  Constrained bilevel optimization tackles nested structures present in
constrained learning tasks like constrained meta-learning, adversarial
learning, and distributed bilevel optimization. However, existing bilevel
optimization methods mostly are typically restricted to specific constraint
settings, such as linear lower-level constraints. In this work, we overcome
this limitation and develop a new single-loop, Hessian-free constrained bilevel
algorithm capable of handling more general lower-level constraints. We achieve
this by employing a doubly regularized gap function tailored to the constrained
lower-level problem, transforming constrained bilevel optimization into an
equivalent single-level optimization problem with a single smooth constraint.
We rigorously establish the non-asymptotic convergence analysis of the proposed
algorithm under the convexity of lower-level problem, avoiding the need for
strong convexity assumptions on the lower-level objective or coupling convexity
assumptions on lower-level constraints found in existing literature.
Additionally, the generality of our method allows for its extension to bilevel
optimization with minimax lower-level problem. We evaluate the effectiveness
and efficiency of our algorithm on various synthetic problems, typical
hyperparameter learning tasks, and generative adversarial network.
