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gridworld.py
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from samba.dcerpc.misc import policy_handle
__author__ = 'nick'
# Value iteration algorithm for a small 4*4 gridworld with 4 move actions. Goal state is state (4,4)
import mdptoolbox as mdp
import numpy as np
# We have four actions. Move north, move south, move east and move west
P = np.zeros((4, 4, 4))
# Populate the transition probability per action
for i in range(4):
for j in range(4):
for k in range(4): # For each action
if k == 0: # Action move north
if i == 0:
P[i, j, k] = 1
else:
P[i-1, j, k] = 1
elif k == 1: # Action move south
if i == 3:
P[i, j, k] = 1
else:
P[i+1, j, k] = 1
elif k == 2: # Action move east
if j == 3:
P[i, j, k] = 1
else:
P[i, j+1, k] = 1
elif k == 3: # Action move west
if j == 0:
P[i, j, k] = 1
else:
P[i, j-1, k] = 1
# print ("Action move north:")
# print(P[:, :, 0])
# print ("Action move south:")
# print(P[:, :, 1])
# print ("Action move east:")
# print(P[:, :, 2])
# print ("Action move west:")
# print(P[:, :, 3])
# Populate the reward function
R = np.zeros((4, 4, 4))
goali = 3
goalj = 3
for i in range(4):
for j in range(4):
for k in range(4): # For each action of this state
if k == 0: # Action move north
if i == 0:
nexti = 0
else:
nexti = i - 1
nextj = j
if nexti == goali and nextj == goalj:
R[i, j, k] = 100
else:
R[i, j, k] = -1
if nexti == 2 and nextj == 2:
R[i, j, k] = -1000
if k == 1: # Action move south
if i == 3:
nexti = i
else:
nexti = i + 1
nextj = j
if nexti == goali and nextj == goalj:
R[i, j, k] = 100
else:
R[i, j, k] = -1
if nexti == 2 and nextj == 2:
R[i, j, k] = -1000
if k == 2: # Action move east
if j == 3:
nextj = j
else:
nextj = j + 1
nexti = i
if nexti == goali and nextj == goalj:
R[i, j, k] = 100
else:
R[i, j, k] = -1
if nexti == 2 and nextj == 2:
R[i, j, k] = -1000
if k == 3: # Action move west
if j == 0:
nextj = j
else:
nextj = j - 1
nexti = i
if nexti == goali and nextj == goalj:
R[i, j, k] = 100
else:
R[i, j, k] = -1
if nexti == 2 and nextj == 2:
R[i, j, k] = -1000
# print(R[:,:,0])
# print(R[:,:,1])
# print(R[:,:,2])
# print(R[:,:,3])
# Perform value iteration
# Initialisation
theta = 0.00001
gamma = 0.9
V = np.zeros((4,4))
while True:
delta = 0
oldV = V
for i in range(4):
for j in range(4):
v = V[i, j]
V[i, j] = 0
for k in range(4):
if k == 0: # Action move north
if i == 0:
nexti = 0
else:
nexti = i - 1
nextj = j
if k == 1: # Action move south
if i == 3:
nexti = i
else:
nexti = i + 1
nextj = j
if k == 2: # Action move east
if j == 3:
nextj = j
else:
nextj = j + 1
nexti = i
if k == 3: # Action move west
if j == 0:
nextj = j
else:
nextj = j - 1
nexti = i
tmpVal = R[i, j, k] + gamma*V[nexti,nextj]
if tmpVal > V[i,j]:
V[i,j] = tmpVal
if delta < abs(v - V[i, j]):
delta = abs(v - V[i, j])
if delta < theta:
break
print(V)
# Calculate the policy
policy = np.zeros((4,4,4))
for i in range(4):
for j in range(4):
values = np.zeros(4)
for k in range(4):
if k == 0: # Action move north
if i == 0:
nexti = 0
else:
nexti = i - 1
nextj = j
if k == 1: # Action move south
if i == 3:
nexti = i
else:
nexti = i + 1
nextj = j
if k == 2: # Action move east
if j == 3:
nextj = j
else:
nextj = j + 1
nexti = i
if k == 3: # Action move west
if j == 0:
nextj = j
else:
nextj = j - 1
nexti = i
values[k] = R[i,j,k] + gamma*V[nexti,nextj]
max = np.amax(values)
idx = np.argwhere(values == max).flatten().tolist()
prob = 1.0/len(idx)
for k in range(len(idx)):
policy[i, j, idx[k]] = prob
print(policy[:,:,0])
print(policy[:,:,1])
print(policy[:,:,2])
print(policy[:,:,3])
P = np.zeros((4,16,16))
for i in range(4): # For each action
for j in range(4):
for k in range(4):
if i == 0:
if j == 0:
nextj = j
else:
nextj = j - 1
nextk = k
if i == 1:
if j == 3:
nextj = j
else:
nextj = j + 1
nextk = k
if i == 2:
if k == 3:
nextk = k
else:
nextk = k + 1
nextj = j
if i == 3:
if k == 0:
nextk = k
else:
nextk = k - 1
nextj = j
P[i,j*4+k,nextj*4+nextk] = 1
print(P[0,:,:])
R = np.zeros((4, 16))
for i in range(4):
for j in range(4):
for k in range(4):
if i == 0:
if j == 0:
nextj = j
else:
nextj = j - 1
nextk = k
if i == 1:
if j == 3:
nextj = j
else:
nextj = j + 1
nextk = k
if i == 2:
if k == 3:
nextk = k
else:
nextk = k + 1
nextj = j
if i == 3:
if k == 0:
nextk = k
else:
nextk = k - 1
nextj = j
if nextj == goali and nextk == goalj:
R[i,j*4+k] = 100
else:
R[i,j*4+k] = -1
if nextj == 2 and nextk == 2:
R[i,j*4+k] = -1000
R = R.transpose()
print(R)
vi = mdp.mdp.ValueIteration(P, R, 0.9)
vi.setVerbose()
vi.run()
print(vi.V)
print(vi.policy) # result is (0, 0, 0)
print(vi.max_iter)