I have done a bit more testing and some things start to become a
little more clear to me. But I still have some open questions.
What I did was to rewrite my search such that I can set a constant
that determines after how many simulations the tree gets expanded.
And I have a switch to turn AMAF on or off. When the tree is expanded
always with no AMAF this should behave the same as my original search
algorithm. There's one caveat though. In the UCT formula sqrt( 2 *
(log(parent-visits) / (10* visits)) the number of visits can not be
zero of course. In my original implementation this was never the
case, as it always did a simulation and update of the visit count
upon expansion of a node. In the new implementation when expansion
occurs it creates many nodes with a visit-count of zero. So I have to
have a provision: if (visits==0) return MAX_VALUE; That will
guarantee it to behave the same as my original allgorithm. I have
tested enough games now that I'm reasonably confident that they are
indeed the same.
This provision overwhelmes any value in visited nodes. That is
actually by design of course, forcing all the moves at the current
depth to be visited at least once before expanding a level deeper.
But when using AMAF you want to postpone visiting nodes as long as
possible as long as you seem to have a very good candidate. I have a
strong suspicion that in my current tests UCT+AMAF shows a playing
level very close to just plain UCT simply because MAX_VALUE
overwhelmes any AMAF statistics gathered.
So I think if we're going to make AMAF part of the reference
definition of a UCT search bot, then we need some consensus about
what is a good formula for the 'virtual-value'. Especially for the
case where vists==0. I call it 'virtual-value' where a node-value is
virtual-value + win/visits. Part of virtual-value will be the UCT
value, part of it will be based on the virtual-win/virtual-visits
ratio. I can probably invent such a formula myself but I'd be
interested to hear what people that have had a UCT-AMAF bot a bit
longer are using that has been tried and tested.
Mark
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