Bayesian Programming and Learning for Multi-Player Video Games ...

that this average “missed” (unpredicted or wrongly predicted) building can be very important
(for instance if it unlocks game changing technology). We think that this robustness to noise
is due to P(T |BT ) being precise with the amount of data that we used, and the build tree
structure.
Secondly, Figure 7.9 displays (at the bottom) the evolution of the predictive power (number
of buildings ahead from the build tree that it can predict) with the same increase of noise.
Predicting 2 building ahead with d = 1 (1 building of tolerance) gives that we predict right (for
sure) at least one building, at that is realized up to almost 50% of noise. In this case, this “one
building ahead” right prediction (with only 50% of the information) can give us enough time to
adapt our strategy (against a game changing technology).
7.5.3 Possible improvements
We recall that we used the prediction of build trees (or tech trees), as a proxy for the estimation
of an opponent’s technologies and production capabilities.
This work can be extended by having a model for the two players (the bot/AI and the
opponent):
P(BTbot, BTop, Oop,1:N, T, λ)
So that we could ask this (new) model:
P(BTbot|obsop,1:N, t, λ = 1)
This would allow for simple and dynamic build tree adaptation to the opponent strategy (dynamic
re-planning), by the inference path:
P(BTbot|obsop,1:N, t, λ = 1)
∝ �
P(BTbot|BTop) (learned)
BTop
×P(BTop)P(oop,1:N) (priors)
×P(λ|BTop, oop,1:N) (consistency)
×P(t|BTop) (learned)
That way, one can ask “what build/tech tree should I go for against what I see from my opponent”,
which tacitly seeks the distribution on BTop to break the complexity of the possible combinations
of O1:N. It is possible to not marginalize over BTop, but consider only the most probable(s)
BTop. In this usage, a filter on BTbot (as simple as P(BT t t−1
bot |BTbot ) can and should be added to
prevent switching build orders or strategies too often.
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