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Commit 5b516cdf authored by Steven Cordwell's avatar Steven Cordwell
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added class LP

parent 31712f2c
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Showing with 113 additions and 42 deletions
mdp.py
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......@@ -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_span(Vnext - V);
variation = self.getSpan(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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