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RL_Module_Velocity_MIMO_SMDP.py
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RL_Module_Velocity_MIMO_SMDP.py
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"""
Off-Policy model-free Q-learning with Upper Confidence Bound.
Rui Nian
Patch 1.04
Patch: Added Linear Interpolation
"""
import numpy as np
import random
from copy import deepcopy
class ReinforceLearning:
"""
states_start: Min value of states
states_end: Max value of states
states_interval: Distance between consecutive state values
actions_start: Min value of actions
actions_end: Max value of actions
actions_interval: Distance between consecutive state values
learning_rate: The speed the Q-table is uploaded. DEFAULT VALUE: 0.7
epsilon: Percentage of time random action taken. DEFAULT VALUE = 0.5
doe: Degree of exploration for UCB. Higher doe equates to higher exploration. DEFAULT VALUE = 1.2
Discount factor: Discounts future Q values due to uncertainty. DEFAULT VALUE = 0.95
eval_period: How many time steps between evaluation of RL. DEFAULT VALUE = 1
"""
def __init__(self, states_start, states_stop, states_interval, actions_start, actions_stop,
actions_interval, learning_rate=0.7, epsilon=0.5, doe=1.2, discount_factor=0.95, eval_period=1,
random_seed=None):
self.states = list(np.arange(states_start, states_stop, states_interval * 0.99))
self.actions = list(np.arange(actions_start, actions_stop, actions_interval * 0.99))
self.learning_rate_0 = learning_rate
self.learning_rate = learning_rate
self.discount_factor = discount_factor
self.epsilon_0 = epsilon
self.epsilon = epsilon
self.doe = doe
self.Q = np.zeros((len(self.states), len(self.actions)))
self.NT = np.zeros((len(self.states), len(self.actions)))
self.T = np.ones((len(self.states), len(self.actions)))
self.eval_period = eval_period
self.eval_feedback = 999
# State and action lists for multiple input multiple output systems
self.x1 = []
self.x2 = []
self.u1 = []
self.u2 = []
# SMDP Changes
# Last time RL action selection was evaluated
self.eval = -9999
# Should action selection be evaluated on the immediate next step
self.next_eval = False
self.beta = 0.1
# Seed the results for reproducability
if random_seed is not None:
random.seed(random_seed)
np.random.seed(random_seed)
@staticmethod
def rargmax(vector):
"""
Random argmax
vector: input of numbers
return: Index of largest number, breaking ties randomly
"""
m = np.amax(vector)
indices = np.nonzero(vector == m)[0]
return random.choice(indices)
"""
Load in user defined states rather than use auto-generated states
state: User defined list of states
"""
def user_states(self, state):
self.states = state
self.Q = np.zeros((len(self.states), len(self.actions)))
self.NT = np.zeros((len(self.states), len(self.actions)))
self.T = np.ones((len(self.states), len(self.actions)))
"""
Load in user defined actions rather than use auto-generated actions
action: User defined list of actions
"""
def user_actions(self, action):
self.actions = action
self.Q = np.zeros((len(self.states), len(self.actions)))
self.NT = np.zeros((len(self.states), len(self.actions)))
self.T = np.ones((len(self.states), len(self.actions)))
"""
Load in pre-trained Q, T, and NT matrices
action: User defined list of actions
"""
def user_matrices(self, q, t, nt):
self.Q = q
self.T = t
self.NT = nt
# Ensure the matrices have proper dimensions so RL can run
assert(self.Q.shape == (len(self.states), len(self.actions)))
assert(self.T.shape == (len(self.states), len(self.actions)))
assert(self.NT.shape == (len(self.states), len(self.actions)))
print('Loaded Q, T, and NT matrices successfully!')
