Notebook: Tabular Q-Learning
Reinforcement Learning Algorithms
Q-learning
1. Some terminologies
- State: s
- Available actions: a «««< HEAD
-
Greedy police: [\epsilon]
- Greedy police:
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- Learning rate: [\alpha]
- Discount factor: [\gamma]
- Maximum episodes
2. Sudo Algorithm:
- Initialize Q(s,a) arbirarily
- For each episode, repeat:
- Choose action a from state s using policy derived from Q value
- Take action a and then observe r, s’(next state)
- update Q value by [Q(s, a) \leftarrow Q(s, a) + \alpha \cdot (r + \gamma \text{max}_{a’}Q(s’,a’) - Q(s,a))]
- update s by s’
stop till s reaches termination
import numpy as np
import pandas as pd
import time
np.random.seed(803) ## reproducible random seed
Now consider we want an agent to play a one-dimensinal game. There is a diamond at the right end. Agent can move left and right to get the diamond.
## Initialize parameters
N_STATES = 8 # the length of the 1 dimensional world
ACTIONS = ['left', 'right'] ## available actions
EPSILON = 0.9 ## greedy police
ALPHA = 0.1 ## learning rate
GAMMA = 0.9 ## discount factor
MAX_EPISODES = 13 ## maximum episodes
FRESH_TIME = 0.01 ## fresh time for one move
def build_q_table(n_states, actions):
table = pd.DataFrame(
np.zeros((n_states, len(actions))), # q_table initial values
columns=actions, # actions's name
)
# print(table) # show table
return table
def choose_action(state, q_table):
# This is how to choose an action
state_actions = q_table.iloc[state, :]
# act non-greedy or state-action have no value
if (np.random.uniform() > EPSILON) or ((state_actions == 0).all()):
action_name = np.random.choice(ACTIONS)
else: # act greedy
# replace argmax to idxmax as argmax means a different function in newer version of pandas
action_name = state_actions.idxmax()
return action_name
def get_env_feedback(S, A):
# This is how agent will interact with the environment
if A == 'right': # move right
if S == N_STATES - 2: # terminate
S_ = 'terminal'
R = 1
else:
S_ = S + 1
R = 0
else: # move left
R = 0
if S == 0:
S_ = S # reach the wall
else:
S_ = S - 1
return S_, R
def update_env(S, episode, step_counter):
# This is how environment be updated
env_list = ['-']*(N_STATES-1) + ['T'] # '---------T' our environment
if S == 'terminal':
interaction = 'Episode %s: total_steps = %s' % (episode+1, step_counter)
print('\r{}'.format(interaction), end='')
time.sleep(2)
print('\r ', end='')
else:
env_list[S] = 'o'
interaction = ''.join(env_list)
print('\r{}'.format(interaction), end='')
time.sleep(FRESH_TIME)
def rl():
# main part of RL loop
q_table = build_q_table(N_STATES, ACTIONS)
for episode in range(MAX_EPISODES):
step_counter = 0
S = 0
is_terminated = False
update_env(S, episode, step_counter)
while not is_terminated:
A = choose_action(S, q_table)
S_, R = get_env_feedback(S, A) # take action & get next state and reward
q_predict = q_table.loc[S, A]
if S_ != 'terminal':
q_target = R + GAMMA * q_table.iloc[S_, :].max() # next state is not terminal
else:
q_target = R # next state is terminal
is_terminated = True # terminate this episode
q_table.loc[S, A] += ALPHA * (q_target - q_predict) # update
S = S_ # move to next state
update_env(S, episode, step_counter+1)
step_counter += 1
return q_table
if __name__ == "__main__":
q_table = rl()
print('\r\nQ-table:\n')
print(q_table)
Q-table:
left right
0 2.433154e-06 0.000054
1 3.491567e-08 0.000780
2 5.095377e-05 0.004544
3 0.000000e+00 0.027191
4 0.000000e+00 0.117596
5 0.000000e+00 0.356041
6 1.212525e-02 0.745813
7 0.000000e+00 0.000000