def graph_PI():
n_states = 10
n_actions = 2
det_pis = utils.get_deterministic_policies(n_states, n_actions)
print('n pis: {}'.format(len(det_pis)))
mdp = utils.build_random_sparse_mdp(n_states, n_actions, 0.5)
A = graph.mdp_topology(det_pis)
G = nx.from_numpy_array(A)
pos = nx.spring_layout(G, iterations=200)
basis = graph.construct_mdp_basis(det_pis, mdp)
init_pi = utils.softmax(np.random.standard_normal((n_states, n_actions)))
init_v = utils.value_functional(mdp.P, mdp.r, init_pi, mdp.discount).squeeze()
a = graph.sparse_coeffs(basis, init_v, lr=0.1)
pis = utils.solve(search_spaces.policy_iteration(mdp), init_pi)
print("\n{} policies to vis".format(len(pis)))
for i, pi in enumerate(pis[:-1]):
print('Iteration: {}'.format(i))
v = utils.value_functional(mdp.P, mdp.r, pi, mdp.discount).squeeze()
a = graph.sparse_coeffs(basis, v, lr=0.1, a_init=a)
plt.figure(figsize=(16,16))
nx.draw(G, pos, node_color=a, node_size=150)
# plt.show()
plt.savefig('figs/pi_graphs/{}.png'.format(i))
plt.close()
def generate_pi(mdp, c):
init_pi = utils.random_policy(mdp.S,mdp.A)
pis = utils.solve(ss.policy_iteration(mdp), init_pi)
vs = np.stack([utils.value_functional(mdp.P, mdp.r, pi, mdp.discount) for pi in pis])[:,:,0]
n = vs.shape[0]
plt.scatter(vs[0, 0], vs[0, 1], c=c, s=30, label='{}'.format(n-2))
plt.scatter(vs[1:-1, 0], vs[1:-1, 1], c=range(n-2), cmap='viridis', s=10)
plt.scatter(vs[-1, 0], vs[-1, 1], c='m', marker='x')
for i in range(len(vs)-2):
dv = 0.1*(vs[i+1, :] - vs[i, :])
plt.arrow(vs[i, 0], vs[i, 1], dv[0], dv[1], color=c, alpha=0.5, width=0.005)
def policy_iteration(mdp, pis):
# pi_star = utils.solve(ss.policy_iteration(mdp), pis[0])[-1]
lens, pi_stars = [], []
for pi in pis:
pi_traj = clip_solver_traj(utils.solve(ss.policy_iteration(mdp), pi))
pi_star = pi_traj[-1]
pi_stars.append(pi_star)
lens.append(len(pi_traj))
return lens, pi_stars
def onoffpolicy_abstraction(mdp, pis):
tol = 0.01
init = np.random.random((mdp.S, mdp.A))
init = init / np.sum(init, axis=1, keepdims=True)
# ### all policy abstraction
# # n x |S| x |A|
# Qs = np.stack([utils.bellman_operator(mdp.P, mdp.r, utils.value_functional(mdp.P, mdp.r, pi, mdp.discount), mdp.discount) for pi in pis], axis=0)
# similar_states = np.sum(np.sum(np.abs(Qs[:, :, None, :] - Qs[:, None, :, :]), axis=3), axis=0) # |S| x |S|
# all_idx, all_abstracted_mdp, all_f = abs.build_state_abstraction(similar_states, mdp)
### optimal policy abstraction
pi_star = utils.solve(ss.policy_iteration(mdp), np.log(init))[-1]
Q_star = utils.bellman_operator(
mdp.P, mdp.r,
utils.value_functional(mdp.P, mdp.r, pi_star, mdp.discount),
mdp.discount)
# similar_states = np.sum(np.abs(Q_star[:, None, :] - Q_star[None, :, :]), axis=-1) # |S| x |S|. preserves optimal policy's value (for all actions)
# similar_states = np.abs(np.max(Q_star[:, None, :],axis=-1) - np.max(Q_star[None, :, :],axis=-1)) # |S| x |S|. preserves optimal action's value
#
V = utils.value_functional(mdp.P, mdp.r, init, mdp.discount)
similar_states = np.abs(V[None, :, :] - V[:, None, :])[:, :, 0]
optimal_idx, optimal_abstracted_mdp, optimal_f = abs.build_state_abstraction(
similar_states, mdp, tol)
mdps = [mdp, optimal_abstracted_mdp]
names = ['ground', 'optimal_abstracted_mdp']
solvers = [abs.Q, abs.SARSA, abs.VI]
lifts = [np.eye(mdp.S), optimal_f]
idxs = [range(mdp.S), optimal_idx]
# if all_f.shape[0] == optimal_f.shape[0]:
# raise ValueError('Abstractions are the same so we probs wont see any difference...')
print('\nAbstraction:', optimal_f.shape)
truth = abs.PI(init, mdp, np.eye(mdp.S))
results = []
for n, M, idx, f in zip(names, mdps, idxs, lifts):
for solve in solvers:
err = np.max(np.abs(truth - solve(init[idx, :], M, f)))
results.append((n, solve.__name__, err))
return results
def compare_mdp_lmdp():
n_states, n_actions = 2, 2
mdp = utils.build_random_mdp(n_states, n_actions, 0.9)
pis = utils.gen_grid_policies(7)
vs = utils.polytope(mdp.P, mdp.r, mdp.discount, pis)
plt.figure(figsize=(16, 16))
plt.scatter(vs[:, 0], vs[:, 1], s=10, alpha=0.75)
# solve via LMDPs
p, q = lmdps.mdp_encoder(mdp.P, mdp.r)
u, v = lmdps.lmdp_solver(p, q, mdp.discount)
pi_u_star = lmdps.lmdp_decoder(u, mdp.P)
pi_p = lmdps.lmdp_decoder(p, mdp.P)
# solve MDP
init = np.random.standard_normal((n_states, n_actions))
pi_star = utils.solve(search_spaces.policy_iteration(mdp), init)[-1]
