Below is an example of how to implement the A* algorithm with Q-learning in Python:
import numpy as np
# Define the grid environment
grid = np.array([
[0, 0, 0, 0],
[0, -1, -1, 0],
[0, 0, 0, 0],
[0, -1, 0, 0],
[0, 0, 0, -1],
[0, 0, 0, 0]
])
# Define the rewards for each state
rewards = np.array([
[0, 0, 0, 0],
[0, -1, -1, 0],
[0, 0, 0, 0],
[0, -1, 0, 0],
[0, 0, 0, -1],
[0, 0, 0, 0]
])
# Define the Q-learning algorithm
def q_learning(start, goal, alpha, gamma, num_episodes):
Q = np.zeros_like(rewards) # Initialize Q-values with zeros
for episode in range(num_episodes):
state = start
while state != goal:
# Select an action based on the Q-values (e.g. epsilon-greedy policy)
if np.random.rand() < epsilon:
action = np.random.choice(len(actions))
else:
action = np.argmax(Q[state])
# Update the Q-value based on the action and expected future rewards
next_state = actions[action]
next_reward = rewards[next_state[0], next_state[1]]
Q[state][action] += alpha * (next_reward + gamma * np.max(Q[next_state]) - Q[state][action])
state = next_state
return Q
# Define the A* algorithm
def a_star(start, goal, Q):
open_list = [(start, 0)]
closed_list = set()
g_scores = np.inf * np.ones_like(rewards)
g_scores[start] = 0
f_scores = np.inf * np.ones_like(rewards)
f_scores[start] = heuristic(start, goal)
while open_list:
current, _ = min(open_list, key=lambda x: f_scores[x[0]]) # Select the node with the lowest f-score
open_list = [(node, score) for node, score in open_list if node != current]
closed_list.add(current)
if current == goal:
return True
for neighbor in actions:
if grid[neighbor] == -1 or neighbor in closed_list:
continue
g_score = g_scores[current] + 1 # Cost to reach the neighbor
f_score = g_score + heuristic(neighbor, goal) # Estimated total cost from start to goal through the neighbor
if f_score < f_scores[neighbor]:
g_scores[neighbor] = g_score
f_scores[neighbor] = f_score
open_list.append((neighbor, f_score))
return False
# Define the heuristic function (Manhattan distance)
def heuristic(state, goal):
return abs(goal[0] - state[0]) + abs(goal[1] - state[1])
# Set the hyperparameters
start = (0, 0)
goal = (5, 3)
alpha = 0.1 # Learning rate
gamma = 0.9 # Discount factor
epsilon = 0.1 # Exploration rate
num_episodes = 1000
# Define the actions (up, down, left, right)
actions = [(0, 1), (0, -1), (-1, 0), (1, 0)]
# Run the Q-learning algorithm
Q = q_learning(start, goal, alpha, gamma, num_episodes)
# Run the A* algorithm using the learned Q-values
path_found = a_star(start, goal, Q)
if path_found:
print("Path found!")
else:
print("Path not found!")