Early stopping on validation loss

Background

Early stopping is a simple, effective regularizer: you monitor validation loss each epoch and stop training once it stops improving, restoring the best checkpoint. This prevents the model from over-fitting in later epochs while saving compute. The key knob is patience — how many epochs of no improvement to tolerate before halting.

Problem statement

Implement early_stopping(val_losses, patience, min_delta) that scans the per-epoch validation losses and returns a tuple (stop_epoch, best_epoch):

• Track the best (lowest) loss seen. An epoch counts as an improvement only if its loss is below best_loss - min_delta.
• Count consecutive non-improving epochs. When that count reaches patience, stop and return the current epoch as stop_epoch.
• If the count never reaches patience, stop_epoch is the last epoch index.
• best_epoch is the epoch index of the lowest qualifying loss.

Input

• val_losses — list[float], validation loss at each epoch (0-indexed).
• patience — int, allowed consecutive epochs without improvement.
• min_delta — float, minimum decrease in loss to count as an improvement.

Output

A tuple (stop_epoch, best_epoch) of two ints.

Examples

Example 1

Input:  val_losses = [0.9, 0.8, 0.75, 0.77, 0.76, 0.77, 0.78], patience = 2, min_delta = 0.01
Output: (4, 2)

Explanation: the best loss 0.75 occurs at epoch 2. Epochs 3 and 4 do not improve on it by at least min_delta, so after 2 non-improving epochs training stops at epoch 4. The best epoch remains 2.

Constraints

• Improvement test is strict: loss < best_loss - min_delta.
• Reset the no-improvement counter to 0 whenever an improvement occurs.
• Stop as soon as the counter is >= patience.

Notes

• min_delta guards against declaring "improvement" for negligible noise-level decreases.
• Returning best_epoch lets the trainer roll back to the checkpoint with the lowest validation loss, not the (worse) checkpoint at the stopping epoch.