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Commit 60e89bf1 authored by Steven Cordwell's avatar Steven Cordwell
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various small fixes

parent 8757cec0
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Showing with 136 additions and 172 deletions
mdp.py
View file @ 60e89bf1
...@@ -240,28 +240,36 @@ class MDP(object): ...@@ -240,28 +240,36 @@ class MDP(object):
def __init__(self, transitions, reward, discount, max_iter): def __init__(self, transitions, reward, discount, max_iter):
"""""" """"""
# the verbosity is by default turned off
self.verbose = False
# Initially the time taken to perform the computations is set to None if (type(discount) is int) or (type(discount) is float):
self.time = None if (discount <= 0) or (discount > 1):
raise ValueError(mdperr["discount_rng"])
if (discount <= 0) or (discount > 1): else:
raise ValueError(mdperr["discount_rng"]) self.discount = discount
else: elif not discount is None:
self.discount = discount raise ValueError("PyMDPtoolbox: the discount must be a positive real number less than or equal to one.")
if (max_iter <= 0): if (type(max_iter) is int) or (type(max_iter) is float):
raise ValueError(mdperr["maxi_min"]) if (max_iter <= 0):
else: raise ValueError(mdperr["maxi_min"])
self.max_iter = max_iter else:
self.max_iter = max_iter
elif not max_iter is None:
raise ValueError("PyMDPtoolbox: max_iter must be a positive real number greater than zero.")
self.check(transitions, reward) self.check(transitions, reward)
self.computePR(transitions, reward) self.computePR(transitions, reward)
# the verbosity is by default turned off
self.verbose = False
# Initially the time taken to perform the computations is set to None
self.time = None
# set the initial iteration count to zero # set the initial iteration count to zero
self.iter = 0 self.iter = 0
self.value = None
self.policy = None
def bellmanOperator(self): def bellmanOperator(self):
""" """
...@@ -448,12 +456,14 @@ class MDP(object): ...@@ -448,12 +456,14 @@ class MDP(object):
def checkSquareStochastic(self, Z): def checkSquareStochastic(self, Z):
"""Check if Z is a square stochastic matrix """Check if Z is a square stochastic matrix
Arguments Parameters
-------------------------------------------------------------- ----------
Z = a numpy ndarray SxS, possibly sparse (csr_matrix) Z : a SxS matrix. It could be a numpy ndarray SxS, or a scipy.sparse
csr_matrix
Evaluation Evaluation
------------------------------------------------------------- ----------
error_msg = error message or None if correct Returns None if no error has been detected
""" """
s1, s2 = Z.shape s1, s2 = Z.shape
if (s1 != s2): if (s1 != s2):
...@@ -582,33 +592,30 @@ class FiniteHorizon(MDP): ...@@ -582,33 +592,30 @@ class FiniteHorizon(MDP):
""" """
def __init__(self, P, R, discount, N, h): def __init__(self, transitions, reward, discount, N, h=None):
""""""
if N < 1: if N < 1:
raise ValueError('MDP Toolbox ERROR: N must be upper than 0') raise ValueError('MDP Toolbox ERROR: N must be upper than 0')
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: else:
S = size(P,1) self.N = N
V = zeros(S,N+1) MDP.__init__(self, transitions, reward, discount, None)
if nargin == 5: self.value = zeros(self.S, N + 1)
V[:,N+1] = h
PR = mdp_computePR(P,R); if not h is None:
self.value[:, N + 1] = h
def iterate(): def iterate(self):
""""""
self.time = time() self.time = time()
for n in range(N-1): for n in range(self.N - 1):
W, X = self.bellmanOperator(P,PR,discount,V[:,N-n+1]) W, X = self.bellmanOperator(self.P, self.R, self.discount, self.value[:, self.N - n + 1])
V[:,N-n] = W self.value[:, self.N - n] = W
policy[:, N-n] = X self.policy[:, self.N - n] = X
#if mdp_VERBOSE if self.verbose:
# disp(['stage:' num2str(N-n) ' policy transpose : ' num2str(policy(:,N-n)')]) print("stage: %s ... policy transpose : %s") % (self.N - n, self.policy[:, self.N - n].T)
self.time = time() - self.time self.time = time() - self.time
...@@ -642,26 +649,18 @@ class LP(MDP): ...@@ -642,26 +649,18 @@ class LP(MDP):
-------- --------
""" """
def __init__(self, P, R, discount): def __init__(self, transitions, reward, discount):
""""""
try: try:
from cvxopt import matrix, solvers from cvxopt import matrix, solvers
self.linprog = solvers.lp
except ImportError: except ImportError:
raise ImportError("The python module cvxopt is required to use linear programming functionality.") raise ImportError("The python module cvxopt is required to use linear programming functionality.")
