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mdp_matrix.py
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mdp_matrix.py
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import numpy as np
class MDP:
def __init__(self, T, S, R, A, act_list, terminal_states):
# State space
# Integer number of states
self.S = S
# Transition probabilities
# Form: np ndarray of shape (start_state, action, end_state)
self.T = np.array(T)
# Reward space
# Form: vector, rewards for each state
self.R = np.array(R)
# Action space
# integer, number of possible actions
self.A = A
# Possible actions in the MDP
self.actions = act_list
self.terminal_states = terminal_states
def is_terminal(self, s):
return s in self.terminal_states
class GridWorld(MDP):
def __init__(self, grid_size, reward_pos, terminal_states):
S = grid_size*grid_size
R = np.zeros((grid_size, grid_size))
# Each row of reward_pos is a tuple: x, y, reward
for row in reward_pos:
R[row[0], row[1]] = row[2]
R = R.flatten()
A = 4
act_list = ['S', 'E', 'N', 'W']
T = np.zeros((S, A, S))
for start_state in range(S):
state_i = start_state/grid_size
state_j = (start_state)%grid_size
# Actions indexed as: 0:S, 1:E, 2:N, 3:W
for act in range(A):
feas_grid = np.zeros((grid_size, grid_size))
if(act == 0 ):
if(state_i+1 < grid_size):
feas_grid[state_i+1, state_j] = 1
else:
feas_grid[state_i, state_j] = 1
elif(act == 1):
if(state_j+1 < grid_size):
feas_grid[state_i, state_j+1] = 1
else:
feas_grid[state_i, state_j] = 1
elif(act == 2):
if(state_i-1 >= 0):
feas_grid[state_i-1, state_j] = 1
else:
feas_grid[state_i, state_j] = 1
elif(act == 3):
if(state_j-1 >= 0):
feas_grid[state_i, state_j-1] = 1
else:
feas_grid[state_i, state_j] = 1
# Flatten the feasibility grid and assign to transition matrix
T[start_state, act, :] = feas_grid.flatten()
MDP.__init__(self, T, S, R, A, act_list, terminal_states)
class StochasticGridWorld(MDP):
def __init__(self, grid_size, reward_pos, terminal_states, p_success = 0.7):
S = grid_size*grid_size
R = np.zeros((grid_size, grid_size))
# Each row of reward_pos is a tuple: x, y, reward
for row in reward_pos:
R[row[0], row[1]] = row[2]
R = R.flatten()
A = 4
act_list = ['S', 'E', 'N', 'W']
T = np.zeros((S, A, S))
for start_state in range(S):
state_i = start_state/grid_size
state_j = (start_state)%grid_size
# Actions indexed as: 0:S, 1:E, 2:N, 3:W
for act in range(A):
feas_grid = np.zeros((grid_size, grid_size))
if(act == 0 ): # Going South
if state_i+1 < grid_size:
feas_grid[state_i+1, state_j] = p_success
else:
feas_grid[state_i, state_j] = p_success
if state_j+1 < grid_size:
feas_grid[state_i, state_j+1] = (1.0-p_success)/3.0
else:
feas_grid[state_i, state_j ] += (1.0-p_success)/3.0
if state_i-1 >= 0:
feas_grid[state_i-1, state_j] = (1.0-p_success)/3.0
else:
feas_grid[state_i, state_j ] += (1.0-p_success)/3.0
if state_j-1 >= 0:
feas_grid[state_i, state_j-1] = (1.0-p_success)/3.0
else:
feas_grid[state_i, state_j ] += (1.0-p_success)/3.0
elif(act == 1): # Going East
if state_j+1 < grid_size:
feas_grid[state_i, state_j+1] = p_success
else:
feas_grid[state_i, state_j] = p_success
if state_i+1 < grid_size:
feas_grid[state_i+1, state_j] = (1.0-p_success)/3.0
else:
feas_grid[state_i, state_j ] += (1.0-p_success)/3.0
if state_i-1 >= 0:
feas_grid[state_i-1, state_j] = (1.0-p_success)/3.0
else:
feas_grid[state_i, state_j ] += (1.0-p_success)/3.0
if state_j-1 >= 0:
feas_grid[state_i, state_j-1] = (1.0-p_success)/3.0
else:
feas_grid[state_i, state_j ] += (1.0-p_success)/3.0
elif(act == 2): # Going North
if state_i-1 >= 0:
feas_grid[state_i-1, state_j] = p_success
else:
feas_grid[state_i, state_j] = p_success
if state_j+1 < grid_size:
feas_grid[state_i, state_j+1] = (1.0-p_success)/3.0
else:
feas_grid[state_i, state_j ] += (1.0-p_success)/3.0
if state_i+1 < grid_size:
feas_grid[state_i+1, state_j] = (1.0-p_success)/3.0
else:
feas_grid[state_i, state_j ] += (1.0-p_success)/3.0
if state_j-1 >= 0:
feas_grid[state_i, state_j-1] = (1.0-p_success)/3.0
else:
feas_grid[state_i, state_j ] += (1.0-p_success)/3.0
elif(act == 3): # Going West
if state_j-1 >= 0:
feas_grid[state_i, state_j-1] = p_success
else:
feas_grid[state_i, state_j] = p_success
if state_j+1 < grid_size:
feas_grid[state_i, state_j+1] = (1.0-p_success)/3.0
else:
feas_grid[state_i, state_j ] += (1.0-p_success)/3.0
if state_i+1 < grid_size:
feas_grid[state_i+1, state_j] = (1.0-p_success)/3.0
else:
