The insights gained from the analysis of AdamW's implicit bias can indeed be extended to other adaptive optimization algorithms beyond just Adam. The key takeaway from the analysis is the understanding of how the optimization dynamics of AdamW lead to implicit regularization towards solutions with specific properties, such as bounded ℓ∞ norms.
By applying similar analysis techniques to other adaptive optimization algorithms, researchers can uncover the implicit biases and regularization effects of these algorithms. Understanding how different optimization algorithms bias the optimization process can provide valuable insights into their behavior and performance. This knowledge can be used to design and optimize new adaptive algorithms that leverage these implicit biases to improve training efficiency, generalization performance, and robustness of deep learning models.