Judge an Action Against What Was Expected, Not Against Zero
Last timeWhy the Estimate Is So Noisy
Anything not depending on the action can be subtracted from the weight for free, and subtracting what the position was already worth turns a return into a judgement.
The last lesson ended with a diagnosis. The weight on every action contains a
large part shared by all of them, carrying no information and all of the noise.
This lesson removes it, and the removal turns out to be free.
- the probabilities of the available actions, which add to one by definition
- the gradient of a constant, which is zero no matter how the parameters move
Why anything can be subtracted
Multiply that zero average by any quantity that does not depend on which action
was drawn and it is still zero. So that quantity can be subtracted from every
weight without changing the gradient in the slightest.
- any number that depends on the state but not on the action taken there
- what was earned, compared against what was expected rather than against zero
What to subtract
The obvious candidate is what the position was already worth, which the second
lesson called the value of the state. Subtracting it leaves the part of the weight
that differs between the actions available at that moment, which is the only part
that says anything about the decision.
The lesson stops here
4 more paragraphs to go
You have read the opening. The rest of the argument, the problems that check whether it landed, and the lines worth keeping at the end all come with a plan.
The first lesson of every course in the library reads the whole way through, free, so you can see exactly what the rest of them are.
See the planThe contentsThis is the reading half
Starting the course gives you your own copy of it. Every idea on every page has problems standing under it, marked with a reason rather than a tick, and any sentence you do not believe can be opened and argued with. None of that can happen on a page nobody owns.
The contents