Re: computer-go: A problem with understanding lookahead

[Vincent Diepeveen <diep@xxxxxxxxx>]

DID YOU DO THE EXPERIMENT?

HOW ABOUT JUST TRYING, I EVEN GAVE AN 
EXPLANATION WHY IT WORKS!!

If you write down the alfabetasearch algorithm
in a mathetmatical way and you give each leaf
a random score, then write down till the bottom 
it's pretty simple why it works.

Because lost lines the winning side has more leafs with 
random scores hence he can maximize over more random 
numbers so there is a statistical bigger chance a line 
for him is better, then minimaxing this back to the root 
of course the chance is bigger that the backtracked score 
is a better score as a score given at the root.

This random search lemma applies not only to 
chess,go,draughts,shogi but about all serious board games.

For suicide chess it's a bit harder to directly write down
whether it works or not as minimizing searchspace there usually
is a good idea as the game is about getting rid of a part of
your material.


At 10:13 AM 1/18/01 -0500, you wrote:
>No offense, but this is stupid.  It is completely clear that
>n-ply search with random evaluation always plays a uniform
>random move.
>
>On Thu, 18 Jan 2001, Vincent Diepeveen wrote:
>
>> O yes there is a very good experiment on this
>> using a RANDOM evaluation.
>>
>> It appears that basically a random evaluation is going
>> to favour playing for space.
>>
>> so a 10 ply search random evaluation beats a program
>> with 1 ply random evaluation easily.
>>
>> This is also the case with GO as the goal of the game is
>> to optimize your own space. In other words: i beat my
>> opponent if i have more space as him.
>>
>> So the chance is bigger that a deeper search will increase your
>> winning chances.
>>
>> It is of course very QUESTIONABLE whether any depth of search
>> from a random evaluating program will EVER beat evan a simple
>> evaluation of a 1 ply searching go program.
>>
>> This is however a completely different question which still is
>> getting asked in all kind of different game playing programs.
>>
>> Very sure is that searching deeper is even with random evaluation going
>> to improve your program as long as you compare with the same
>> program at a smaller search depth.
>>
>> It took however a few years to discover that playing with a random
>> evaluation is a very very vague definition of playing for optimizing
>> the open space for the side to move, but some clever mathematicians
>> might write it down for you if they like Knuth can also work with
>> alfabeta in math.
>>
>> At 06:08 PM 1/17/01 -0500, you wrote:
>> >
>> >Yes, if your evaluation is totally out of whack I agree with you.  The
>> >power of  the search is that  it helps you reach  your  goals, even if
>> >your goals are stupid and out of line.  You might regret reaching your
>> >goals, but you get better at it with increasing search depth.
>> >
>> >So  I think the  thought experiment is valid.   If  your evaluation is
>> >this far out of  whack, then your  program really just doesn't have  a
>> >clue about  what is good  and what isn't and  thus a 1 ply search does
>> >the least damage.  In fact, maybe  you should just  change the sign of
>> >the evaluation!
>> >
>> >Don
>> >
>> >
>> >   From: "Mark Boon" <tesuji@xxxxxxxxxxxxxxxxx>
>> >
>> >   Well, your thought experiment is a good one in case of a reliable
>> evaluation
>> >   but it's not necessarily applicable in the case of an unreliable
>> evaluation.
>> >   Most search strategies rely on alfa-beta cut-off or something similar
>> to cut
>> >   down the tree-size which means you need to use evaluations to determine
>> what
>> >   to cut-off. If the evaluation is unreliable, the actual tree becomes
>> just as
>> >   unreliable. I think David has written several times here that he
>> experienced
>> >   that there's a point where more reading made it less reliable
because you
>> >   give it more opportunity to construct a false search-tree.
>> >
>> >   This is not the case in Chess because it's so much easier to make a
>> reliable
>> >   evaluation function.
>> >
>> >   Did anyone do any research on this? I mean, trying to quantify
>> theoretically
>> >   how much the evaluation has to be wrong to get a less reliable tree
at a
>> >   given depth. It might possibly be that it's only the case for really
very
>> >   unreliable functions, which will of course be the case for Go. That
>> would be
>> >   very useful information.
>> >
>> >       Mark
>> >
>> >   From: Don Dailey <drd@xxxxxxxxxxxxxxxxx>
>> >   To: <computer-go@xxxxxxxxxxxxxxxxx>
>> >   Sent: Wednesday, January 17, 2001 3:16 AM
>> >   Subject: Re: computer-go: A problem with understanding lookahead
>> >
>> >
>> >   >
>> >   > Lookahead  is a simple  concept  but very  few  people seem  to
have a
>> >   > significant grasp of what it is all about.
>> >   >
>> >   > In a  nutshell, if I have a  clearly defined goal  and a function
