Learning Regularizers: Learning Optimizers that can Regularize

Learned Optimizers (LOs), a type of Meta-learning, have gained traction due to their ability to be parameterized and trained for efficient optimization. Traditional gradient-based methods incorporate explicit regularization techniques such as Sharpness-Aware Minimization (SAM), Gradient-norm Aware Minimization (GAM), and Gap-guided Sharpness-Aware Minimization (GSAM) to enhance generalization and convergence. In this work, we explore a fundamental question: $\mathbf{\text{Can}}\mathbf{\text{regularizers}}\mathbf{\text{be}}\mathbf{\text{learned?}}$ We empirically demonstrate that LOs can be trained to learn and internalize the effects of traditional regularization techniques without explicitly applying them to the objective function. We validate this through extensive experiments on standard benchmarks (including MNIST, FMNIST, CIFAR and Neural Networks such as MLP, MLP-Relu and CNN), comparing LOs trained with and without access to explicit regularizers. Regularized LOs consistently outperform their unregularized counterparts in terms of test accuracy and generalization. Furthermore, we show that LOs retain and transfer these regularization effects to new optimization tasks by inherently seeking minima similar to those targeted by these regularizers. Our results suggest that LOs can inherently learn regularization properties, \textit{challenging the conventional necessity of explicit optimizee loss regularization.