$μ$LO: Compute-Efficient Meta-Generalization of Learned Optimizers

Learned optimizers (LOs) can significantly reduce the wall-clock training time of neural networks, substantially reducing training costs. However, they can struggle to optimize unseen tasks (meta-generalize), especially when training networks wider than those seen during meta-training. To address this, we derive the Maximal Update Parametrization ($\mu$P) for two state-of-the-art learned optimizer architectures and propose a simple meta-training recipe for $\mu$-parameterized LOs ($\mu$LOs). Our empirical evaluation demonstrates that LOs meta-trained with our recipe substantially improve meta-generalization to wider unseen tasks when compared to LOs trained under standard parametrization (SP), as they are trained in existing work. We also empirically observe that $\mu$LOs trained with our recipe exhibit unexpectedly improved meta-generalization to deeper networks ($5\times$ meta-training) and surprising generalization to much longer training horizons ($25\times$ meta-training) when compared to SP LOs.