that
>> >   > recognizes  it, then in  a 2 player  perfect information game like
Go,
>> >   > Chess, Checkers, tic-tac-toe etc,  you can  try all possibilities
and
>> >   > discover that you  can either achieve your  goal or not.  There
are no
>> >   > exceptions,  this always works,  as long as the   goal can be
measured
>> >   > with 100% certainty.
>> >   >
>> >   > But with     imperfect evaluation  functions,    things are
different.
>> >   > Whether you search  deep or shallow,  your end-node evaluation is
just
>> >   > as imperfect.   So why does  passing it  down  the  tree makes it
any
>> >   > better?  Or does it?
>> >   >
>> >   > The answer is  that there  is  some magic   in the fact  that a
score
>> >   > actually survived the journey to the root node!  This single score
had
>> >   > to  compete with a vicious adversary  (during the min-max process)
who
>> >   > has  the opposite goal.  In  a nutshell, it  boils down  to this:
It's
>> >   > better to  be happy 20 moves  from now, that it  is  to be happy
right
>> >   > now!   That's the key to  mini-max  and why it  works.   It works
with
>> >   > humans too, consider:
>> >   >
>> >   > Let's do a strange  thought experiment.  Suppose,  as a Go player,
you
>> >   > had the  ability  to know exactly  how  you would feel  20 moves
later
>> >   > about any move you make.  Let's say I like a certain move, but a
voice
>> >   > in my head magically tells me that  20 moves later  I will not
like my
>> >   > position.  Let's say this ability  is integrated in a nicely
recursive
>> >   > fashion into your  brain, so that I know  that the  move I'm
currently
>> >   > thinking of playing is the culprit, not one I  might play later
(which
>> >   > is exactly what a search does.)  Would this ability  make you a
better
>> >   > player?  In my  opinion it would make a  very good  player
practically
>> >   > unbeatable, and a weak player much better.
>> >   >
>> >   > The "magic" seems to  be that if  you can survive  many moves  and
you
>> >   > still  like your position (which  a search with an evaluation
function
>> >   > proves because it  "knows" it will like  it's position n moves
later),
>> >   > then it's probably a pretty good move.
>> >   >
>> >   > People used to wonder, in Chess, why just  doing a single extra
ply of
>> >   > searching  was so powerful,  despite the fact that  it  SEEMED
like we
>> >   > needed a whole lot more just to get a little improvement.  But
this is
>> >   > why.  The "obvious" conclusions were completely wrong.  Even very
weak
>> >   > players  often realize  after  seeing  the opponents  reply that
they
>> >   > "screwed up."  I do this  in Go myself.   If 1 ply error free
searches
>> >   > were  built into the  human brain, every chess  player would
improve a
>> >   > class.
>> >   >
>> >   > I think it's true of Go too.  However we have to assume a
"reasonable"
>> >   > evaluation function and FULL WIDTH search for these things to be
true.
>> >   > Unfortunately, anything more than a 1 or 2 ply FULL WIDTH search
seems
>> >   > to be unreasonably difficult  in GO, if  you also require a
reasonably
>> >   > good evaluation function!
>> >   >
>> >   >
>> >   > Don
>> >   >
>> >   >
>> >   >
>> >   >
>> >   >    X-Sender: gl7@xxxxxxxxxxxxxxxxx
>> >   >    X-Mailer: QUALCOMM Windows Eudora Version 5.0.2
>> >   >    Date: Tue, 16 Jan 2001 21:03:22 +0100
>> >   >    From: "GL7: David Elsdon" <gl7@xxxxxxxxxxxxxxxxx>
>> >   >    References: <20010108235912Z4277-62332+78@xxxxxxxxxxxxxxxxx>
>> >   >    Mime-Version: 1.0
>> >   >    Sender: owner-computer-go@xxxxxxxxxxxxxxxxx
>> >   >    Precedence: bulk
>> >   >    Reply-To: computer-go@xxxxxxxxxxxxxxxxx
>> >   >    Content-Type: text/plain; charset="us-ascii"; format=flowed
>> >   >    Content-Length: 780
>> >   >
>> >   >    Hello all,
>> >   >
>> >   >    I have a serious problem with lookahead. I don't understand why it
>> >   works.
>> >   >    Why should the backed up values of a, say, 7 ply full width
>> alpha-beta
>> >   >    minimax search be any better than the values my evaluation
function
>> >   gives
>> >   >    me by simply evaluating the positions at ply 1. I can
understand that
>> >   if
>> >   >    the end of the game is in sight then lookahead is useful. I can
>> >   >    understand  that if I use a quiesence measure or some such and
only
>> >   >    evaluate positions when I know that my evaluation function will
work
>> >   best
>> >   >    then lookahead is useful. But if neither of these is the case then
>> does
>> >   >    lookahead help. Is there some way in which the backing up of
>> values and
>> >   >    minimaxing somehow reduces the error in the evaluations.
>> >   >
>> >   >    I really am seriously stuck with this one.
>> >   >
>> >   >    Cheers
>> >   >
>> >   >    David
>> >   >
>> >   >
>> >   >
>> >
>> >
>> >
>> >
>>
>
>
>