in the context of our application.