When choosing batch sizes in machine learning, how does size affect learning rate?

Larger batch sizes require smaller learning rates because the dynamics of gradient descent are influenced by the size of the batch being used for training. When using larger batches, the gradients computed tend to be more stable and less noisy because they average out the variability present in the individual samples. Consequently, since the gradients are more precise, using a larger batch allows for smaller learning rates, which can lead to more stable convergence and avoid overshooting the optimal solution.

Moreover, with larger batches, there's a reduced variance in the parameter updates compared to smaller batches. Therefore, a smaller learning rate is preferable to ensure that each update is more deliberate and refined, minimizing the risk of diverging from the optimal parameter values. This adjustment effectively balances the learning process, allowing the model to learn effectively without instability.

In contrast, smaller batch sizes produce noisier gradient estimates, which can benefit from a larger learning rate that can help the model traverse the parameter space more aggressively and escape local minima. Hence, the interaction between batch size and learning rate is critical in shaping the training dynamics of machine learning models.