  Learning to Optimize (L2O) has drawn increasing attention as it often
remarkably accelerates the optimization procedure of complex tasks by
``overfitting" specific task type, leading to enhanced performance compared to
analytical optimizers. Generally, L2O develops a parameterized optimization
method (i.e., ``optimizer") by learning from solving sample problems. This
data-driven procedure yields L2O that can efficiently solve problems similar to
those seen in training, that is, drawn from the same ``task distribution".
However, such learned optimizers often struggle when new test problems come
with a substantially deviation from the training task distribution. This paper
investigates a potential solution to this open challenge, by meta-training an
L2O optimizer that can perform fast test-time self-adaptation to an
out-of-distribution task, in only a few steps. We theoretically characterize
the generalization of L2O, and further show that our proposed framework (termed
as M-L2O) provably facilitates rapid task adaptation by locating well-adapted
initial points for the optimizer weight. Empirical observations on several
classic tasks like LASSO and Quadratic, demonstrate that M-L2O converges
significantly faster than vanilla L2O with only $5$ steps of adaptation,
echoing our theoretical results. Codes are available in
https://github.com/VITA-Group/M-L2O.