# pi_star = onehot(np.argmax(qs, axis=1), n_actions)
# evaluate both policies.
v_star = utils.value_functional(mdp.P, mdp.r, pi_star, mdp.discount)
v_u_star = utils.value_functional(mdp.P, mdp.r, pi_u_star, mdp.discount)
v_p = utils.value_functional(mdp.P, mdp.r, pi_p, mdp.discount)
plt.scatter(v_star[0, 0],
v_star[1, 0],
c='m',
alpha=0.5,
marker='x',
label='mdp')
plt.scatter(v_u_star[0, 0],
v_u_star[1, 0],
c='g',
alpha=0.5,
marker='x',
label='lmdp')
plt.scatter(v_p[0, 0], v_p[1, 0], c='k', marker='x', alpha=0.5, label='p')
plt.legend()
plt.show()
def compare_acc():
n_states, n_actions = 2, 2
lmdp = []
lmdp_rnd = []
for _ in range(10):
mdp = utils.build_random_mdp(n_states, n_actions, 0.5)
# solve via LMDPs
p, q = lmdps.mdp_encoder(mdp.P, mdp.r)
u, v = lmdps.lmdp_solver(p, q, mdp.discount)
pi_u_star = lmdps.lmdp_decoder(u, mdp.P)
# solve MDP
init = np.random.standard_normal((n_states, n_actions))
pi_star = utils.solve(search_spaces.policy_iteration(mdp), init)[-1]
# solve via LMDPs
# with p set to the random dynamics
p, q = lmdps.mdp_encoder(mdp.P, mdp.r)
p = np.einsum('ijk,jk->ij', mdp.P,
np.ones((n_states, n_actions)) / n_actions)
# q = np.max(mdp.r, axis=1, keepdims=True)
u, v = lmdps.lmdp_solver(p, q, mdp.discount)
pi_u_star_random = lmdps.lmdp_decoder(u, mdp.P)
# evaluate both policies.
v_star = utils.value_functional(mdp.P, mdp.r, pi_star, mdp.discount)
v_u_star = utils.value_functional(mdp.P, mdp.r, pi_u_star,
mdp.discount)
v_u_star_random = utils.value_functional(mdp.P, mdp.r,
pi_u_star_random,
mdp.discount)
lmdp.append(np.isclose(v_star, v_u_star, 1e-3).all())
lmdp_rnd.append(np.isclose(v_star, v_u_star_random, 1e-3).all())
print([np.sum(lmdp), np.sum(lmdp_rnd)])
plt.bar(range(2), [np.sum(lmdp), np.sum(lmdp_rnd)])
plt.show()
def mdp_lmdp_optimality():
n_states, n_actions = 2, 2
n = 5
plt.figure(figsize=(8, 16))
plt.title('Optimal control (LMDP) vs optimal policy (MDP)')
for i in range(n):
mdp = utils.build_random_mdp(n_states, n_actions, 0.5)
# solve via LMDPs
p, q = lmdps.mdp_encoder(mdp.P, mdp.r)
u, v = lmdps.lmdp_solver(p, q, mdp.discount)
init = np.random.standard_normal((n_states, n_actions))
pi_star = utils.solve(search_spaces.policy_iteration(mdp), init)[-1]
P_pi_star = np.einsum('ijk,jk->ij', mdp.P, pi_star)
plt.subplot(n, 2, 2 * i + 1)
plt.imshow(u)
plt.subplot(n, 2, 2 * i + 2)
plt.imshow(P_pi_star)
plt.savefig('figs/lmdp_mdp_optimal_dynamics.png')
plt.show()
def PI(init, M, f):
pi_star = utils.solve(ss.policy_iteration(M), np.log(init))[-1]
return utils.value_functional(M.P, M.r, np.dot(f.T, pi_star), M.discount)
V_star = utils.solve(ss.value_iteration(M, 0.01), V_init)[-1]
# lift
return np.dot(f.T, V_star)
if __name__ == '__main__':
tol = 0.01
n_states, n_actions = 512, 2
mdp = utils.build_random_mdp(n_states, n_actions, 0.5)
init = np.random.random((mdp.S, mdp.A))
init = init / np.sum(init, axis=1, keepdims=True)
pi_star = utils.solve(ss.policy_iteration(mdp), np.log(init))[-1]
Q_star = utils.bellman_operator(
mdp.P, mdp.r,
utils.value_functional(mdp.P, mdp.r, pi_star, mdp.discount),
mdp.discount)
similar_states = np.sum(np.abs(Q_star[:, None, :] - Q_star[None, :, :]),
axis=-1) # |S| x |S|
optimal_idx, optimal_abstracted_mdp, optimal_f = build_state_abstraction(
similar_states, mdp, tol)
truth = PI(init, mdp, np.eye(mdp.S))
approx = Q(init[optimal_idx], optimal_abstracted_mdp, optimal_f)
print(