"""
Detect current state
Cur_state: The current state
State: The state that the current state is closest to
"""
def state_detection(self, cur_state):
if type(cur_state) == np.float64:
state = min(self.states, key=lambda x_current: abs(x_current - cur_state))
state = self.states.index(state)
else:
state1 = min(self.x1, key=lambda x: abs(x - cur_state[0]))
state2 = min(self.x2, key=lambda x: abs(x - cur_state[1]))
state = self.states.index([state1, state2])
return state
"""
Calculating the learning rate for Reinforcement Learning
The decay is extremely slow and can be shown as:
e = e0 / 1 + (nt^(1/10) - 1), so it takes 970,299 visits to reach a eps value of 0.01 if e0 = 1
no_decay: Number of visits to a state-action pair before decay occurs
sa_pair: Number of times a state action pair was visited
min_eps_rate: The minimum epsilon rate. Default value = 0.001
"""
def epsilon_greedy(self, no_decay, sa_pair, min_eps_rate=0.001):
if sa_pair < no_decay:
pass
else:
self.epsilon = self.epsilon_0 / (1 + (sa_pair**(1/12) - 1))
self.epsilon = max(self.epsilon, min_eps_rate)
def action_selection(self, cur_state, last_input, no_decay, ep_greedy, time, min_eps_rate=0.001):
"""
Selects an action from a list of actions. Can be either UCB or epsilon-greedy
state: Current state of the process
action: Last performed action
last_input: The last state the system was in
no_decay: Amount of time for learning rate and epsilon to not decay
ep_greedy: Whether to perform epsilon greedy action selection or not
time: Simulation time
min_eps_rate: The minimum epsilon rate. Default value = 0.001
control: New set point / value for the item being controlled
action: Action index preformed at current time
"""
"""
UCB action selection portion
"""
state = self.state_detection(cur_state)
q_list = deepcopy(self.Q[state, :])
for action in range(len(self.actions)):
q_list[action] = q_list[action] + self.doe * np.sqrt(np.log(self.T[state, action]) /
(self.NT[state, action] + 0.01))
action = self.rargmax(q_list)
"""
Regular action selection portion
"""
# If epsilon greedy action is desired, calculate new epsilon value
if ep_greedy is True:
self.epsilon_greedy(no_decay, self.NT[state, action], min_eps_rate)
else:
self.epsilon = 0
q_list = deepcopy(self.Q[state, :])
# Returns the index of the action to be taken
number = np.random.rand()
if number < self.epsilon:
action = random.randint(0, len(q_list) - 1)
else:
action = self.rargmax(q_list)
# control = self.actions[action]
control = last_input + self.actions[action]
# Update feedback timer
self.feedback_evaluation(time)
return state, control, action
"""
Calculating the learning rate for Reinforcement Learning
no_decay: Number of visits to a state-action pair before decay occurs
sa_pair: Number of times a state action pair was visited
min_learn_rate: Minimum value for learning rate. Default value is 0.001
"""
def learn_rate(self, no_decay, sa_pair, min_learn_rate=0.001):
# During no decay period
if sa_pair < no_decay:
pass
# Decaying learning rate
else:
self.learning_rate = self.learning_rate_0 / (sa_pair - no_decay + 1)
self.learning_rate = max(self.learning_rate, min_learn_rate)
def matrix_update(self, action, rewards, old_state, cur_state, no_decay, tau, min_learn_rate=0.001):
"""
Q-value update
action: Index of the latest action
rewards: Reward received from the latest state action pair
old_state: The index of the state the system was in before the action was performed
new_state: The index of the state the system is in after the action was performed
no_decay: Amount of times state/action pair can be visited before decay in learning rate and epsilon occurs
min_learn_rate: Minimum value for learning rate. Default value is 0.0008
"""
# State detection for new state
new_state = self.state_detection(cur_state)
# Learning rate update
self.learn_rate(no_decay, self.NT[old_state, action], min_learn_rate)
