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def evaluate_policy(theta, F):
"""
Given theta (scalar, dtype=float) and policy F (array_like), returns the
value associated with that policy under the worst case path for {w_t}, as
well as the entropy level.
"""
rlq = qe.robustlq.RBLQ(Q, R, A, B, C, beta, theta)
K_F, P_F, d_F, O_F, o_F = rlq.evaluate_F(F)
x0 = np.array([[1.], [0.], [0.]])
value = - x0.T.dot(P_F.dot(x0)) - d_F
entropy = x0.T.dot(O_F.dot(x0)) + o_F
return list(map(float, (value, entropy)))
df = df.dropna(how='any')
return df
# -------------------------------------------------------------------------- #
# Main
# -------------------------------------------------------------------------- #
# == Compute the optimal rule == #
optimal_lq = qe.lqcontrol.LQ(Q, R, A, B, C, β)
Po, Fo, do = optimal_lq.stationary_values()
# == Compute a robust rule given θ == #
baseline_robust = qe.robustlq.RBLQ(Q, R, A, B, C, β, θ)
Fb, Kb, Pb = baseline_robust.robust_rule()
# == Check the positive definiteness of worst-case covariance matrix to == #
# == ensure that θ exceeds the breakdown point == #
test_matrix = np.identity(Pb.shape[0]) - (C.T @ Pb @ C) / θ
eigenvals, eigenvecs = eig(test_matrix)
assert (eigenvals >= 0).all(), 'θ below breakdown point.'
emax = 1.6e6
optimal_best_case = value_and_entropy(emax, Fo, 'best')
robust_best_case = value_and_entropy(emax, Fb, 'best')
optimal_worst_case = value_and_entropy(emax, Fo, 'worst')
robust_worst_case = value_and_entropy(emax, Fb, 'worst')
def evaluate_policy(θ, F):
"""
Given θ (scalar, dtype=float) and policy F (array_like), returns the
value associated with that policy under the worst case path for {w_t}, as
well as the entropy level.
"""
rlq = qe.robustlq.RBLQ(Q, R, A, B, C, β, θ)
K_F, P_F, d_F, O_F, o_F = rlq.evaluate_F(F)
x0 = np.array([[1.], [0.], [0.]])
value = - x0.T @ P_F @ x0 - d_F
entropy = x0.T @ O_F @ x0 + o_F
return list(map(float, (value, entropy)))
df = df.dropna(how='any')
return df
#-----------------------------------------------------------------------------#
# Main
#-----------------------------------------------------------------------------#
# == Compute the optimal rule == #
optimal_lq = qe.lqcontrol.LQ(Q, R, A, B, C, beta)
Po, Fo, do = optimal_lq.stationary_values()
# == Compute a robust rule given theta == #
baseline_robust = qe.robustlq.RBLQ(Q, R, A, B, C, beta, theta)
Fb, Kb, Pb = baseline_robust.robust_rule()
# == Check the positive definiteness of worst-case covariance matrix to == #
# == ensure that theta exceeds the breakdown point == #
test_matrix = np.identity(Pb.shape[0]) - np.dot(C.T, Pb.dot(C)) / theta
eigenvals, eigenvecs = eig(test_matrix)
assert (eigenvals >= 0).all(), 'theta below breakdown point.'
emax = 1.6e6
optimal_best_case = value_and_entropy(emax, Fo, 'best')
robust_best_case = value_and_entropy(emax, Fb, 'best')
optimal_worst_case = value_and_entropy(emax, Fo, 'worst')
robust_worst_case = value_and_entropy(emax, Fb, 'worst')