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Zahra Rajabi
pymdptoolbox
Commits
5b516cdf
Commit
5b516cdf
authored
Jan 21, 2013
by
Steven Cordwell
Browse files
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added class LP
parent
31712f2c
Changes
1
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1 changed file
with
113 additions
and
42 deletions
+113
-42
mdp.py
mdp.py
+113
-42
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mdp.py
View file @
5b516cdf
...
...
@@ -462,7 +462,7 @@ class MDP(object):
"""This is a placeholder method. Child classes should define their own
iterate() method.
"""
raise
NotImplementedError
(
"You should create an iterate method."
)
raise
NotImplementedError
(
"You should create an iterate
()
method."
)
def
getSpan
(
self
,
W
):
"""Returns the span of W
...
...
@@ -520,37 +520,109 @@ class FiniteHorizon(MDP):
def
__init__
(
self
,
P
,
R
,
discount
,
N
,
h
):
if
N
<
1
:
raise
ValueError
(
'MDP Toolbox ERROR: N must be upper than 0'
)
if
discount
<=
0
||
discount
>
1
:
if
discount
<=
0
or
discount
>
1
:
raise
ValueError
(
'MDP Toolbox ERROR: Discount rate must be in ]0; 1]'
)
if
iscell
(
P
):
S
=
size
(
P
{
1
}
,
1
)
else
:
S
=
size
(
P
,
1
)
V
=
zeros
(
S
,
N
+
1
)
if
nargin
==
5
:
V
(:,
N
+
1
)
=
h
PR
=
mdp_computePR
(
P
,
R
);
if
iscell
(
P
):
S
=
size
(
P
[
1
]
,
1
)
else
:
S
=
size
(
P
,
1
)
V
=
zeros
(
S
,
N
+
1
)
if
nargin
==
5
:
V
[:,
N
+
1
]
=
h
PR
=
mdp_computePR
(
P
,
R
);
def
iterate
():
self
.
time
=
time
()
for
n
=
0
:
N
-
1
:
[
W
,
X
]
=
mdp_bellman_operator
(
P
,
PR
,
discount
,
V
(:,
N
-
n
+
1
)
)
V
(:,
N
-
n
)
=
W
policy
(:,
N
-
n
)
=
X
for
n
in
range
(
N
-
1
)
:
W
,
X
=
self
.
bellmanOperator
(
P
,
PR
,
discount
,
V
[:,
N
-
n
+
1
]
)
V
[:,
N
-
n
]
=
W
policy
[:,
N
-
n
]
=
X
#if mdp_VERBOSE
# disp(['stage:' num2str(N-n) ' policy transpose : ' num2str(policy(:,N-n)')])
self
.
time
=
time
()
-
self
.
time
class
LP
(
MDP
):
"""Resolution of discounted MDP with linear programming.
"""Resolution of discounted MDP with linear programming
Arguments
---------
Let S = number of states, A = number of actions
P(SxSxA) = transition matrix
P could be an array with 3 dimensions or
a cell array (1xA), each cell containing a matrix (SxS) possibly sparse
R(SxSxA) or (SxA) = reward matrix
R could be an array with 3 dimensions (SxSxA) or
a cell array (1xA), each cell containing a sparse matrix (SxS) or
a 2D array(SxA) possibly sparse
discount = discount rate, in ]0; 1[
h(S) = terminal reward, optional (default [0; 0; ... 0] )
Evaluation
----------
V(S) = optimal values
policy(S) = optimal policy
cpu_time = used CPU time
Notes
-----
In verbose mode, displays the current stage and policy transpose.
Examples
--------
"""
raise
NotImplementedError
(
"This class has not been implemented yet."
)
def
__init__
(
self
,
P
,
R
,
discount
):
try
:
from
cvxopt
import
matrix
,
solvers
except
ImportError
:
raise
ImportError
(
"The python module cvxopt is required to use linear programming functionality."
)
self
.
linprog
=
solvers
.
lp
if
discount
<=
0
or
discount
>=
1
:
print
(
'MDP Toolbox ERROR: Discount rate must be in ]0; 1['
)
if
iscell
(
P
):
S
=
size
(
P
[
1
],
1
)
A
=
length
(
P
)
else
:
S
=
size
(
P
,
1
)
A
=
size
(
P
,
3
)
PR
=
self
.
computePR
(
P
,
R
)
# The objective is to resolve : min V / V >= PR + discount*P*V
# The function linprog of the optimisation Toolbox of Mathworks resolves :
# min f'* x / M * x <= b
# So the objective could be expressed as : min V / (discount*P-I) * V <= - PR
# To avoid loop on states, the matrix M is structured following actions M(A*S,S)
f
=
ones
(
S
,
1
)
M
=
[]
if
iscell
(
P
):
for
a
in
range
(
A
):
M
=
hstack
((
M
,
discount
*
P
[
a
]
-
speye
(
S
)))
else
:
for
a
in
range
(
A
):
M
=
hstack
((
M
,
discount
*
P
[:,:,
a
]
-
speye
(
S
)))
def
iterate
(
self
,
linprog
):
self
.
time
=
time
()
V
=
self
.
linprog
(
f
,
M
,
-
PR
)
V
,
policy
=
self
.
bellmanOperator
(
P
,
PR
,
discount
,
V
)
self
.
time
=
time
()
-
self
.
time
class
PolicyIteration
(
MDP
):
"""Resolution of discounted MDP with policy iteration algorithm.
