μLO: Compute-Efficient Meta-Generalization of Learned Optimizers
Authors: name: Benjamin Thérien, name: Charles-Étienne Joseph, name: Boris Knyazev, name: Edouard Oyallon, name: Irina Rish, name: Eugene Belilovsky

Learned optimizers (LOs) can significantly reduce the wall-clock training
time of neural networks, substantially reducing training costs. However, they
often suffer from poor meta-generalization, especially when training networks
larger than those seen during meta-training. To address this, we use the
recently proposed Maximal Update Parametrization (muP), which allows
zero-shot generalization of optimizer hyperparameters from smaller to larger
models. We extend muP theory to learned optimizers, treating the
meta-training problem as finding the learned optimizer under muP. Our
evaluation shows that LOs meta-trained with muP substantially improve
meta-generalization as compared to LOs trained under standard parametrization
(SP). Notably, when applied to large-width models, our best muLO, trained
for 103 GPU-hours, matches or exceeds the performance of VeLO, the largest
publicly available learned optimizer, meta-trained with 4000 TPU-months of
compute. Moreover, muLOs demonstrate better generalization than their SP
counterparts to deeper networks and to much longer training horizons (25 times
longer) than those seen during meta-training.