Abstract Learning to optimize (L2O) is a technique that uses neural networks to learn optimization algorithms automatically. While it holds promise for diverse optimization problems, achieving consistently ideal results remains a challenge. Typically, L2O through a parameterized optimization method (i.e. “ optimizer”) learns from training samples and generalizes to test tasks with the same distribution. However, the new test tasks usually have some deviation from the training set distribution. In this case, the generic L2O methods may not produce good optimization results. Thus, we introduce a step-size control mechanism based on the generic L2O to solve the common problem of insufficient control of the iteration amplitude in L2O and adopt different update strategies for various optimization problems to adapt to complex optimization scenarios. Additionally, we also innovatively use the gated recurrent unit network as the core model of the optimizer to achieve better optimization results. Finally, the experimental outcomes from numerical simulations and real-world datasets show that our proposed methods are significantly better than other optimization algorithms.