7.3. EVOLVING GAMES FOR DIFFERENT AGENTS 121
7.3.1 THE N -TUPLE BANDIT EVOLUTIONARY ALGORITHM
N
N
122 7. AUTOMATIC GENERAL GAME TUNING
N-Tuple Bandit
Fitness Landscape Model
Evolutionary
Algorithm
Noisy Fitness
Evaluator
current point
the model
Estimating UCB Values: an N -Tuple Approach
a
D argmax
a2A.s/
(
Q.s; a/ C C
s
ln N.s/
N.s; a/ C
)
:
Q.s; a/
C
N.s/
N.s; a/
a
7.3. EVOLVING GAMES FOR DIFFERENT AGENTS 123
super-bandits d
n
n
d
N N N N
N
j
.x/ j x
x
m
v
UCB
.x/ D
1
m
m
X
j D1
N
j
.x/
:
N d
N N 1 d 2
d
N
N
current point
N
124 7. AUTOMATIC GENERAL GAME TUNING
Algorithm 7.7 N
1
Input: n 2 N
C
Input: p 2 .0; 1/
Input: flipOnce 2 ftrue; falseg
Output: LModel
procedure n; p; flipOnce
t 0
LModel ¿
current 2 S
while t < nbEvals do
value fitnesscurrent
< current; value > LModel
Population LModel; current; n; p; flipOnce
current arg max
x2Population
v
UCB
.x/
t t C 1
end while
return LModel
procedure model; x; n; p; flipOnce
Population ¿
d jxj
for k 2 f1; : : : ; ng do
neighbor x
i 0
if flipOnce then
i f1; 2; : : : ; d g
for j 2 f1; : : : ; d g do
if i DD j or RAN < p then
neighbor
j
end if
end for
end if
neighbor Population
end for
return Population
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