L3-09 · Optimization and learning

Learn¶

Optimization chooses parameters to reduce a stated loss function. A loss measures error under a chosen rule. In gradient descent, subtract a learning rate times the gradient from the current parameters. A small step follows a local direction of decreasing loss when regularity conditions hold.

The learning rate controls the step size. A large value can overshoot a minimum or make the procedure diverge. A very small value can require many steps. Some loss functions contain several local minima or nearly flat regions, so a small gradient need not certify a useful solution.

Learning requires more than minimizing training loss. Evaluate predictions on data that the fitting procedure did not use. For causal learning, also test whether the target intervention is identifiable. For quantum learning, include data encoding, measurement, and classical computation costs when comparing methods.

Practice¶

Check your understanding¶

What does a smaller training loss establish by itself?

• A. A correct causal model

• B. Better fit under that training objective

• C. A quantum computational advantage

Sources¶

This lesson draws on Illowsky & Dean, 2023Schölkopf et al., 2021.

Next: L3-10 · Estimation, intervals, and repeated tests