The development of artificial intelligence (AI) for science has led to the
emergence of learning-based research paradigms, necessitating a compelling
reevaluation of the design of multi-objective optimization (MOO) methods. The
new generation MOO methods should be rooted in automated learning rather than
manual design. In this paper, we introduce a new automatic learning paradigm
for optimizing MOO problems, and propose a multi-gradient learning to optimize
(ML2O) method, which automatically learns a generator (or mappings) from
multiple gradients to update directions. As a learning-based method, ML2O
acquires knowledge of local landscapes by leveraging information from the
current step and incorporates global experience extracted from historical
iteration trajectory data. By introducing a new guarding mechanism, we propose
a guarded multi-gradient learning to optimize (GML2O) method, and prove that
the iterative sequence generated by GML2O converges to a Pareto critical point.
The experimental results demonstrate that our learned optimizer outperforms
hand-designed competitors on training multi-task learning (MTL) neural network.

通过引入自动学习范式，我们介绍了一种新的自动优化多目标优化问题的学习方法，并提出了一种多梯度学习优化（ML2O）方法，通过自动学习多个梯度以更新方向。通过引入新的守卫机制，我们提出了一种守卫多梯度学习优化（GML2O）方法，并证明了 GML2O 生成的迭代序列收敛到一个 Pareto 临界点。实验结果表明，我们学习的优化器在训练多任务学习神经网络方面胜过手动设计竞争对手。