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 value_graph():
# vs = [np.sum(utils.value_functional(mdp.P, mdp.r, pi, mdp.discount).squeeze()**2) for pi in det_pis]
# plt.figure(figsize=(16,16))
# nx.draw(G, pos, node_color=vs, node_size=150)
# plt.savefig('figs/pi_graphs/val.png')
# plt.close()
n_states = 10
n_actions = 2
det_pis = utils.get_deterministic_policies(n_states, n_actions)
n = len(det_pis)
print('n pis: {}'.format(n))
# how does discount effect these!?
mdp = utils.build_random_mdp(n_states, n_actions, 0.5)
values = [utils.value_functional(mdp.P, mdp.r, pi, mdp.discount).squeeze() for pi in det_pis]
vs = np.stack(values).reshape((n, n_states))
W = 1/(np.abs(np.sum(vs[None, :, :] - vs[:, None, :], axis=-1)) + 1e-8)
A = graph.mdp_topology(det_pis)
adj = A*W
G = nx.from_numpy_array(adj)
pos = nx.spring_layout(G, iterations=200)
plt.figure(figsize=(16,16))
nx.draw(G, pos, node_color=[np.sum(v) for v in values], node_size=150)
plt.savefig('figs/value_graphs/value_graph-{}-{}.png'.format(n_states, n_actions))
plt.close()
def graph_PG():
# ffmpeg -framerate 10 -start_number 0 -i %d.png -c:v libx264 -r 30 -pix_fmt yuv420p out.mp4
n_states = 6
n_actions = 4
det_pis = utils.get_deterministic_policies(n_states, n_actions)
print('n pis: {}'.format(len(det_pis)))
mdp = utils.build_random_mdp(n_states, n_actions, 0.9)
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_logits = np.random.standard_normal((n_states, n_actions))
init_v = utils.value_functional(mdp.P, mdp.r, utils.softmax(init_logits), mdp.discount).squeeze()
a = graph.sparse_coeffs(basis, init_v, lr=0.1)
print('\nSolving PG')
pis = utils.solve(search_spaces.policy_gradient_iteration_logits(mdp, 0.1), init_logits)
print("\n{} policies to vis".format(len(pis)))
n = len(pis)
# pis = pis[::n//100]
pis = pis[0:20]
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()
nx.draw(G, pos, node_color=a)
# plt.show()
plt.savefig('figs/pg_graphs/{}.png'.format(i))
plt.close()
def test_topology():
n_states = 5
n_actions = 2
det_pis = utils.get_deterministic_policies(n_states, n_actions)
A = graph.mdp_topology(det_pis)
print(A)
G = nx.from_numpy_array(A)
nx.draw(G)
plt.show()
def test_everything():
n_states = 5
n_actions = 2
det_pis = utils.get_deterministic_policies(n_states, n_actions)
mdp = utils.build_random_mdp(n_states, n_actions, 0.9)
A = graph.mdp_topology(det_pis)
basis = graph.construct_mdp_basis(det_pis, mdp)
# v = np.random.random((n_states, ))
v = utils.value_functional(mdp.P, mdp.r, det_pis[2],
mdp.discount).squeeze()
a = graph.sparse_coeffs(basis, v)
G = nx.from_numpy_array(A)
pos = nx.spring_layout(G, iterations=200)
nx.draw(G, pos, node_color=a)
plt.show()
def value_graph_laplacian():
n_states = 8
n_actions = 2
det_pis = utils.get_deterministic_policies(n_states, n_actions)
n = len(det_pis)
print('n pis: {}'.format(n))
mdp = utils.build_random_mdp(n_states, n_actions, 0.5)
values = [utils.value_functional(mdp.P, mdp.r, pi, mdp.discount).squeeze() for pi in det_pis]
Vs = np.stack(values).reshape((n, n_states))
A = graph.mdp_topology(det_pis)
W = 1/(np.abs(np.sum(Vs[None, :, :] - Vs[:, None, :], axis=-1)) + 1e-8)
adj = A*W
G = nx.from_numpy_array(adj)
pos = nx.spring_layout(G, iterations=200)
plt.figure(figsize=(16,16))
nx.draw(G, pos, node_color=[np.sum(v) for v in values], node_size=150)
plt.savefig('figs/value_graphs/value_graph-{}-{}.png'.format(n_states, n_actions))
plt.close()
# how can you calulate expected eignenvalues!?
# observation. the underlying complexity of the value topology is linear!?!?
# how hard is it to estimate the main eigen vec from noisy observations!?
# that would tell us the complexity!?!?
for i, alpha in enumerate(np.linspace(0, 1, 10)):
us = []
for _ in range(50):
vs = Vs + alpha*np.random.standard_normal(Vs.shape)
W = 1/(np.abs(np.sum(vs[None, :, :] - vs[:, None, :], axis=-1)) + 1e-8)
adj = A*W
u, v = graph_laplacian_spectra(adj)
us.append(u)
us = np.stack(us, axis=0)
mean = np.mean(us, axis=0)
var = np.var(us, axis=0)
plt.bar(range(len(mean)), mean, yerr=np.sqrt(var))
plt.savefig('figs/value_graphs/{}-lap.png'.format(i))
plt.close()
def value_graph_laplacians():
n_states = 8
n_actions = 2
det_pis = utils.get_deterministic_policies(n_states, n_actions)
N = len(det_pis)
print('n pis: {}'.format(N))
for i in range(1):
mdp = utils.build_random_mdp(n_states, n_actions, 0.5)
values = [utils.value_functional(mdp.P, mdp.r, pi, mdp.discount).squeeze() for pi in det_pis]
Vs = np.stack(values).reshape((N, n_states))
A = graph.mdp_topology(det_pis)
W = np.exp(-np.linalg.norm(Vs[None, :, :] - Vs[:, None, :], ord=np.inf, axis=-1)+1e-8)
# mVs = np.mean(Vs, axis=0) # n_states
# W = np.dot((Vs - mVs) , (Vs - mVs).T)
adj = W * A
G = nx.from_numpy_array(adj)
pos = nx.spectral_layout(G) #, iterations=500)
plt.figure(figsize=(16,16))
nx.draw(G, pos, node_color=[np.sum(v) for v in values], node_size=150)
plt.savefig('figs/value_graphs/{}-value_graph-{}-{}.png'.format(i, n_states, n_actions))
plt.close()
u, v = graph_laplacian_spectra(adj)
plt.figure(figsize=(8,8))
plt.bar(range(len(u)), u)
plt.savefig('figs/value_graphs/{}-lap.png'.format(i))
plt.close()
plt.figure(figsize=(16,16))
n = 5
for j in range(n*n):
plt.subplot(n,n,j+1)
nx.draw(G, pos, node_color=u[10*j] * v[10*j], node_size=150)
plt.savefig('figs/value_graphs/{}-spectra.png'.format(i, n_states, n_actions))
plt.close()