  We address the challenge of estimating the learning rate for adaptive
gradient methods used in training deep neural networks. While several
learning-rate-free approaches have been proposed, they are typically tailored
for steepest descent. However, although steepest descent methods offer an
intuitive approach to finding minima, many deep learning applications require
adaptive gradient methods to achieve faster convergence. In this paper, we
interpret adaptive gradient methods as steepest descent applied on
parameter-scaled networks, proposing learning-rate-free adaptive gradient
methods. Experimental results verify the effectiveness of this approach,
demonstrating comparable performance to hand-tuned learning rates across
various scenarios. This work extends the applicability of learning-rate-free
methods, enhancing training with adaptive gradient methods.
