  We study the problem of multi-task non-smooth optimization that arises
ubiquitously in statistical learning, decision-making and risk management. We
develop a data fusion approach that adaptively leverages commonalities among a
large number of objectives to improve sample efficiency while tackling their
unknown heterogeneities. We provide sharp statistical guarantees for our
approach. Numerical experiments on both synthetic and real data demonstrate
significant advantages of our approach over benchmarks.
