Generative design problems often encompass complex action spaces that may be divergent over time, contain state-dependent constraints, or involve hybrid (discrete and continuous) domains. To address those challenges, this work introduces Design Strategy network (DSN), a data-driven deep hierarchical framework that can learn strategies over these arbitrary complex action spaces. The hierarchical architecture decomposes every action decision into first predicting a preferred spatial region in the design space and then outputting a probability distribution over a set of possible actions from that region. This framework comprises a convolutional encoder to work with image-based design state representations, a multi-layer perceptron to predict a spatial region, and a weight-sharing network to generate a probability distribution over unordered set-based inputs of feasible actions. Applied to a truss design study, the framework learns to predict the actions of human designers in the study, capturing their truss generation strategies in the process. Results show that DSNs significantly outperform nonhierarchical methods of policy representation, demonstrating their superiority in complex action space problems.