  Multi-Objective Bi-Level Optimization (MOBLO) addresses nested
multi-objective optimization problems common in a range of applications.
However, its multi-objective and hierarchical bilevel nature makes it notably
complex. Gradient-based MOBLO algorithms have recently grown in popularity, as
they effectively solve crucial machine learning problems like meta-learning,
neural architecture search, and reinforcement learning. Unfortunately, these
algorithms depend on solving a sequence of approximation subproblems with high
accuracy, resulting in adverse time and memory complexity that lowers their
numerical efficiency. To address this issue, we propose a gradient-based
algorithm for MOBLO, called gMOBA, which has fewer hyperparameters to tune,
making it both simple and efficient. Additionally, we demonstrate the
theoretical validity by accomplishing the desirable Pareto stationarity.
Numerical experiments confirm the practical efficiency of the proposed method
and verify the theoretical results. To accelerate the convergence of gMOBA, we
introduce a beneficial L2O neural network (called L2O-gMOBA) implemented as the
initialization phase of our gMOBA algorithm. Comparative results of numerical
experiments are presented to illustrate the performance of L2O-gMOBA.
