tech tree / stats Reinvestment problems

In the 4X TBS genre it's typical to have a tech tree. In the RPG genre
it's typical to have a bunch of stats that you level up. In both cases,
fascists like myself spend a lot of time thinking about how to
optimally minimax the tech tree, so as to ramp up productivity /
military power the fastest and thereby dominate the globe / the dungeon
/ whatever. I call this the "Reinvestment" problem, although perhaps
others know it by a different name.

I find myself quite baffled as to how to analyze complex Reinvestment
problems. Usually a given investment is a tradeoff between costs now
and benefits later. Occasionally there's a straightforward solution,
i.e. some action is always profitable. But usually, the interactions of
game state are so complicated, that I really can't tell whether a given
course of action is more profitable or not. And so I end up iterating
through 4X TBSes over and over again, looking for the Golden Paths
through the game. (Current whipping boy is C-Evo.) I'm chagrined to
find that even as a smart human, I discover things upon long, repeated
iterations through such games.

I have wondered if an AI could do a better job of accounting than I
can, i.e. not get tired after playing for 5 hours, be more disciplined
about comparing the exact ongoing profitabilities of different games.
But it seems that such an AI would rely on a massive database of
previously played games. So often, the Reinvestment problem can be
decided only by trial and error.

Is there any better way to tackle such problems than to recognize them
as NP-complete?

The only thing I've been able to come up with is to create ad hoc
metrics for various kinds of "progress," and then do a search over the
cross product of all such notions of "progress." In other words, use my
human judgement to decide what kinds of things are to be searched, and
then search everything. Perhaps it can work if the metrics are
reasonably compressed / compact representations of complex data. It may
not matter, for instance, what's happening on most of the squares of
the board. If I subsample the game phenomena in some drastic way,
perhaps I will have ad hoc heuristics that are good enough. I am
wondering if the human mind works somewhat like this, in the way it
compresses data for long term memory.

I don't think the spontaneous, random generation of new ad hoc metrics
is going to work, because the game state is so complex that it's
probably like throwing darts at infinity. Small wonder evolution has
taken so long.

SeaFuncSpam.TakeThisOut@gmail.com wrote:
> I have wondered if an AI could do a better job of accounting than I
> can, i.e. not get tired after playing for 5 hours, be more disciplined
> about comparing the exact ongoing profitabilities of different games.

this post is rather to subscribe to follow-ups, and not to give an
exhausting answer, so you might want to skip it

it's very dumb idea.

suppose you have this coordinates:

spendings
^
|
|
+-------> investment options

than, your investments might look like this:

* *
* *
* * * *

(supposed to look like gaussian curve)

depending on game results, you adjust your spendings, like, ++
something
on the left

* * *
* *
* * *

and (since you have take extra resourcesfrom somewhere), -- something
on the right
* *
* *
* * * *

the results of this is (roughly) shifting gauss curve to the left (and,
perhaps, adjusting its width a litle). this is exactly what happens
with typical RBFN neuron, as it "learns".

so, the idea is to find the way and arrange your spendings so that
those you have to keep high (or low) at the same time would be placed
near each other, and then build RBFN in that space (not necessary 1D,
as in example above).