mdp_policy_iteration.html

MDP Toolbox for MATLAB

mdp_policy_iteration

Solves discounted MDP with policy iteration algorithm.

Syntax

[V, policy, iter, cpu_time] = mdp_policy_iteration (P, R, discount)
[V, policy, iter, cpu_time] = mdp_policy_iteration (P, R, discount, policy0)
[V, policy, iter, cpu_time] = mdp_policy_iteration (P, R, discount, policy0, max_iter)
[V, policy, iter, cpu_time] = mdp_policy_iteration (P, R, discount, policy0, max_iter, eval_type)

Description

mdp_policy_iteration applies the policy iteration algorithm to solve discounted MDP. The algorithm consists in improving the policy iteratively, using the evaluation of the current policy.
Iterating is stopped when two successive policies are identical or when a specified number (max_iter) of iterations have been performed.
This function uses verbose and silent modes. In verbose mode, the function displays the number of different actions between the policies n-1 and n after each iteration.

Arguments

• P : transition probability array.

P can be a 3 dimensions array (SxSxA) or a cell array (1xA), each cell containing a sparse matrix (SxS).

• R : reward array.

R can be a 3 dimensions array (SxSxA) or a cell array (1xA), each cell containing a sparse matrix (SxS) or a 2D array (SxA) possibly sparse.

• discount : discount factor.

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

• policy0 (optional) : starting policy.

policy0 is a (Sx1) vector.
By default, policy0 is the policy which maximizes the expected immediate reward.

• max_iter (optional) : maximum number of iterations to be done.

max_iter is an integer greater than 0.
By default, max_iter is set to 1000.

• eval_type (optional) : define function used to evaluate a policy.

eval_type is 0 for mdp_eval_policy_matrix use, mdp_eval_policy_iterative is used in all other cases.
By default, eval_type is set to 0.

Evaluations

• V : optimal value fonction.

V is a (Sx1) vector.

• policy : optimal policy.

policy is a (Sx1) 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.

Example
In grey, verbose mode display.

>> P(:,:,1) = [ 0.5 0.5;   0.8 0.2 ];
>> P(:,:,2) = [ 0 1;   0.1 0.9 ];
>> R = [ 5 10;   -1 2 ];

>> [V, policy, iter, cpu_time] = mdp_policy_iteration(P, R, 0.9)
  Iteration Number_of_different_actions
        1            1
        2            0
V =
   42.4419
   36.0465
policy =
   2
   1
iter =
   2
cpu_time =
   0.0200

In the above example, P can be a cell array containing sparse matrices:
>> P{1} = sparse([ 0.5 0.5;  0.8 0.2 ]);
>> P{2} = sparse([ 0 1;  0.1 0.9 ]);
The function call is unchanged.

MDP Toolbox for MATLAB

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MDPtoolbox/documentation/mdp_policy_iteration.html
Page created on July 31, 2001. Last update on August 31, 2009.