Original Source Here
Safe and efficient off-policy reinforcement learning.
This work was co-authored by my colleague Kais Cheikh.
 Thomas G. Dietterich. Hierarchical Reinforcement Learning with the MAXQ Value Function Decomposition. Journal of Artificial Intelligence Research,13 :227–303, 2000.
 Rémi Munos, Thomas Stepleton, Anna Harutyunyan, and Marc G. Bellemare.Safe and efficient off-policy reinforcement learning. Advances in Neural Information Processing Systems, (Nips) :1054–1062, 2016.
'''This code was implemented in the course MAP670C Reinfocement Learning by Bechir Trabelsi and Kais Cheikh from this article comes from.This code was done to implement the algorithm proposed in the paper " Safe and efficient off-policy reinforcement learning "'''# Packages importimport numpy as npimport gymimport random# Function to compute cs parameter depending on the algorithm.def compute_cs(algo, mu, pi, Lambda):# Possible values for algo are IS, Off-policy, TB, Retraceif algo == "IS":return pi/muif algo == "Off-policy":return Lambdaif algo == "TB":return Lambda * piif algo == "Retrace":return Lambda * min(1, pi/mu)# The simulator that runs the algorithmsdef simulator(env, algo= "Retrace", epsilon= 0.5, decay_rate= 0.99, total_episodes= 10, max_steps= 100, Lambda= 1, gamma= 1):''' function that simulate the training of an algorithm.inputs:env: a gym object containing the environment.algo: a string in this list ["IS", "Off-policy", "TB", "Retrace"], represent the algorithme used to compute the Q-value.epsilon: a float between 0 and 1 for the epsilon-greedy part.decay_rate: a flot between 0 and 1 it represent the speed of decay of the epsilion term in the epsilon-greedy part.total_episodes: a positive intger represent the number of episodes to be simulated.max_steps: a positive intger represent the number of steps taken at each episode.Lambda: a float represnt the update in the Q-values.gamma: discount factor.outputs:rewards: a list of rewards at each episode.Q: the Q values matrix.'''# Environment parametersn_actions= env.action_space.n # number of actionsn_states = env.observation_space.n # number of statesQ = np.zeros((n_states, n_actions)) # Initialize the Q matrixrewards =  # List of rewards''' The algorithm '''# Simulate different episodesfor episode in range(total_episodes):# Reset the environmentstate = env.reset()step = 0done = False # Boolean variable, in case the game is over to stop looping over the steps.total_rewards = 0cs = 1# strat playing/interactingfor step in range(max_steps):''' epsilon greedy part'''# Compute the random variablet = random.uniform(0, 1)# We initialize the probabilty mumu = 1# Exploitation choose the most likely action to be done.if t > epsilon:action = np.argmax(Q[state,:])mu = 1 - epsilon# Exploration choose a random action.else:action = env.action_space.sample()mu = epsilon / (n_actions - 1)# Compute the new state, it's reward and whenever the game is over or not.new_state, reward, done, info = env.step(action)a_star = np.argmax(Q[new_state])probabilities = [epsilon / n_actions] * n_actionsprobabilities[a_star] += 1 - epsilonsum_prb = 0# compute cscs *= compute_cs(algo= algo, mu= mu,pi= probabilities[a_star], Lambda= Lambda)# compute the Expectation over pi of Q.for i in range(n_actions):sum_prb += probabilities[i] * Q[new_state, i]# Update the Q(x,a) using the equation in (3) in the paper and (1) in our report.Q[state, action] += (gamma**step) * cs * (reward + gamma * sum_prb - Q[state,action])# We add the new rewardtotal_rewards += reward# We switch to the new statestate = new_state# If done (if we're dead) : finish episodeif done == True:break# Reduce The epsilon value since with time we prefer more exploitation than exploration.epsilon *= decay_raterewards.append(total_rewards)return rewards, Q
Simulation code :
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