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Commit dd6ea7be authored by Steven Cordwell's avatar Steven Cordwell
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improve ValueIteration docstring

parent 8d56b9ee
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src/mdptoolbox/mdp.py
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......@@ -852,7 +852,7 @@ class PolicyIterationModified(PolicyIteration):
# Run the modified policy iteration algorithm.
if self.verbose:
print(' Iteration V_variation')
print('\tIteration\tV-variation')
self.time = time()
......@@ -865,7 +865,7 @@ class PolicyIterationModified(PolicyIteration):
variation = getSpan(Vnext - self.V)
if self.verbose:
print(" %s %s" % (self.iter, variation))
print("\t%s\t%s" % (self.iter, variation))
self.V = Vnext
if variation < self.thresh:
......@@ -1169,57 +1169,61 @@ class ValueIteration(MDP):
Description
-----------
mdp.ValueIteration applies the value iteration algorithm to solve
discounted MDP. The algorithm consists in solving Bellman's equation
ValueIteration applies the value iteration algorithm to solve a
discounted MDP. The algorithm consists of solving Bellman's equation
iteratively.
Iterating is stopped when an epsilon-optimal policy is found or after a
Iteration is stopped when an epsilon-optimal policy is found or after a
specified number (max_iter) of iterations.
This function uses verbose and silent modes. In verbose mode, the function
displays the variation of V (value function) for each iteration and the
condition which stopped iterations: epsilon-policy found or maximum number
of iterations reached.
displays the variation of V (the value function) for each iteration and the
condition which stopped the iteration: epsilon-policy found or maximum
number of iterations reached.
Let S = number of states, A = number of actions.
Parameters
----------
P : array
transition matrix
P could be a numpy ndarray with 3 dimensions (AxSxS) or a
numpy ndarray of dytpe=object with 1 dimenion (1xA), each
element containing a numpy ndarray (SxS) or scipy sparse matrix.
The transition probability matrices. There are several object type
options for P. It can be a list or tuple of length A, where each
element stores an SxS numpy array, matrix or sparse matrix. It can also
be an AxSxS numpy array. In summary, each action's transition matrix
must be indexable like ``P[a]`` where ``a`` ∈ {0, 1⋯A-1}.
R : array
reward matrix
R could be a numpy ndarray with 3 dimensions (AxSxS) or numpy
ndarray of dtype=object with 1 dimension (1xA), each element
containing a sparse matrix (SxS). R also could be a numpy
ndarray with 2 dimensions (SxA) possibly sparse.
The reward array. The same as for ``P`` except that in the list/tuple
case each element can be either a 1xA or SxS array. In addition to the
AxSxS array, an SxA array can also be specified. Any array can be
sparse.
discount : float
discount rate
Greater than 0, less than or equal to 1. Beware to check conditions of
convergence for discount = 1.
epsilon : float, optional
epsilon-optimal policy search
Greater than 0, optional (default: 0.01).
max_iter : int, optional
maximum number of iterations to be done
Greater than 0, optional (default: computed)
initial_value : array, optional
starting value function
optional (default: zeros(S,)).
The discount rate. This must be greater than 0, and less than or equal
to 1. Beware to check conditions of convergence for ``discount`` of 1.
A warning is issued if discount equals 1.
epsilon : float, optional (default: 0.01)
The epsilon-optimal policy search value. This must be greater than 0
if sepcified, and is used to decide when to stop iterating.
max_iter : int, optional (default: computed)
The maximum number of iterations. This must be greater than 0 if
specified. If the value given in argument is greater than a computed
bound, a warning informs that the computed bound will be considered.
By default, if discount is not egal to 1, a bound for max_iter is
computed, if not max_iter = 1000.
initial_value : array, optional (default: zeros(S,))
The starting value function. By default ``initial_value`` is composed
of 0 elements.
Data Attributes
---------------
V : value function
A vector which stores the optimal value function. Prior to calling the
_iterate() method it has a value of None. Shape is (S, ).
policy : epsilon-optimal policy
A vector which stores the optimal policy. Prior to calling the
_iterate() method it has a value of None. Shape is (S, ).
iter : number of iterations taken to complete the computation
An integer
time : used CPU time
A float
V : tuple
The optimal value function. Each element is a float corresponding to
the expected value of being in that state assuming the optimal policy
is followed.
policy : tuple
The optimal policy function. Each element is an integer corresponding
to an action which maximises the value function in that state.
iter : int
The number of iterations taken to complete the computation.
time : float
The amount of CPU time used to run the algorithm.
Methods
-------
......@@ -1247,8 +1251,6 @@ class ValueIteration(MDP):
(0, 0, 0)
>>> vi.iter
4
>>> vi.time
0.0009911060333251953
>>> import mdptoolbox
>>> import numpy as np
......@@ -1261,8 +1263,6 @@ class ValueIteration(MDP):
(1, 0)
>>> vi.iter
26
>>> vi.time
0.0066509246826171875
>>> import mdptoolbox
>>> import numpy as np
......@@ -1289,16 +1289,12 @@ class ValueIteration(MDP):
if initial_value == 0:
self.V = zeros(self.S)
else:
if len(initial_value) != self.S:
raise ValueError("PyMDPtoolbox: The initial value must be "
"a vector of length S.")
else:
try:
self.V = initial_value.reshape(self.S)
except AttributeError:
self.V = array(initial_value)
except:
raise
assert len(initial_value) == self.S, "PyMDPtoolbox: The " \
"initial value must be a vector of length S."
try:
self.V = initial_value.reshape(self.S)
except AttributeError:
self.V = array(initial_value).reshape(self.S)
if self.discount < 1:
# compute a bound for the number of iterations and update the
# stored value of self.max_iter
......@@ -1345,9 +1341,7 @@ class ValueIteration(MDP):
PP[aa] = self.P[aa][:, ss]
except ValueError:
PP[aa] = self.P[aa][:, ss].todense().A1
except:
raise
# the function "min()" without any arguments finds the
# the method "min()" without any arguments finds the
# minimum of the entire array.
h[ss] = PP.min()
......@@ -1365,11 +1359,10 @@ class ValueIteration(MDP):
# Run the value iteration algorithm.
if self.verbose:
print(' Iteration V_variation')
print('\tIteration\tV-variation')
self.time = time()
done = False
while not done:
while True:
self.iter += 1
Vprev = self.V.copy()
......@@ -1383,18 +1376,18 @@ class ValueIteration(MDP):
variation = getSpan(self.V - Vprev)
if self.verbose:
print(" %s %s" % (self.iter, variation))
print("\t%s\t%s" % (self.iter, variation))
if variation < self.thresh:
done = True
if self.verbose:
print("...iterations stopped, epsilon-optimal policy "
"found.")
print("PyMDPToolbox: iterations stopped, epsilon-optimal "
"policy found.")
break
elif (self.iter == self.max_iter):
done = True
if self.verbose:
print("...iterations stopped by maximum number of "
"iteration condition.")
print("PyMDPToolbox: iterations stopped by maximum number "
"of iterations condition.")
break
# store value and policy as tuples
self.V = tuple(self.V.tolist())
......
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