def mdp(G_, R_, RT_, L_, d_, x0_, gamma_):
G = cp.deepcopy(G_)
R = cp.deepcopy(R_)
RT = cp.deepcopy(RT_)
L = cp.deepcopy(L_)
d = cp.deepcopy(d_)
x0 = cp.deepcopy(x0_)
gamma = cp.deepcopy(gamma_)
[T, n, A]=R.shape
T=T+1
# prelocating
#numpy zero matrices prelocating
##############################################################
# unconstrained policy
un_U=np.zeros((n, T))
un_Q=np.zeros((T-1, n, A))
un_M=np.zeros((T-1, n, n))
un_x=np.zeros((n, T))
# basic feasible policy
phi_U=np.zeros((n, T))
phi_Q=np.zeros((T-1, n, A))
phi_M=np.zeros((T-1, n, n))
phi_x=np.zeros((n, T))
phi_opt=np.zeros((1,T-1))
# heuristic policy-projection
pro_U=np.zeros((n, T))
pro_Q=np.zeros((T-1, n, A))
pro_M=np.zeros((T-1, n, n))
pro_x=np.zeros((n, T))
# heuristic policy-backward forward induction
bf_U=np.zeros((n, T))
bf_Q=np.zeros((T-1, n, A))
bf_M=np.zeros((T-1, n, n))
bf_x=np.zeros((n, T))
##############################################################################
# Initialization
un_U[:,[T-1]]=RT
phi_U[:,[T-1]]=RT
pro_U[:,[T-1]]=RT
bf_U[:,[T-1]]=RT
# Backward Induction
for j in range(T-2,-1,-1):
[un_U[:,[j]],un_Q[j,:,:],un_M[j,:,:]]=un.policy(G, R[j,:,:], un_U[:,[j+1]], gamma)
[phi_U[:,[j]],phi_Q[j,:,:],phi_M[j,:,:],phi_opt[0,j]]=phi.policy(G, R[j,:,:], L, d, phi_U[:,j+1], gamma)
#[pro_U[:,j],pro_Q[j,:,:],pro_M[j,:,:]]=pro_policy(G, R[j,:,:], d, pro_U[:,j+1], gamma);
un_x=MC.mc_x(x0,un_M)
phi_x=MC.mc_x(x0,phi_M)
TO=100;
i=0;
bf_x=cp.deepcopy(phi_x)
while i <= TO:
# print(i)
temp_x=cp.deepcopy(bf_x)
for j in range(T-2,-1,-1):
[bf_U[:,[j]],bf_Q[j,:,:],bf_M[j,:,:]]=bf.policy(G, R[j,:,:], L, d, bf_x[:,[j]], bf_U[:,j+1], phi_U[:,j], phi_opt[0,j], gamma)
bf_x=MC.mc_x(x0,bf_M)
if LA.norm(bf_x-temp_x,np.inf) < 1e-5:
break
i=i+1
# print("M shape", np.shape(phi_M))
return un_Q, un_x, phi_Q, phi_x, bf_Q, bf_x
def mdp_cvxpy(G_3D, R, RT, L, d, x0, gamma):
[T, n, A] = R.shape
T = T + 1
# if using cvxpy, G matrix is 2D instead of 3D
G = cp.deepcopy(G_3D[0,:,:])
for act in range(1, A):
G = np.hstack((G, G_3D[act,:,:]))
# unconstrained policy
un_U=np.zeros((n, T))
un_Q=np.zeros((T-1, n, A))
un_M=np.zeros((T-1, n, n))
un_x=np.zeros((n, T))
# basic feasible policy
phi_U=np.zeros((n, T))
phi_Q=np.zeros((T-1, n, A))
phi_M=np.zeros((T-1, n, n))
phi_x=np.zeros((n, T))
phi_opt=np.zeros((1,T-1))
# heuristic policy-projection
pro_U=np.zeros((n, T))
pro_Q=np.zeros((T-1, n, A))
pro_M=np.zeros((T-1, n, n))
pro_x=np.zeros((n, T))
# heuristic policy-backward forward induction
bf_U=np.zeros((n, T))
