mdp_Q_learning {MDPtoolbox}

Solves discounted MDP using the Q-learning algorithm (Reinforcement Learning)

Description

Solves discounted MDP with the Q-learning algorithm (Reinforcement learning)

Usage

mdp_Q_learning(P, R, discount, N)

Arguments

P

transition probability array. P can be a 3 dimensions array [S,S,A] or a list [[A]], each element containing a sparse matrix [S,S].

R

reward array. R can be a 3 dimensions array [S,S,A] or a list [[A]], each element containing a sparse matrix [S,S] or a 2 dimensional matrix [S,A] possibly sparse.

discount

discount factor. discount is a real which belongs to ]0; 1[

N

(optional) : number of iterations to perform. N is an integer that must be greater than the default value. By default, N is set to 10000.

Details

mdp_Q_learning computes the Q matrix, the mean discrepancy and gives the optimal value function and the optimal policy when allocated enough iterations. It uses an iterative method.

Value

Q

an action-value function that gives the expected utility of taking a given action in a given state and following an optimal policy thereafter. Q is a [S,A] matrix.

mean_discrepancy

discrepancy means over 100 iterations. mean_discrepancy is a vector of V discrepancy mean over 100 iterations. Then the length of the vector for the default value of N is 100.

V

value function. V is a S length vector.

policy

policy. policy is a S length vector. Each element is an integer corresponding to an action which maximizes the value function

Examples

# With a non-sparse matrix
P <- array(0, c(2,2,2))
P[,,1] <- matrix(c(0.5, 0.5, 0.8, 0.2), 2, 2, byrow=TRUE)
P[,,2] <- matrix(c(0, 1, 0.1, 0.9), 2, 2, byrow=TRUE)
R <- matrix(c(5, 10, -1, 2), 2, 2, byrow=TRUE)
# Not run
# mdp_Q_learning(P, R, 0.9)

# With a sparse matrix
P <- list()
P[[1]] <- Matrix(c(0.5, 0.5, 0.8, 0.2), 2, 2, byrow=TRUE, sparse=TRUE)
P[[2]] <- Matrix(c(0, 1, 0.1, 0.9), 2, 2, byrow=TRUE, sparse=TRUE)
# Not run
# mdp_Q_learning(P, R, 0.9)