Human culture relies on innovation: our ability to continuously explore how existing elements can be combined to create new ones. Innovation is not solitary, it relies on collective search and accumulation. Reinforcement learning (RL) approaches commonly assume that fully-connected groups are best suited for innovation. However, human laboratory and field studies have shown that hierarchical innovation is more robustly achieved by dynamic social network structures. In dynamic settings, humans oscillate between innovating individually or in small clusters, and then sharing outcomes with others. To our knowledge, the role of social network structure on innovation has not been systematically studied in RL. Here, we use a multi-level problem setting (WordCraft), with three different innovation tasks to test the hypothesis that the social network structure affects the performance of distributed RL algorithms. We systematically design networks of DQNs sharing experiences from their replay buffers in varying structures (fully-connected, small world, dynamic, ring) and introduce a set of behavioral and mnemonic metrics that extend the classical reward-focused evaluation framework of RL. Comparing the level of innovation achieved by different social network structures across different tasks shows that, first, consistent with human findings, experience sharing within a dynamic structure achieves the highest level of innovation in tasks with a deceptive nature and large search spaces. Second, experience sharing is not as helpful when there is a single clear path to innovation. Third, the metrics we propose, can help understand the success of different social network structures on different tasks, with the diversity of experiences on an individual and group level lending crucial insights.