[From Bill Powers (2002.05.20.1156 MDT)]
Martin Taylor 2002.05.20 09:38--
>The "Ass between haystacks" issue strikes me as being not well solved
by an ad-hoc gain-reducer control system, or by the UEC. Why? Because
it seems like one of a much larger class of choice problems, such as
"do I take the bike, the car, or the bus to work." You can't do more
than one of those, but for any of them, if the others were not
available, the gain would be quite sufficient to make the event
happen.
So you're stuck somewhere among the goals unless something happens to make
the situation unstable. That's what the NEC (formerly UEC) does. If the
gain of any system rises as the distance to its goal decreases, and falls
as the distance increases, then any move toward one goal will weaken the
gain for all systems with opposed goals while increasing the gain toward
that one goal. If the gain-changing effect is very small, so the gain
changes only slightly with distance, this will simply make the stable
virtual reference position a little less stable. But if the gain changes
rapidly with error for each system, the compomise position will become
unstable: any small perturbation will cause the gain in that direction to
increase and the increase will cause an even greater move in that
direction, until one system has acquired full control, and the others are
exerting only negligible efforts away from that goal.
If I choose the car, it doesn't feel as if there is a conflict
situation any more. The "take the bus" and "take the bike" control
systems aren't still tugging me away from the car--they simply aren't
active at all. It seems much more like a switch than a gain reduction.
The switching effect also arises from the relationship of gain change to
error change. This will all be clearer in a model. The model can easily be
set up with multiple goals.
Who is going to do it? Bill W., since you've started, do you want to carry
it on? Or Rick? Or I? Somebody volunteer. If not Bill W., then Rick. If
not Rick then me. Or anyone else if I'm overlooking a willing programmer.
Of course, this is just intuition, but how could you set up a test to
compare a switch with a drastic positive-feedback gain reduction
mechanism (a flip-flop, in other words)?
In the model I'm proposing, you move from having a small bias to a full
flip-flop action just by varying the sensitivity of the gain-changing system.
>I don't think either example speaks to the existence or non-existence
of the UEC. The "Ass" example seems even to be a counter-example, in
that if you remove one haystack, the ass still is going to go to the
other at a pretty high gain, and would do, even if it had initially
been put a long way beyond the magically removed haystack.
I could argue that Dollard & Miller's (??) "approach grandient" experiment
shows the effect even when there is only one haystack ( one food dish -- I
don't think they tried it with two). Of course that was 60-odd years ago
and with rats. The gain at large distances is low, but not zero. And as the
move toward the goal progresses (with no opposition) it would speed up.
Best,
Bill P.