# mdp_policy_iteration_modified: Solves discounted MDP using modified policy iteration... In MDPtoolbox: Markov Decision Processes Toolbox

## Description

Solves discounted MDP using modified policy iteration algorithm

## Usage

 `1` ```mdp_policy_iteration_modified(P, R, discount, epsilon, max_iter) ```

## 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 number which belongs to [0; 1[. For discount equals to 1, a warning recalls to check conditions of convergence. `epsilon` (optional) search for an epsilon-optimal policy. epsilon is a real in ]0; 1]. By default, epsilon = 0.01. `max_iter` (optional) maximum number of iterations to be done. max_iter is an integer greater than 0. By default, max_iter = 1000.

## Details

mdp_policy_iteration_modified applies the modified policy iteration algorithm to solve discounted MDP. The algorithm consists, like policy iteration one, in improving the policy iteratively but in policy evaluation few iterations (max_iter) of value function updates done. Iterating is stopped when an epsilon-optimal policy is found.

## Value

 `V ` optimal value fonction. V is a S length vector `policy ` optimal policy. policy is a S length vector. Each element is an integer corresponding to an action which maximizes the value function. `iter ` number of iterations `cpu_time ` CPU time used to run the program

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```# 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) mdp_policy_iteration_modified(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) mdp_policy_iteration_modified(P, R, 0.9) ```

MDPtoolbox documentation built on May 30, 2017, 5:15 a.m.