self.linprog = solvers.lp from scipy.sparse import eye as speye
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) MDP.__init__(self, transitions, reward, discount, None)
# The objective is to resolve : min V / V >= PR + discount*P*V # The objective is to resolve : min V / V >= PR + discount*P*V
# The function linprog of the optimisation Toolbox of Mathworks resolves : # The function linprog of the optimisation Toolbox of Mathworks resolves :
...@@ -669,23 +668,22 @@ class LP(MDP): ...@@ -669,23 +668,22 @@ class LP(MDP):
# So the objective could be expressed as : min V / (discount*P-I) * V <= - PR # 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) # To avoid loop on states, the matrix M is structured following actions M(A*S,S)
f = ones(S,1) self.f = ones(self.S, 1)
M = [] self.M = zeros((self.A * self.S, self.S))
if iscell(P): for aa in range(self.A):
for a in range(A): pos = (aa + 1) * self.S
M = hstack((M, discount * P[a] - speye(S))) self.M[(pos - self.S):pos, :] = discount * self.P[aa] - speye(self.S, self.S)
else:
for a in range(A):
M = hstack((M, discount * P[:,:,a] - speye(S)))
def iterate(self, linprog):
self.M = matrix(self.M)
def iterate(self):
""""""
self.time = time() self.time = time()
V = self.linprog(f, M, -PR) self.value = self.linprog(self.f, self.M, -self.R)
V, policy = self.bellmanOperator(P, PR, discount, V) self.value, self.policy = self.bellmanOperator(self.P, self.R, self.discount, self.value)
self.time = time() - self.time self.time = time() - self.time
...@@ -808,15 +806,11 @@ class PolicyIterationModified(MDP): ...@@ -808,15 +806,11 @@ class PolicyIterationModified(MDP):
def __init__(self, transitions, reward, discount, epsilon=0.01, max_iter=10): def __init__(self, transitions, reward, discount, epsilon=0.01, max_iter=10):
"""""" """"""
MDP.__init__(self, discount, max_iter) MDP.__init__(self, transitions, reward, discount, max_iter)
if epsilon <= 0: if epsilon <= 0:
raise ValueError("epsilon must be greater than 0") raise ValueError("epsilon must be greater than 0")
self.check(transitions, reward)
self.computePR(transitions, reward)
# computation of threshold of variation for V for an epsilon-optimal policy # computation of threshold of variation for V for an epsilon-optimal policy
if self.discount != 1: if self.discount != 1:
self.thresh = epsilon * (1 - self.discount) / self.discount self.thresh = epsilon * (1 - self.discount) / self.discount
...@@ -827,9 +821,11 @@ class PolicyIterationModified(MDP): ...@@ -827,9 +821,11 @@ class PolicyIterationModified(MDP):
self.value = matrix(zeros((self.S, 1))) self.value = matrix(zeros((self.S, 1)))
else: else:
# min(min()) is not right # min(min()) is not right
self.value = 1 / (1 - discount) * min(min(self.PR)) * ones((self.S, 1)) self.value = 1 / (1 - discount) * min(min(self.R)) * ones((self.S, 1))
self.iter = 0 def evalPolicyIterative(self):
""""""
pass
def iterate(self): def iterate(self):
"""""" """"""
...@@ -838,7 +834,7 @@ class PolicyIterationModified(MDP): ...@@ -838,7 +834,7 @@ class PolicyIterationModified(MDP):
print(' Iteration V_variation') print(' Iteration V_variation')
self.time = time() self.time = time()
done = False done = False
while not done: while not done:
self.iter = self.iter + 1 self.iter = self.iter + 1
...@@ -846,23 +842,23 @@ class PolicyIterationModified(MDP): ...@@ -846,23 +842,23 @@ class PolicyIterationModified(MDP):
