DiscreteDP: Allow beta=1

quantecon/markov/ddp.py

@@ -109,6 +109,7 @@
 
 """
 from __future__ import division
+import warnings
 import numpy as np
 import scipy.sparse as sp
 
@@ -165,7 +166,7 @@ class DiscreteDP(object):
  Transition probability array.
 
  beta : scalar(float)
- Discount factor. Must be 0 <= beta < 1.
+ Discount factor. Must be in [0, 1].
 
  s_indices : array_like(int, ndim=1), optional(default=None)
  Array containing the indices of the states.
@@ -190,6 +191,13 @@ class DiscreteDP(object):
  max_iter : scalar(int), default=250
  Default value for the maximum number of iterations.
 
+ Notes
+ -----
+ DiscreteDP accepts beta=1 for convenience. In this case, infinite
+ horizon solution methods are disabled, and the instance is then seen
+ as merely an object carrying the Bellman operator, which may be used
+ for backward induction for finite horizon problems.
+
  Examples
  --------
  Consider the following example, taken from Puterman (2005), Section
@@ -401,8 +409,12 @@ def s_wise_max(vals, out=None, out_argmax=None):
  # Check that for every state, at least one action is feasible
  self._check_action_feasibility()
 
- if not (0 <= beta < 1):
- raise ValueError('beta must be in [0, 1)')
+ if not (0 <= beta <= 1):
+ raise ValueError('beta must be in [0, 1]')
+ if beta == 1:
+ msg = 'infinite horizon solution methods are disabled with beta=1'
+ warnings.warn(msg)
+ self._error_msg_no_discounting = 'method invalid for beta=1'
  self.beta = beta
 
  self.epsilon = 1e-3
@@ -561,6 +573,9 @@ def evaluate_policy(self, sigma):
  Value vector of `sigma`, of length n.
 
  """
+ if self.beta == 1:
+ raise NotImplementedError(self._error_msg_no_discounting)
+
  # Solve (I - beta * Q_sigma) v = R_sigma for v
  R_sigma, Q_sigma = self.RQ_sigma(sigma)
  b = R_sigma
@@ -678,6 +693,9 @@ def value_iteration(self, v_init=None, epsilon=None, max_iter=None):
  `solve` method.
 
  """
+ if self.beta == 1:
+ raise NotImplementedError(self._error_msg_no_discounting)
+
  if max_iter is None:
  max_iter = self.max_iter
  if epsilon is None:
@@ -718,6 +736,9 @@ def policy_iteration(self, v_init=None, max_iter=None):
  `solve` method.
 
  """
+ if self.beta == 1:
+ raise NotImplementedError(self._error_msg_no_discounting)
+
  if max_iter is None:
  max_iter = self.max_iter
 
@@ -755,6 +776,9 @@ def modified_policy_iteration(self, v_init=None, epsilon=None,
  the `solve` method.
 
  """
+ if self.beta == 1:
+ raise NotImplementedError(self._error_msg_no_discounting)
+
  if max_iter is None:
  max_iter = self.max_iter
  if epsilon is None: