Production Engineering: Mini-Batch Training

The problem, from first principles

05-training-loop uses every row for every update, which is clear but becomes expensive as datasets grow. Mini-batches let training update from small groups while still eventually seeing the whole dataset. The practical challenge is preserving feature-target pairing, handling the final short group, and making shuffled training reproducible when a seed is supplied.

From theory to code

Implement train_linear_regression_production. Use the earlier MSE gradient and gradient-descent step for one shuffled batch at a time; Theory explains the epoch-level ordering and the single long-lived random generator.

Constraints

• input has shape (n_samples, in_features) and target has shape (n_samples,).
• Return zero-initialized then trained weight with shape (1, in_features) and bias with shape (1,).
• Reshape targets to (n_samples, 1) once before training.
• Shuffle sample indices once per epoch and take one step for each batch, including a final batch smaller than batch_size.
• Construct np.random.default_rng(seed) once before the epoch loop.
• The same non-None seed and arguments must produce bit-identical parameters; seed=None must not force a fixed order.
• Slice only the current batch from input and target; reuse mse_gradient and gd_step.

Hints

Open one at a time. Each gives away a little more than the last.