# Update Q matrix using the Q-learning equation
smdp_discount = np.exp(-self.beta * tau)
reward_discount = np.divide(1 - smdp_discount, self.beta)
self.Q[old_state, action] = self.Q[old_state, action] + self.learning_rate * (reward_discount * rewards +
smdp_discount *
np.max(self.Q[new_state, :]) -
self.Q[old_state, action])
# Update memory matrix T
for element in range(self.T.shape[1]):
if element != action:
self.T[old_state, element] = self.T[old_state, element] + 1
else:
pass
# Update memory matrix NT
for j in range(self.NT.shape[1]):
if j == action:
self.NT[old_state, j] = self.NT[old_state, j] + 1
else:
pass
def feedback_evaluation(self, time):
"""
Determines when the next feedback evaluation period is
time: Current simulation time
"""
self.eval_feedback = time + self.eval_period - 1
def autosave(self, sim_time, time):
"""
Auto save Q, T, and NT matrices
sim_time: Current time step in simulation
time: After this many time steps, auto save the Q, T and NT matrices
"""
if sim_time % time == 0 and sim_time != 0:
print("Auto-saving... Iteration number: ", sim_time)
np.savetxt("Q_Matrix.txt", self.Q)
np.savetxt("T_Matrix.txt", self.T)
np.savetxt("NT_Matrix.txt", self.NT)
def interpolation(self, x):
"""
Linear Interpolation to get "continuous" actions
y = y0 + (x - x0) * (y1 - y0) / (x1 - x0)
"""
i = 0
# Find the state that x is less than (i.e., the upper bound of x).
while x > self.states[i]:
i += 1
if i > len(self.states):
raise ValueError("x is too big, cannot find element greater than x.")
x0 = self.states[i - 1]
x1 = self.states[i]
y0_index = np.argmax(self.Q[i - 1, :])
y1_index = np.argmax(self.Q[i, :])
y0 = self.actions[int(y0_index)]
y1 = self.actions[int(y1_index)]
y = y0 + (x - x0) * (y1 - y0) / (x1 - x0)
return y
def weighted_interpolation(self, x, eta=1):
"""
Weighted Linear Interpolation to use the Q-value information efficiently
y = y0 + (x - x0) * (ay1 - by0) / (x1 - x0)
a = eta * Q1 / Q0
b = eta * Q0 / Q1
"""
i = 0
# Find the state that x is less than (i.e., the upper bound of x).
while x > self.states[i]:
i += 1
if i > len(self.states):
raise ValueError("x is too big, cannot find element greater than x.")
x0 = self.states[i - 1]
x1 = self.states[i]
y0_index = np.argmax(self.Q[i - 1, :])
y1_index = np.argmax(self.Q[i, :])
y0 = self.actions[int(y0_index)]
y1 = self.actions[int(y1_index)]
q0 = deepcopy(self.Q[i - 1, int(y0_index)])
q1 = deepcopy(self.Q[i, int(y1_index)])
a = eta * (q1 / (q0 + 0.001))
b = eta * (q0 / (q1 + 0.001))
y = y0 + (x - x0) * (a * y1 - b * y0) / (x1 - x0)
return y
def __repr__(self):
"""
This output is used for debugging purposes. Prints the initialization code of the RL.
"""
return "ReinforceLearning(".format(len(self.states), len(self.actions))
def __str__(self):
"""
Meaningful output if this class is printed. Tells the users the amount of states and actions.
"""
return "RL controller with {} states and {} actions".format(len(self.states), len(self.actions))
class AdvantageLearning(ReinforceLearning):
"""
Most attributes are inherited from the main reinforcement learning class.
deltaT: Time step, this allows advantage learning to be more stable than RL in continuous processes where the change
in Q value is very small.
advantage: How much better is this action over other actions? Will also be normalized where the best action has a
0 advantage.
"""
def __init__(self, states_start, states_stop, states_interval, actions_start, actions_stop, actions_interval,
deltat=1, learning_rate=0.7, epsilon=0.5, doe=0.05, discount_factor=0.95, eval_period=1):
super().__init__(states_start, states_stop, states_interval, actions_start, actions_stop,
actions_interval, learning_rate, epsilon, doe, discount_factor, eval_period)
self.deltaT = deltat
self.advantage = np.random.uniform(-0.005, 0.005, [len(self.states), len(self.actions)])
"""
This output is used for debugging purposes. Prints the initialization code of the RL.
