Cascaded Transfer: Learning Many Tasks under Budget Constraints

In distributed applications, such as energy demand forecasting at the substation level or federated learning, a large number of related tasks must be learned by different models, while the exact task relationships are unknown. We propose the novel Cascaded Transfer Learning (CTL) paradigm in which model parameters cascade hierarchically through tasks organized as a rooted tree, respecting a global training budget. Starting from a source task, the tree specifies the order in which tasks are learned and refined, with the budget allocated along its branches. We design cascade mechanisms based on spanning trees that connect all tasks by minimizing an objective combining pairwise task distances and the available training budget, which yield geometry-aware and depth-bounded transfer graphs. We theoretically characterize how transfer errors accumulate and attenuate along cascade paths: errors introduced at any upstream node are contracted by every downstream refinement, and balanced tree topologies bound this accumulation. Experiments on synthetic and real many-task settings, time-series forecasting and image classification, show that CTL enables more accurate and cost-effective adaptation across large task collections than alternative approaches, with the largest gains at the tightest budgets.