Online library learning in human visual puzzle solving

When learning a novel complex task, people often form efficient reusable abstractions that simplify future work, despite uncertainty about the future. We study this process in a visual puzzle task where participants define and reuse helpers -- intermediate constructions that capture repeating structure. In an online experiment, participants solved puzzles of increasing difficulty. Early on, they created many helpers, favouring completeness over efficiency. With experience, helper use became more selective and efficient, reflecting sensitivity to reuse and cost. Access to helpers enabled participants to solve puzzles that were otherwise difficult or impossible. Computational modelling shows that human decision times and number of operations used to complete a puzzle increase with search space estimated by a program induction model with library learning. In contrast, raw program length predicts failure but not effort. Together, these results point to online library learning as a core mechanism in human problem solving, allowing people to flexibly build, refine, and reuse abstractions as task demands grow.