Vnext, policy = self.bellmanOperator(self.P, self.PR, self.discount, self.V) Vnext, policy = self.bellmanOperator(self.P, self.PR, self.discount, self.V)
#[Ppolicy, PRpolicy] = mdp_computePpolicyPRpolicy(P, PR, policy); #[Ppolicy, PRpolicy] = mdp_computePpolicyPRpolicy(P, PR, policy);
variation = self.getSpan(Vnext - V); variation = self.getSpan(Vnext - self.value);
if self.verbose: if self.verbose:
print(" %s %s" % (self.iter, variation)) print(" %s %s" % (self.iter, variation))
V = Vnext self.value = Vnext
if variation < thresh: if variation < self.thresh:
done = True done = True
else: else:
is_verbose = False is_verbose = False
if self.verbose: if self.verbose:
self.verbose = False self.setSilent
is_verbose = True is_verbose = True
V = self.evalPolicyIterative(self.P, self.PR, self.discount, self.policy, self.V, self.epsilon, self.max_iter) self.value = self.evalPolicyIterative()
if is_verbose: if is_verbose:
self.verbose = True self.setVerbose
self.time = time() - self.time self.time = time() - self.time
...@@ -1055,13 +1051,8 @@ class RelativeValueIteration(MDP): ...@@ -1055,13 +1051,8 @@ class RelativeValueIteration(MDP):
if epsilon <= 0: if epsilon <= 0:
print('MDP Toolbox ERROR: epsilon must be upper than 0') print('MDP Toolbox ERROR: epsilon must be upper than 0')
if iscell(P): self.U = zeros(self.S, 1)
S = size(P[1], 1) self.gain = self.U[self.S]
else:
S = size(P, 1)
self.U = zeros(S, 1)
self.gain = U(S)
def iterate(self): def iterate(self):
"""""" """"""
...@@ -1076,7 +1067,7 @@ class RelativeValueIteration(MDP): ...@@ -1076,7 +1067,7 @@ class RelativeValueIteration(MDP):
self.iter = self.iter + 1; self.iter = self.iter + 1;
Unext, policy = self.bellmanOperator(self.P, self.PR, 1, self.U) Unext, policy = self.bellmanOperator(self.P, self.R, 1, self.U)
Unext = Unext - self.gain Unext = Unext - self.gain
variation = self.getSpan(Unext - self.U) variation = self.getSpan(Unext - self.U)
...@@ -1320,7 +1311,7 @@ class ValueIteration(MDP): ...@@ -1320,7 +1311,7 @@ class ValueIteration(MDP):
self.time = time() - self.time self.time = time() - self.time
class ValueIterationGS(MDP): class ValueIterationGS(ValueIteration):
"""Resolution of discounted MDP with value iteration Gauss-Seidel algorithm """Resolution of discounted MDP with value iteration Gauss-Seidel algorithm
Arguments Arguments
...@@ -1359,7 +1350,7 @@ class ValueIterationGS(MDP): ...@@ -1359,7 +1350,7 @@ class ValueIterationGS(MDP):
def __init__(self, transitions, reward, discount, epsilon=0.01, max_iter=10, initial_value=0): def __init__(self, transitions, reward, discount, epsilon=0.01, max_iter=10, initial_value=0):
"""""" """"""
MDP.__init__(self, discount, max_iter) MDP.__init__(self, transitions, reward, discount, max_iter)
# initialization of optional arguments # initialization of optional arguments
if (initial_value == 0): if (initial_value == 0):
...@@ -1371,57 +1362,25 @@ class ValueIterationGS(MDP): ...@@ -1371,57 +1362,25 @@ class ValueIterationGS(MDP):
if epsilon <= 0: if epsilon <= 0:
raise ValueError("epsilon must be greater than 0") raise ValueError("epsilon must be greater than 0")
#if discount == 1 if discount == 1:
# disp('--------------------------------------------------------') print('PyMDPtoolbox WARNING: check conditions of convergence.'
