cost functions

CSGnet Archive CSG1995
1

[From Bill Powers (951220.1245 MST)]

Fred Nickols (951220) --

     I'm not at all sure I get the point of your remark to Mr. Taylor
     about his not keeping the books. Were you equating cost with
     price? The favor of a reply is requested . . .

Yes I was, more or less facetiously. See below.

···

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Martin Taylor 951219 13:20 --

     What's in the environment has nothing to do with it. Or so I would
     assume. How would you ever know how much was in the environment?

and, earlier

know how much of the resource is left, as well as how much it is
getting,

     What does "how much it is getting" (of food pellets) have to do
     with how much of the resource (energy, time, number of
     paws...whatever) it has available? These things come together only
     in some sense of value.

In order to use depletion as a fraction of remaining resources to
compute cost, the computer must know (i.e., perceive) both quantities.
You hinted as much in asking how you would ever know how much of a
resource was in the environment. If the resource is inside the organism,
the same question applies. The organism must know both how much of the
expended resource remains and how much it is spending versus how much it
is getting, in order to evaluate cost as you define it. So you are
proposing a pretty complex model.

This whole discussion is moot, because all we need in order to make the
reinforcement model avoid runaway is to propose any cost function that
rises with behavior at a rate faster than proportionally. One parameter
can adjust the curvature, and the other the point of balance. This is an
ad-hoc model anyway, so it doesn't matter where you get the cost
function. Why go further into even vaguer and less quantitative ad-hoc
assumptions which don't lead to any specific form of nonlinearity
anyway? The problem at hand requires a specific function, not a
generality.
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Best,

Bill P.

2

[Martin Taylor 951221 00:45]

Bill Powers (951220.1245 MST)

This whole discussion is moot, because all we need in order to make the
reinforcement model avoid runaway is to propose any cost function that
rises with behavior at a rate faster than proportionally.

Agreed.

Why go further into even vaguer and less quantitative ad-hoc
assumptions which don't lead to any specific form of nonlinearity
anyway? The problem at hand requires a specific function, not a
generality.

I thought that even if SS hadn't provided a specific function, at least
I did. But I tempered that by saying essentially what you said above,
that the exact form of the function didn't matter, so long as it had
a sufficient increasing derivative, and that everyday exprience with
resource limitations suggest that our _perceived_ cost functions do
have that characteristic.

The organism must know both how much of the
expended resource remains and how much it is spending versus how much it
is getting,

I'm not so sure. All I see that it needs to "know" is how hard it is
to get a unit of the resource. I don't visualize the resource as being
like the money purse I used as an example, at least not necessarily.
The "money" could be strewn over the whole house, in nooks and crannies
and out on the open floor. There's no real need to know how much is
left provided that the reducing amount makes it harder to get more.
In my reply earlier to Shannon, I suggested that the real cost may well
be in the disturbances to the environmental feedback functions of other
control loops. But to talk about it in that way one has to be talking
within PCT, which isn't of much value to someone (not me) who might
want to model reinforcement.

Martin