# mdp_value_iteration_bound_iter: Computes a bound for the number of iterations for the value... In MDPtoolbox: Markov Decision Processes Toolbox

## Description

Computes a bound on the number of iterations for the value iteration algorithm

## Usage

 `1` ```mdp_value_iteration_bound_iter(P, R, discount, epsilon, V0) ```

## 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[. `epsilon` (optional) : search for an epsilon-optimal policy epsilon is a real in ]0; 1]. By default, epsilon is set to 0.01. `V0` (optional) : starting value function. V0 is a S length vector. By default, V0 is only composed of 0 elements.

## Details

mdp_value_iteration_bound_iter computes a bound on the number of iterations for the value iteration algorithm to find an epsilon-optimal policy with use of span for the stopping criterion.

## Value

 `max_iter ` maximum number of iterations to be done. max_iter is an integer greater than 0. `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_value_iteration_bound_iter(P, R, 0.9) # With a sparse matrix P <- list() P[] <- Matrix(c(0.5, 0.5, 0.8, 0.2), 2, 2, byrow=TRUE, sparse=TRUE) P[] <- Matrix(c(0, 1, 0.1, 0.9), 2, 2, byrow=TRUE, sparse=TRUE) mdp_value_iteration_bound_iter(P, R, 0.9) ```

MDPtoolbox documentation built on May 2, 2019, 2:10 p.m.