def to_instance(game):
((index,U),demonstrated) = game
(M,actions,_) = index
N = len(actions)
K = U[0].shape[1]
deviation_offset = [0]*N
offset = 0
for i in range(N):
deviation_offset[i] = offset
offset = offset + actions[i]*(actions[i]-1)
deviations = offset
A = []
row = []
col = []
for outcome in range(M):
for i in range(N):
action = indexing.unindex(index, outcome)
x = action[i]
for y in range(actions[i]):
if x != y:
outcomep = indexing.reindex(index, outcome, i, y)
deviation = deviation_offset[i] + (actions[i]-1)*x + y
if x < y:
deviation = deviation - 1
for k in range(K):
A.append(U[i][outcomep,k] - U[i][outcome,k])
row.append(outcome)
col.append(K*deviation+k)
return (demonstrated, K, scipy.sparse.csr_matrix((A,(row,col)), shape=(M, K*deviations)))
def solve(game, c, w, opt):
(index, U) = game
(M, actions, _) = index
N = len(actions)
K = U[0].shape[1]
deviation_offset = [0] * N
offset = 0
for i in range(N):
deviation_offset[i] = offset
offset = offset + actions[i] * (actions[i] - 1)
deviations = offset
Uw = zeros((M, N))
for outcome in range(M):
for i in range(N):
Uw[outcome, i] = dot(U[i][outcome], w)
cp = zeros(M)
for outcome in range(M):
for i in range(N):
cp[outcome] += c[i] * Uw[outcome, i]
R = zeros((M, deviations))
for outcome in range(M):
for i in range(N):
action = indexing.unindex(index, outcome)
x = action[i]
for y in range(actions[i]):
if x != y:
outcomep = indexing.reindex(index, outcome, i, y)
deviation = deviation_offset[i] + (actions[i] - 1) * x + y
if x < y:
deviation = deviation - 1
R[outcome, deviation] = Uw[outcomep, i] - Uw[outcome, i]
def predict(x):
regrets = cp - dot(R, x)
offset = regrets.max()
sigma = exp(regrets - offset)
Z = sum(sigma)
return sigma / Z
def gradient(x):
sigma = predict(x)
g = dot(sigma, R)
return g
return predict(opt(deviations, gradient))
def solve(game, c, w, opt):
(index,U) = game
(M,actions,_) = index
N = len(actions)
K = U[0].shape[1]
deviation_offset = [0]*N
offset = 0
for i in range(N):
deviation_offset[i] = offset
offset = offset + actions[i]*(actions[i]-1)
deviations = offset
Uw = zeros((M, N))
for outcome in range(M):
for i in range(N):
Uw[outcome,i] = dot(U[i][outcome], w)
cp = zeros(M)
for outcome in range(M):
for i in range(N):
cp[outcome] += c[i]*Uw[outcome,i]
R = zeros((M, deviations))
for outcome in range(M):
for i in range(N):
action = indexing.unindex(index, outcome)
x = action[i]
for y in range(actions[i]):
if x != y:
outcomep = indexing.reindex(index, outcome, i, y)
deviation = deviation_offset[i] + (actions[i]-1)*x + y
if x < y:
deviation = deviation - 1
R[outcome,deviation] = Uw[outcomep,i] - Uw[outcome,i]
def predict(x):
regrets = cp - dot(R,x)
offset = regrets.max()
sigma = exp(regrets-offset)
Z = sum(sigma)
return sigma/Z
def gradient(x):
sigma = predict(x)
g = dot(sigma, R)
return g
return predict(opt(deviations, gradient))
def create(N):
assert N > 1
actions = [4] * N
idx = indexing.create(actions)
(M, _, _) = idx
U = [zeros((M, 4)) for i in range(N)]
for outcome in range(M):
a = indexing.unindex(idx, outcome)
left = 0
back = 0
for x in a:
if x % 2 == 0:
left += 1
if x // 2 == 0:
back += 1
v = array([1.5 + .2 * N, 9.0, 1.0 / 8.0 + 0.04 * N, 7 + 0.4 * N])
for i in range(N):
if a[i] % 2 == 0:
u = v + array([1.0, 1.5, 1.0 / 20.0, 2.0])
else:
u = v + array([
1.0 + 2.0 * left, 1.0, 1.0 / 20.0 + 0.04 * left,
1.5 + .4 * left
])
if a[i] // 2 == 0:
u = v + array([
6.0 + 0.5 * back, 12.0, 1.0 / 7.0 + 0.01 * back,
10.0 + 3.0 * back
])
else:
u = v + array([2.0, 20.0, 1.0 / 8.0, 15.0])
U[i][outcome, :] = -u
return (idx, U)
def to_instance(game):
((index, U), demonstrated) = game
(M, actions, _) = index
N = len(actions)
K = U[0].shape[1]
deviation_offset = [0] * N
offset = 0
for i in range(N):
deviation_offset[i] = offset
offset = offset + actions[i] * (actions[i] - 1)
deviations = offset
A = []
row = []
col = []
for outcome in range(M):
for i in range(N):
action = indexing.unindex(index, outcome)
x = action[i]
for y in range(actions[i]):
if x != y:
outcomep = indexing.reindex(index, outcome, i, y)
deviation = deviation_offset[i] + (actions[i] - 1) * x + y
if x < y:
deviation = deviation - 1
for k in range(K):
A.append(U[i][outcomep, k] - U[i][outcome, k])
row.append(outcome)
col.append(K * deviation + k)
return (demonstrated, K,
scipy.sparse.csr_matrix((A, (row, col)),
shape=(M, K * deviations)))