bf_Q=np.zeros((T-1, n, A))
bf_M=np.zeros((T-1, n, n))
bf_x=np.zeros((n, T))
# Initialization
un_U[:,[T-1]] = cp.deepcopy(RT)
phi_U[:,[T-1]] = cp.deepcopy(RT)
pro_U[:,[T-1]] = cp.deepcopy(RT)
bf_U[:,[T-1]] = cp.deepcopy(RT)
# solving unconstrained policy and U
for j in range(T-2,-1,-1):
print("Current step of solving un: ", j)
[un_U[:,[j]],un_Q[j,:,:],un_M[j,:,:]] = un.policy(G_3D, R[j,:,:], un_U[:,[j+1]], gamma)
# using un_U to solve for x using greedy one-step optimization
unbf_Q = np.zeros((T-1, n, A))
unbf_M = np.zeros((T-1, n, n))
unbf_x = np.zeros((n, T))
unbf_x[:,[0]] = cp.deepcopy(x0)
for j in range(0, T - 1):
print("Current step of solving unbf: ",j)
unbf_Q[j,:,:], unbf_M[j,:,:], unbf_x[:,[j + 1]] = bfpy.policy_unU2(G, R[j,:,:], L, d, unbf_x[:,[j]], un_U[:,j + 1], gamma)
# print("un_u: ")
# print(un_U)
# backward induction
for j in range(T-2,-1,-1):
print("Current step of solving phi: ", j)
[phi_U[:,[j]],phi_Q[j,:,:],phi_M[j,:,:],phi_opt[0,j]]=phipy.policy(G, R[j,:,:], L, d, phi_U[:,j+1], gamma)
print("Current step of solving pro: ", j)
[pro_U[:,[j]],pro_Q[j,:,:],pro_M[j,:,:]] = propy.policy(G, R[j,:,:], L, d, un_Q[j,:,:], un_M[j,:,:], un_U[:,j], pro_U[:,j+1], phi_U[:,j], phi_opt[0,j], gamma)
un_x = MC.mc_x(x0,un_M)
phi_x = MC.mc_x(x0,phi_M)
pro_x = MC.mc_x(x0,pro_M)
bf_x=cp.deepcopy(phi_x)
print("Phi_opt", phi_opt)
# number of max iterations
TO = 50;
i = 0;
bf_x=cp.deepcopy(phi_x)
bf_Q = cp.deepcopy(phi_Q)
while i <= TO:
print("Current step of solving bf: ",i)
prev_x=cp.deepcopy(bf_x)
prev_U = cp.deepcopy(bf_U)
prev_Q = cp.deepcopy(bf_Q)
for j in range(T - 2, -1, -1):
bf_U[:,[j]],bf_Q[j,:,:],bf_M[j,:,:]=bfpy.policy(G, R[j,:,:], L, d, bf_x[:,[j]], bf_U[:,j+1], phi_U[:,j], phi_opt[0,j], gamma)
bf_x = MC.mc_x(x0,bf_M)
x_norm = LA.norm(bf_x - prev_x, np.inf)
# print("x norm diff: ", x_norm)
# U_norm = LA.norm(bf_U - prev_U, np.inf) / LA.norm(bf_U, np.inf)
# print("U norm diff: ", U_norm)
# Q_norm = 0
# for i in range(T - 1):
# Q_norm += LA.norm(bf_Q[i,:,:] - prev_Q[i,:,:], np.inf)
# print("Q norm diff: ", Q_norm)
if x_norm < 1e-5:
break
i = i + 1
# print("phi_u: ")
# print(phi_U)
# print("bf_u: ")
# print(bf_U)
# print("pro_u: ")
# print(pro_U)
# print("M shape", np.shape(phi_M))
# print("phiM: ");print(phi_M)
# print("bf_M: "); print(bf_M)
# dim0, dim1, dim2 = phi_M.shape
# for i in range(dim0):
# print(i); print_matrix(phi_M[i,:,:])
# return phi_Q, phi_x, bf_Q, bf_x
return un_Q, un_x, phi_Q, phi_x, bf_Q, bf_x, pro_Q, pro_x, unbf_Q, unbf_x