μLO: Compute-efficient meta-generalization of learned optimizers

Learned optimizers (LOs) have the potential to significantly reduce the wall-clock training time of neural networks. 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 (μP) for two state-of-the-art learned optimizer architectures and propose a simple meta-training recipe for μ-parameterized LOs (μLOs). 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) using the same compute budget. We also empirically observe that μLOs exhibit unexpectedly improved meta-generalization to deeper networks (5× meta-training) and surprising generalization to much longer training horizons (25× meta-training) when compared to SP LOs.