def test_plot_pi_vs_alpha(self, mock_plt):
# Construct game
game = pyspiel.load_matrix_game("matrix_rps")
payoff_tables = utils.game_payoffs_array(game)
_, payoff_tables = utils.is_symmetric_matrix_game(payoff_tables)
payoffs_are_hpt_format = utils.check_payoffs_are_hpt(payoff_tables)
# Compute alpharank
alpha = 1e2
_, _, pi, num_profiles, num_strats_per_population = (
alpharank.compute(payoff_tables, alpha=alpha))
strat_labels = utils.get_strat_profile_labels(payoff_tables,
payoffs_are_hpt_format)
num_populations = len(payoff_tables)
# Construct synthetic pi-vs-alpha history
pi_list = np.empty((num_profiles, 0))
alpha_list = []
for _ in range(2):
pi_list = np.append(pi_list, np.reshape(pi, (-1, 1)), axis=1)
alpha_list.append(alpha)
# Test plotting code (via pyplot mocking to prevent plot pop-up)
alpharank_visualizer.plot_pi_vs_alpha(
pi_list.T,
alpha_list,
num_populations,
num_strats_per_population,
strat_labels,
num_strats_to_label=0)
self.assertTrue(mock_plt.show.called)
def sweep_pi_vs_alpha(payoff_tables,
strat_labels=None,
warm_start_alpha=None,
visualize=False,
return_alpha=False,
m=50,
rtol=1e-5,
atol=1e-8,
num_strats_to_label=10,
legend_sort_clusters=False):
"""Computes stationary distribution, pi, for range of selection intensities.
The range of selection intensities is defined in alpha_list and corresponds
to the temperature of the Fermi selection function.
Args:
payoff_tables: List of game payoff tables, one for each agent identity. Each
payoff_table may be either a numpy array, or a _PayoffTableInterface
object.
strat_labels: Human-readable strategy labels. See get_strat_profile_labels()
in utils.py for formatting details.
warm_start_alpha: Initial value of alpha to use.
visualize: Plot the sweep results.
return_alpha: Whether to return the final alpha used.
m: AlphaRank population size.
rtol: The relative tolerance parameter for np.allclose calls.
atol: The absolute tolerance parameter for np.allclose calls.
num_strats_to_label: Number of strats to label in legend
legend_sort_clusters: If true, strategies in the same cluster are sorted in
the legend according to orderings for earlier alpha values. Primarily for
visualization purposes! Rankings for lower alpha values should be
interpreted carefully.
Returns:
pi: AlphaRank stationary distribution.
alpha: The AlphaRank selection-intensity level resulting from sweep.
"""
payoffs_are_hpt_format = utils.check_payoffs_are_hpt(payoff_tables)
num_populations = len(payoff_tables)
num_strats_per_population = utils.get_num_strats_per_population(
payoff_tables, payoffs_are_hpt_format)
if num_populations == 1:
num_profiles = num_strats_per_population[0]
else:
num_profiles = utils.get_num_profiles(num_strats_per_population)
assert (strat_labels is None or isinstance(strat_labels, dict)
or (len(strat_labels) == num_profiles))
pi_list = np.empty((num_profiles, 0))
alpha_list = []
num_iters = 0
alpha_mult_factor = 2.
if warm_start_alpha is not None:
alpha = warm_start_alpha
alpharank_succeeded_once = False
else:
alpha = 1e-4 # Reasonable default for most games, can be user-overridden
while 1:
try:
_, _, pi, _, _ = compute(payoff_tables, alpha=alpha, m=m)
pi_list = np.append(pi_list, np.reshape(pi, (-1, 1)), axis=1)
alpha_list.append(alpha)
# Stop when pi converges
if num_iters > 0 and np.allclose(pi, pi_list[:, num_iters - 1],
rtol, atol):
break
alpha *= alpha_mult_factor
num_iters += 1
alpharank_succeeded_once = True
except ValueError as _:
if warm_start_alpha is not None and not alpharank_succeeded_once:
# When warm_start_alpha is used, there's a chance that
# the initial warm_start_alpha is too large and causes exceptions due to
# the Markov transition matrix being reducible. So keep decreasing until
# a single success occurs.
alpha /= 2
elif not np.allclose(pi_list[:, -1], pi_list[:, -2], rtol, atol):
# Sweep stopped due to multiple stationary distributions, but pi had
# not converged due to the alpha scaling being too large.
alpha /= alpha_mult_factor
alpha_mult_factor = (alpha_mult_factor + 1.) / 2.
alpha *= alpha_mult_factor
else:
break
if visualize:
if strat_labels is None:
strat_labels = utils.get_strat_profile_labels(
payoff_tables, payoffs_are_hpt_format)
alpharank_visualizer.plot_pi_vs_alpha(
pi_list.T,
alpha_list,
num_populations,
num_strats_per_population,
strat_labels,
num_strats_to_label=num_strats_to_label,
legend_sort_clusters=legend_sort_clusters)
if return_alpha:
return pi, alpha
else:
return pi
def sweep_pi_vs_epsilon(payoff_tables,
strat_labels=None,
warm_start_epsilon=None,
visualize=False,
return_epsilon=False,
min_iters=10,
max_iters=100,
min_epsilon=1e-14,
num_strats_to_label=10,
legend_sort_clusters=False):
"""Computes infinite-alpha distribution for a range of perturbations.
