The general phenomenon you’re noticing here is this: if you’re trying to pick some real number x to maximize f(x), you’ll start with some particular value of x and keep trying out different values. As long as f(x) seems to be increasing in x, you will increment x by larger and larger amounts. At some point, you shoot past the local maximum, and f(x) decreases. So now you start decrementing x, somewhat more slowly than you were previously incrementing it. Soon x becomes smaller than optimal, and you switch directions again. You’ll gradually approach the local maximum, but you actually cross it many times.
I second pjeby, your statement appears to be quite insightful.
If we take this to be an accurate summary… the best way I can think to how we might make the process more efficient or speedy is taking note that we are attempting to reach a maximum- which is probably why OP mentions that knowledge of the cycle helps.
I can’t imagine any other way than just… knowing the maximum, which is hardly something to expect when learning new things.
The general phenomenon you’re noticing here is this: if you’re trying to pick some real number x to maximize f(x), you’ll start with some particular value of x and keep trying out different values. As long as f(x) seems to be increasing in x, you will increment x by larger and larger amounts. At some point, you shoot past the local maximum, and f(x) decreases. So now you start decrementing x, somewhat more slowly than you were previously incrementing it. Soon x becomes smaller than optimal, and you switch directions again. You’ll gradually approach the local maximum, but you actually cross it many times.
I second pjeby, your statement appears to be quite insightful.
If we take this to be an accurate summary… the best way I can think to how we might make the process more efficient or speedy is taking note that we are attempting to reach a maximum- which is probably why OP mentions that knowledge of the cycle helps.
I can’t imagine any other way than just… knowing the maximum, which is hardly something to expect when learning new things.
That is brilliant. It even suggests a brain-hardware implementation that’d be consistent with PCT’s generalized notion of learning.