...
...
@@ -669,9 +741,9 @@ class PolicyIterationModified(MDP):
"""
def
__init__
(
self
,
transitions
,
reward
,
discount
,
epsilon
=
0.01
,
max_iter
=
10
):
""""""
MDP
.
__init__
(
self
,
discount
,
max_iter
)
:
""""""
MDP
.
__init__
(
self
,
discount
,
max_iter
)
if
epsilon
<=
0
:
raise
ValueError
(
"epsilon must be greater than 0"
)
...
...
@@ -700,7 +772,7 @@ class PolicyIterationModified(MDP):
if
self
.
verbose
:
print
(
' Iteration V_variation'
)
self
.
time
=
time
()
self
.
time
=
time
()
done
=
False
while
not
done
:
...
...
@@ -709,7 +781,7 @@ class PolicyIterationModified(MDP):
Vnext
,
policy
=
self
.
bellmanOperator
(
self
.
P
,
self
.
PR
,
self
.
discount
,
self
.
V
)
#[Ppolicy, PRpolicy] = mdp_computePpolicyPRpolicy(P, PR, policy);
variation
=
mdp_s
pan
(
Vnext
-
V
);
variation
=
self
.
getS
pan
(
Vnext
-
V
);
if
self
.
verbose
:
print
(
" %s %s"
%
(
self
.
iter
,
variation
))
...
...
@@ -1150,8 +1222,7 @@ class ValueIterationGS(MDP):
def
__init__
(
self
,
transitions
,
reward
,
discount
,
epsilon
=
0.01
,
max_iter
=
10
,
initial_value
=
0
):
""""""
MDP
.
__init__
(
self
,
discount
,
max_iter
):
MDP
.
__init__
(
self
,
discount
,
max_iter
)
# initialization of optional arguments
if
(
initial_value
==
0
):
...
...
@@ -1170,7 +1241,7 @@ class ValueIterationGS(MDP):
# disp('--------------------------------------------------------')
#end;
PR
=
self
.
computePR
(
P
,
R
)
PR
=
self
.
computePR
(
P
,
R
)
#% initialization of optional arguments
#if nargin < 6; V0 = zeros(S,1); end;
...
...
@@ -1211,7 +1282,7 @@ class ValueIterationGS(MDP):
self
.
iter
=
0
def
iterate
():
def
iterate
(
self
,
PR
):
""""""
V
=
self
.
initial_value
...
...
@@ -1222,18 +1293,18 @@ class ValueIterationGS(MDP):
self
.
time
=
time
()
while
not
done
while
not
done
:
self
.
iter
=
self
.
iter
+
1
Vprev
=
self
.
value
for
s
=
range
(
self
.
S
):
for
a
=
range
(
self
.
A
):
for
s
in
range
(
self
.
S
):
for
a
in
range
(
self
.
A
):
if
iscell
(
P
):
Q
(
a
)
=
PR
(
s
,
a
)
+
discount
*
P
{
a
}(
s
,:)
*
V
Q
[
a
]
=
PR
[
s
,
a
]
+
discount
*
P
[
a
][
s
,:]
*
V
else
:
Q
(
a
)
=
PR
(
s
,
a
)
+
discount
*
P
(
s
,:,
a
)
*
V
V
(
s
)
=
max
(
Q
)
Q
[
a
]
=
PR
[
s
,
a
]
+
discount
*
P
[
s
,:,
a
]
*
V
V
[
s
]
=
max
(
Q
)
variation
=
self
.
getSpan
(
V
-
Vprev
)
...
...
@@ -1245,18 +1316,18 @@ class ValueIterationGS(MDP):
if
self
.
verbose
:
print
(
'MDP Toolbox : iterations stopped, epsilon-optimal policy found'
)
elif
self
.
iter
==
self
.
max_iter
elif
self
.
iter
==
self
.
max_iter
:
done
=
True
if
self
.
verbose
:
print
(
'MDP Toolbox : iterations stopped by maximum number of iteration condition'
)
for
s
=
range
(
S
):
for
a
=
range
(
A
):
for
s
in
range
(
S
):
for
a
in
range
(
A
):
if
iscell
(
P
):
Q
(
a
)
=
PR
(
s
,
a
)
+
P
{
a
}(
s
,:)
*
discount
*
V
Q
[
a
]
=
PR
[
s
,
a
]
+
P
[
a
][
s
,:]
*
discount
*
V
else
:
Q
(
a
)
=
PR
(
s
,
a
)
+
P
(
s
,:,
a
)
*
discount
*
V
Q
[
a
]
=
PR
[
s
,
a
]
+
P
[
s
,:,
a
]
*
discount
*
V
[
V
(
s
)
,
policy
(
s
,
1
)
]
=
max
(
Q
)
V
[
s
],
policy
[
s
,
1
]
=
max
(
Q
)
self
.
time
=
time
()
-
self
.
time
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