The range of response graph perturbations is defined in epsilon_list.
Note that min_iters and max_iters is necessary as it may sometimes appear the
stationary distribution has converged for a game in the first few iterations,
where in reality a sufficiently smaller epsilon is needed for the distribution
to first diverge, then reconverge. This behavior is dependent on both the
payoff structure and bounds, so the parameters min_iters and max_iters can be
used to fine-tune this.
Args:
payoff_tables: List of game payoff tables, one for each agent identity.
Each payoff_table may be either a numpy array, or a
_PayoffTableInterface object.
strat_labels: Human-readable strategy labels. See get_strat_profile_labels()
in utils.py for formatting details.
warm_start_epsilon: Initial value of epsilon to use.
visualize: Plot the sweep results.
return_epsilon: Whether to return the final epsilon used.
min_iters: the minimum number of sweep iterations.
max_iters: the maximum number of sweep iterations.
min_epsilon: the minimum value of epsilon to be tested, at which point the
sweep terminates (if not converged already).
num_strats_to_label: Number of strats to label in legend
legend_sort_clusters: If true, strategies in the same cluster are sorted in
the legend according to orderings for earlier alpha values. Primarily for
visualization purposes! Rankings for lower alpha values should be
interpreted carefully.
Returns:
pi: AlphaRank stationary distribution.
epsilon: The AlphaRank transition matrix noise level resulting from sweep.
"""
payoffs_are_hpt_format = utils.check_payoffs_are_hpt(payoff_tables)
num_populations = len(payoff_tables)
num_strats_per_population = utils.get_num_strats_per_population(
payoff_tables, payoffs_are_hpt_format)
if num_populations == 1:
num_profiles = num_strats_per_population[0]
else:
num_profiles = utils.get_num_profiles(num_strats_per_population)
assert (strat_labels is None or isinstance(strat_labels, dict)
or (len(strat_labels) == num_profiles))
pi_list = np.empty((num_profiles, 0))
pi, alpha, m = None, None, None # Unused in infinite-alpha regime
epsilon_list = []
epsilon_pi_hist = {}
num_iters = 0
epsilon_mult_factor = 0.5
alpharank_succeeded_once = False
if warm_start_epsilon is not None:
epsilon = warm_start_epsilon
else:
epsilon = 0.5
while True:
try:
pi_prev = pi
_, _, pi, _, _ = compute(payoff_tables,
m=m,
alpha=alpha,
use_inf_alpha=True,
inf_alpha_eps=epsilon)
epsilon_pi_hist[epsilon] = pi
# Stop when pi converges
if num_iters > min_iters and np.allclose(pi, pi_prev):
break
epsilon *= epsilon_mult_factor
num_iters += 1
alpharank_succeeded_once = True
assert num_iters < max_iters, (
'Alpharank stationary distr. not found'
'after {} iterations of pi_vs_epsilon'
'sweep'.format(num_iters))
except ValueError as _:
print('Error: ', _, epsilon, min_epsilon)
# Case where epsilon has been decreased beyond desirable limits but no
# distribution found.
assert epsilon >= min_epsilon, (
'AlphaRank stationary distr. not found &'
'epsilon < min_epsilon.')
# Case where epsilon >= min_epsilon, but still small enough that it causes
# causes exceptions due to precision issues. So increase it.
epsilon /= epsilon_mult_factor
# Case where alpharank_succeeded_once (i.e., epsilon_list and pi_list have
# at least one entry), and a) has not converged yet and b) failed on this
# instance due to epsilon being too small. I.e., the rate of decreasing
# of epsilon is too high.
if alpharank_succeeded_once:
epsilon_mult_factor = (epsilon_mult_factor + 1.) / 2.
epsilon *= epsilon_mult_factor
epsilon_list, pi_list = zip(
*[(epsilon, epsilon_pi_hist[epsilon])
for epsilon in sorted(epsilon_pi_hist.keys(), reverse=True)])
pi_list = np.asarray(pi_list)
if visualize:
if strat_labels is None:
strat_labels = utils.get_strat_profile_labels(
payoff_tables, payoffs_are_hpt_format)
alpharank_visualizer.plot_pi_vs_alpha(
pi_list.T,
epsilon_list,
num_populations,
num_strats_per_population,
strat_labels,
num_strats_to_label=num_strats_to_label,
legend_sort_clusters=legend_sort_clusters,
xlabel=r'Infinite-AlphaRank Noise $\epsilon$')
if return_epsilon:
return pi_list[-1], epsilon_list[-1]
else:
return pi_list[-1]