"""
def __repr__(self):
return "AdvantageUpdating(".format(len(self.states), len(self.actions))
"""
Meaningful output if this class is printed. Tells the users the amount of states and actions.
"""
def __str__(self):
return "Adv. Updating RL controller with {} states and {} actions".format(len(self.states), len(self.actions))
def norm_advantage(self):
for i in range(self.advantage.shape[0]):
mean = np.mean(self.advantage[i, :])
st_dev = np.std(self.advantage[i, :])
for j in range(self.advantage.shape[1]):
self.advantage[i, j] = (self.advantage[i, j] - mean) / st_dev
"""
Load in user defined states rather than use auto-generated states
state: User defined list of states
"""
def adv_user_states(self, state):
super().user_states(state)
self.advantage = np.random.uniform(-0.005, 0.005, [len(self.states), len(self.actions)])
"""
Load in user defined actions rather than use auto-generated actions
action: User defined list of actions
"""
def adv_user_actions(self, action):
super().user_actions(action)
self.advantage = np.random.uniform(-0.005, 0.005, [len(self.states), len(self.actions)])
"""
Load in pre-trained Q, T, and NT matrices
action: User defined list of actions
"""
def adv_user_matrices(self, q, t, nt, advantage):
super().user_matrices(q, t, nt)
self.advantage = advantage
# Ensure the matrices have proper dimensions so RL can run
assert (self.advantage.shape == (len(self.states), len(self.actions)))
def adv_action_selection(self, cur_state, last_input, no_decay, ep_greedy, time, min_eps_rate=0.001):
state = self.state_detection(cur_state)
adv_list = deepcopy(self.advantage[state, :])
for action in range(len(self.actions)):
adv_list[action] = adv_list[action] + self.doe * np.sqrt(np.log(self.T[state, action]) /
(self.NT[state, action] + 0.01))
action = self.rargmax(adv_list)
# If epsilon greedy action is desired, calculate new epsilon value
if ep_greedy is True:
self.epsilon_greedy(no_decay, self.NT[state, action], min_eps_rate)
else:
self.epsilon = 0
# Returns the index of the action to be taken
number = np.random.rand()
if number < self.epsilon:
action = random.randint(0, len(adv_list) - 1)
else:
action = action
control = last_input + self.actions[action]
# Update feedback timer
self.feedback_evaluation(time)
return control, state, action
"""
Update the advantage matrix
"""
def adv_update(self, state, action):
self.advantage[state, action] = self.Q[state, action] - np.mean(self.Q[state, :])
"""
If a random action is selected, the advantage matrix will be updated like this instead
"""
def random_adv_update(self, state, action):
self.advantage[state, action] = self.advantage[state, action] - max(self.advantage[state, :])
"""
Update the Q, T, NT and advantage matrices
"""
def adv_mat_update(self, action, rewards, old_state, cur_state, no_decay, min_learn_rate=0.0001):
# State detection for new state
new_state = self.state_detection(cur_state)
# Learning rate update
self.learn_rate(no_decay, self.NT[old_state, action], min_learn_rate)
# Update Q matrix using the Q-learning equation
self.Q[old_state, action] = self.Q[old_state, action] + self.learning_rate*(rewards + self.discount_factor *
np.max(self.Q[new_state, :])
- self.Q[old_state, action])
self.adv_update(old_state, action)
# self.norm_advantage(old_state)
# Update memory matrix T
for element in range(self.T.shape[1]):
if element != action:
self.T[old_state, element] = self.T[old_state, element] + 1
else:
pass
# Update memory matrix NT
for j in range(self.NT.shape[1]):
if j == action:
self.NT[old_state, j] = self.NT[old_state, j] + 1
else:
pass
def adv_autosave(self, sim_time, time):
super().autosave(sim_time, time)
if sim_time % time == 0 and sim_time != 0:
np.savetxt("Adv_Matrix.txt", self.advantage)