# Is it harmful to set the learning rate of training a model to be too high if there is some decay function for the learning rate?

It is known that if $$\alpha$$ is set to high, then the cost function of the model may not converge. However, would a decaying of the learning rate provide some "tuning" of the $$\alpha$$ value during training ? In the sense that if you set a high learning rate but you also have some form of learning rate decay, then eventually $$\alpha$$ value would fall within the "just right" and "too low" range eventually. Is it better to then set an initial learning rate that is more "flexible" in the higher ranges rather than a learning rate that is too low ?