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Fair question. The weights moved, but moving is not the same as improving.
There is a way to check. Pour the same wine again and run it through the new weights.
The bottle is unchanged. The weights are the corrected ones.
guess $13.25
Before the correction it was 12 dollars. The correct price is 22.
So the error went from 10 dollars down to 8 dollars 75.
Better. Not fixed, but better.
That is not a disappointment, it is the design. A nudge of 10 percent is meant to be small.
The greedy method from earlier would have closed that gap completely in one move. Measured only on the bottle in front of us, cranking the weights wins.
The difference is what happens to everything else. A large correction can badly disturb what earlier bottles established. A small correction can disturb them too, but it moves the shared weights less violently. Many bottles then get a chance to pull those weights in their own directions.
The goal is not to protect every earlier guess from change. It is to let evidence from the whole set shape the same four numbers without allowing the newest bottle to seize complete control.
The rule doing that work is called the delta rule, delta being the mathematical word for a change. Bernard Widrow and Marcian Hoff published it in 1960. Error times unit times learning rate. Nothing more than the three numbers on the last slide.
# if you meet a squared error
Courses and papers usually describe this rule as minimising a squared error, where each miss is multiplied by itself before the misses are added up. It is the same rule you just used, scored a different way: this chapter adds plain dollar distances instead, because dollars are easier to read.
If you want the full picture, Google's machine learning course covers squared error and the alternative this chapter uses.
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