feas_grid[state_i, state_j ] += (1.0-p_success)/3.0
if state_i-1 >= 0:
feas_grid[state_i-1, state_j] = (1.0-p_success)/3.0
else:
feas_grid[state_i, state_j ] += (1.0-p_success)/3.0
# Flatten the feasibility grid and assign to transition matrix
T[start_state, act, :] = feas_grid.flatten()
MDP.__init__(self, T, S, R, A, act_list, terminal_states)
class WindyGridCliffMazeWorld(MDP):
def __init__(self, grid_size, reward_pos, terminal_states, traps, initial_state = [0,0], obstacles = [[i, j, 0] for i in range(10) for j in range(10)]
, p_success = 0.7):
S = grid_size*grid_size
R = np.zeros((grid_size, grid_size))
# Each row of reward_pos is a tuple: x, y, reward
for row in reward_pos:
R[row[0], row[1]] = row[2]
R = R.flatten()
for i in range(len(traps)):
if traps[i] == 1:
R[i] = -25
# Define actions
A = 4
act_list = ['S', 'E', 'N', 'W']
# Set start state value
self.initial_state = initial_state[0]*grid_size + initial_state[1]
T = np.zeros((S, A, S))
for start_state in range(S):
state_i = start_state/grid_size
state_j = (start_state)%grid_size
# Actions indexed as: 0:S, 1:E, 2:N, 3:W
for act in range(A):
feas_grid = np.zeros((grid_size, grid_size))
if traps[(state_i)*grid_size + state_j] == 1:
feas_grid[initial_state[0], initial_state[1]] = 1
else:
if(act == 0 ): # Going South
if state_i+1 < grid_size and obstacles[(state_i+1)*grid_size+state_j][2] != 1:
feas_grid[state_i+1, state_j] = p_success
else:
feas_grid[state_i, state_j] = p_success
if state_j+1 < grid_size and obstacles[(state_i)*grid_size+state_j+1][2] != 1:
feas_grid[state_i, state_j+1] = (1.0-p_success)/3.0
else:
feas_grid[state_i, state_j ] += (1.0-p_success)/3.0
if state_i-1 >= 0 and obstacles[(state_i-1)*grid_size+state_j][2] != 1:
feas_grid[state_i-1, state_j] = (1.0-p_success)/3.0
else:
feas_grid[state_i, state_j ] += (1.0-p_success)/3.0
if state_j-1 >= 0 and obstacles[(state_i)*grid_size+state_j-1][2] != 1:
feas_grid[state_i, state_j-1] = (1.0-p_success)/3.0
else:
feas_grid[state_i, state_j ] += (1.0-p_success)/3.0
elif(act == 1): # Going East
if state_j+1 < grid_size and obstacles[state_i*grid_size+state_j+1][2] != 1:
feas_grid[state_i, state_j+1] = p_success
else:
feas_grid[state_i, state_j] = p_success
if state_i+1 < grid_size and obstacles[(state_i+1)*grid_size+state_j][2] != 1:
feas_grid[state_i+1, state_j] = (1.0-p_success)/3.0
else:
feas_grid[state_i, state_j ] += (1.0-p_success)/3.0
if state_i-1 >= 0 and obstacles[(state_i-1)*grid_size+state_j][2] != 1:
feas_grid[state_i-1, state_j] = (1.0-p_success)/3.0
else:
feas_grid[state_i, state_j ] += (1.0-p_success)/3.0
if state_j-1 >= 0 and obstacles[(state_i)*grid_size+state_j-1][2] != 1:
feas_grid[state_i, state_j-1] = (1.0-p_success)/3.0
else:
feas_grid[state_i, state_j ] += (1.0-p_success)/3.0
elif(act == 2): # Going North
if state_i-1 >= 0 and obstacles[(state_i-1)*grid_size+state_j][2] != 1:
feas_grid[state_i-1, state_j] = p_success
else:
feas_grid[state_i, state_j] = p_success
if state_j+1 < grid_size and obstacles[(state_i)*grid_size+state_j+1][2] != 1:
feas_grid[state_i, state_j+1] = (1.0-p_success)/3.0
else:
feas_grid[state_i, state_j ] += (1.0-p_success)/3.0
if state_i+1 < grid_size and obstacles[(state_i+1)*grid_size+state_j][2] != 1:
feas_grid[state_i+1, state_j] = (1.0-p_success)/3.0
else:
feas_grid[state_i, state_j ] += (1.0-p_success)/3.0
if state_j-1 >= 0 and obstacles[(state_i)*grid_size+state_j-1][2] != 1:
feas_grid[state_i, state_j-1] = (1.0-p_success)/3.0
else:
feas_grid[state_i, state_j ] += (1.0-p_success)/3.0
elif(act == 3): # Going West
if state_j-1 >= 0 and obstacles[(state_i)*grid_size+state_j-1][2] != 1:
feas_grid[state_i, state_j-1] = p_success
else:
feas_grid[state_i, state_j] = p_success
if state_j+1 < grid_size and obstacles[(state_i)*grid_size+state_j+1][2] != 1:
feas_grid[state_i, state_j+1] = (1.0-p_success)/3.0
else:
feas_grid[state_i, state_j ] += (1.0-p_success)/3.0
if state_i+1 < grid_size and obstacles[(state_i+1)*grid_size+state_j][2] != 1:
feas_grid[state_i+1, state_j] = (1.0-p_success)/3.0
else:
feas_grid[state_i, state_j ] += (1.0-p_success)/3.0
if state_i-1 >= 0 and obstacles[(state_i-1)*grid_size+state_j][2] != 1:
feas_grid[state_i-1, state_j] = (1.0-p_success)/3.0
else:
feas_grid[state_i, state_j ] += (1.0-p_success)/3.0
# Flatten the feasibility grid and assign to transition matrix
T[start_state, act, :] = feas_grid.flatten()
MDP.__init__(self, T, S, R, A, act_list, terminal_states)