>How often should you check your assumptions? If you check them too often
>then you may be wasting time that may be spent more constuctively
>creating meaning.
Of course there is a tradeoff (which is what the 2-armed bandit is
all about). The actual optimal frequency for checking your assumptions
probably depends on each individual assumption. Give me an example and
I'll tell you how often to check it :-) But seriously, I know of no
algorithm for figuring that out. You can probably define some broad
categories for assumptions: all-important metaphysical axioms
(e.g. objective reality exists), useful scientific premises (e.g.
Newton's laws are excellent approximations for most human-scale
situations), social assumptions (e.g. people hate it when you rip
them off), trivial statements (I remembered to bring my keys), and
perhaps several categories in between. Then, for each category, if
you find yourself wasting a lot of time verifying correct assumptions
you can cut back on the frequency for that category. Likewise, if you
discover you are wrong more often than you would like, increase the
frequence for that category. At least I think this is what I have
been doing unconsciously.
>> The 2-armed bandit is like its familiar single-armed Las Vegas counterpart.
>> Each arm has an associated probability of returning a cash prize, one is
>> higher than the other, but you don't know which is which. The dilemma is
>> how long you spend testing the bandit before deciding which arm is likely
>> the one with the higher probability (and, ipso facto, higher expected
>> value).
>
>Is your goal solely to determine which is the higher probability or is it
>to determine whether you can make money on the probability of one of the
>arms? If the former is your goal are there statistical methods to solve
>this problem?
Neither, your goal is to maximize your winnings. You cannot do that if you
spend all your time experimenting to see which arm is better. And, obviously,
you can't maximize winnings without experimenting at all (i.e. just picking
an arm at random and using it exclusively). Half the time you will luck out
and pick the best arm, but your expected winnings are suboptimal. So there
has to be an optimal tradeoff between experimenting and exploiting the
knowledge you gain.
Here's an interesting application: Say you want to get married but you are
unwilling to get a divorce. How many women should you date before proposing?
-- David McFadzean dbm@merak.com Memetic Engineer http://www.merak.com/~dbm/ Merak Projects Ltd.