# disp('MDP Toolbox WARNING: check conditions of convergence.') 'With no discount, convergence is not always assumed.')
# disp('With no discount, convergence is not always assumed.')
# disp('--------------------------------------------------------')
#end;
PR = self.computePR(P, R)
#% initialization of optional arguments
#if nargin < 6; V0 = zeros(S,1); end;
#if nargin < 4; epsilon = 0.01; end;
#% compute a bound for the number of iterations
#if discount ~= 1
# computed_max_iter = mdp_value_iteration_bound_iter(P, R, discount, epsilon, V0);
#end;
#if nargin < 5
# if discount ~= 1
# max_iter = computed_max_iter;
# else
# max_iter = 1000;
# end;
#else
# if discount ~= 1 && max_iter > computed_max_iter
# disp(['MDP Toolbox WARNING: max_iter is bounded by ' num2str(computed_max_iter,'%12.1f') ])
# max_iter = computed_max_iter;
# end;
#end;
#% computation of threshold of variation for V for an epsilon-optimal policy
#if discount ~= 1
# thresh = epsilon * (1-discount)/discount
#else
# thresh = epsilon
self.discount = discount
if (discount < 1): if (discount < 1):
# compute a bound for the number of iterations # compute a bound for the number of iterations
#self.max_iter = self.boundIter(epsilon) self.boundIter(epsilon)
self.max_iter = 5000 print('MDP Toolbox WARNING: max_iter is bounded by %s') % self.max_iter
# computation of threshold of variation for V for an epsilon-optimal policy # computation of threshold of variation for V for an epsilon-optimal policy
self.thresh = epsilon * (1 - self.discount) / self.discount self.thresh = epsilon * (1 - self.discount) / self.discount
else: # discount == 1 else: # discount == 1
# bound for the number of iterations
self.max_iter = max_iter
# threshold of variation for V for an epsilon-optimal policy # threshold of variation for V for an epsilon-optimal policy
self.thresh = epsilon self.thresh = epsilon
self.iter = 0 self.iter = 0
def iterate(self, PR): def iterate(self):
"""""" """"""
V = self.initial_value V = self.value
done = False done = False
...@@ -1437,18 +1396,15 @@ class ValueIterationGS(MDP): ...@@ -1437,18 +1396,15 @@ class ValueIterationGS(MDP):
for s in range(self.S): for s in range(self.S):
for a in range(self.A): for a in range(self.A):
if iscell(P): Q[a] = self.R[s,a] + self.discount * self.P[a][s,:] * self.value
Q[a] = PR[s,a] + discount * P[a][s,:] * V self.value[s] = max(Q)
else:
Q[a] = PR[s,a] + discount * P[s,:,a] * V
V[s] = max(Q)
variation = self.getSpan(V - Vprev) variation = self.getSpan(V - Vprev)
if self.verbose: if self.verbose:
print(" %s %s" % (self.iter, variation)) print(" %s %s" % (self.iter, variation))
if variation < thresh: if variation < self.thresh:
done = True done = True
if self.verbose: if self.verbose:
print('MDP Toolbox : iterations stopped, epsilon-optimal policy found') print('MDP Toolbox : iterations stopped, epsilon-optimal policy found')
...@@ -1458,13 +1414,10 @@ class ValueIterationGS(MDP): ...@@ -1458,13 +1414,10 @@ class ValueIterationGS(MDP):
if self.verbose: if self.verbose:
print('MDP Toolbox : iterations stopped by maximum number of iteration condition') print('MDP Toolbox : iterations stopped by maximum number of iteration condition')
for s in range(S): for s in range(self.S):
for a in range(A): for a in range(self.A):
if iscell(P): Q[a] = self.R[s,a] + self.P[a][s,:] * self.discount * self.value
Q[a] = PR[s,a] + P[a][s,:] * discount * V
else:
Q[a] = PR[s,a] + P[s,:,a] * discount * V
V[s], policy[s,1] = max(Q) self.value[s], self.policy[s,1] = max(Q)
self.time = time() - self.time self.time = time() - self.time
test_mdptoolbox.py
View file @ 60e89bf1
...@@ -10,7 +10,7 @@ from numpy import array, eye, matrix, zeros ...@@ -10,7 +10,7 @@ from numpy import array, eye, matrix, zeros
from numpy.random import rand from numpy.random import rand
from scipy.sparse import eye as speye from scipy.sparse import eye as speye
from scipy.sparse import csr_matrix as sparse from scipy.sparse import csr_matrix as sparse
from scipy.stats.distributions import poisson #from scipy.stats.distributions import poisson
inst = MDP() inst = MDP()
...@@ -144,39 +144,50 @@ def test_ValueIteration_boundIter(): ...@@ -144,39 +144,50 @@ def test_ValueIteration_boundIter():
inst = ValueIteration(P, R, 0.9, 0.01) inst = ValueIteration(P, R, 0.9, 0.01)
assert (inst.max_iter == 28) assert (inst.max_iter == 28)
def test_JacksCarRental(): # PolicyIteration
S = 21 ** 2 def test_PolicyIteration():
A = 11 P = array([[[0.5, 0.5],[0.8, 0.2]],[[0, 1],[0.1, 0.9]]])
P = zeros((A, S, S)) R = array([[5, 10], [-1, 2]])
R = zeros((A, S, S))
for a in range(A):
for s in range(21):
for s1 in range(21):
c1s = int(s / 21)
c2s = s - c1s * 21
c1s1 = int(s1 / 21)
c2s1 = s - c1s * 21
cs = c1s + c2s
cs1 = c1s1 + c2s1
netmove = 5 - a
if (s1 < s):
pass
else:
pass
P[a, s, s1] = 1
R[a, s, s1] = 10 * (cs - cs1) - 2 * abs(a)
inst = PolicyIteration(P, R, 0.9) inst = PolicyIteration(P, R, 0.9)
inst.iterate() inst.iterate()
#assert (inst.policy == ) assert (abs(inst.value[0] - 42.4419) < 0.001)
assert (abs(inst.value[1] - 36.0465) < 0.001)
def test_JacksCarRental2(): assert (inst.policy == (1, 0))
pass assert (inst.iter == 2)
def test_GamblersProblem(): #def test_JacksCarRental():
inst = ValueIteration() # S = 21 ** 2
inst.iterate() # A = 11
#assert (inst.policy == ) # P = zeros((A, S, S))
# R = zeros((A, S, S))
# for a in range(A):
# for s in range(21):
# for s1 in range(21):
# c1s = int(s / 21)
# c2s = s - c1s * 21
# c1s1 = int(s1 / 21)
# c2s1 = s - c1s * 21
# cs = c1s + c2s
# cs1 = c1s1 + c2s1
# netmove = 5 - a
# if (s1 < s):
# pass
# else:
# pass
# P[a, s, s1] = 1
# R[a, s, s1] = 10 * (cs - cs1) - 2 * abs(a)
#
# inst = PolicyIteration(P, R, 0.9)
# inst.iterate()
# #assert (inst.policy == )
#
#def test_JacksCarRental2():
# pass
#
#def test_GamblersProblem():
# inst = ValueIteration()
# inst.iterate()
# #assert (inst.policy == )
# checkSquareStochastic: not square, stochastic and non-negative # checkSquareStochastic: not square, stochastic and non-negative
......
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