def test_braess_paradox(self): """Test that Braess paradox can be reproduced with the mean field game.""" mfg_game = pyspiel.load_game("python_mfg_dynamic_routing", { "time_step_length": 0.05, "max_num_time_step": 100 }) class NashEquilibriumBraess(policy.Policy): def action_probabilities(self, state, player_id=None): legal_actions = state.legal_actions() if not legal_actions: return {dynamic_routing_utils.NO_POSSIBLE_ACTION: 1.0} elif len(legal_actions) == 1: return {legal_actions[0]: 1.0} else: if legal_actions[0] == 2: return {2: 0.75, 3: 0.25} elif legal_actions[0] == 4: return {4: 2 / 3, 5: 1 / 3} raise ValueError(f"{legal_actions} is not correct.") ne_policy = NashEquilibriumBraess(mfg_game, 1) self.assertEqual( -policy_value.PolicyValue( mfg_game, distribution.DistributionPolicy(mfg_game, ne_policy), ne_policy).value(mfg_game.new_initial_state()), 3.75) self.assertEqual( nash_conv.NashConv(mfg_game, ne_policy).nash_conv(), 0.0) class SocialOptimumBraess(policy.Policy): def action_probabilities(self, state, player_id=None): legal_actions = state.legal_actions() if not legal_actions: return {dynamic_routing_utils.NO_POSSIBLE_ACTION: 1.0} elif len(legal_actions) == 1: return {legal_actions[0]: 1.0} else: if legal_actions[0] == 2: return {2: 0.5, 3: 0.5} elif legal_actions[0] == 4: return {5: 1.0} raise ValueError(f"{legal_actions} is not correct.") so_policy = SocialOptimumBraess(mfg_game, 1) self.assertEqual( -policy_value.PolicyValue( mfg_game, distribution.DistributionPolicy(mfg_game, so_policy), so_policy).value(mfg_game.new_initial_state()), 3.5) self.assertEqual( nash_conv.NashConv(mfg_game, so_policy).nash_conv(), 0.75)
def iteration(self, rl_br_agent=None, learning_rate=None): """Returns a new `TabularPolicy` equivalent to this policy. Args: rl_br_agent: An instance of the RL approximation method to use to compute the best response value for each iteration. If none provided, the exact value is computed. learning_rate: The learning rate. """ self._fp_step += 1 distrib = distribution.DistributionPolicy(self._game, self._policy) if rl_br_agent: joint_avg_policy = rl_agent_policy.RLAgentPolicy( self._game, rl_br_agent, rl_br_agent.player_id, use_observation=True) br_value = policy_value.PolicyValue(self._game, distrib, joint_avg_policy) else: br_value = best_response_value.BestResponse( self._game, distrib, value.TabularValueFunction(self._game)) greedy_pi = greedy_policy.GreedyPolicy(self._game, None, br_value) greedy_pi = greedy_pi.to_tabular(states=self._states) distrib_greedy = distribution.DistributionPolicy(self._game, greedy_pi) weight = learning_rate if learning_rate else 1.0 / (self._fp_step + 1) self._policy = MergedPolicy( self._game, list(range(self._game.num_players())), [self._policy, greedy_pi], [distrib, distrib_greedy], [1.0 - weight, weight]).to_tabular(states=self._states)
def nash_conv(self): """Returns the nash conv.""" distrib = distribution.DistributionPolicy(self._game, self._policy) pi_value = policy_value.PolicyValue(self._game, distrib, self._policy) br_value = best_response_value.BestResponse(self._game, distrib) return (br_value.eval_state(self._game.new_initial_state()) - pi_value.eval_state(self._game.new_initial_state()))
def __init__(self, game, policy: policy_std.Policy, root_state=None): """Initializes the nash conv. Args: game: The game to analyze. policy: A `policy.Policy` object. root_state: The state of the game at which to start. If `None`, the game root state is used. """ self._game = game self._policy = policy if root_state is None: self._root_states = game.new_initial_states() else: self._root_states = [root_state] self._distrib = distribution.DistributionPolicy(self._game, self._policy, root_state=root_state) self._pi_value = policy_value.PolicyValue(self._game, self._distrib, self._policy, value.TabularValueFunction( self._game), root_state=root_state) self._br_value = best_response_value.BestResponse( self._game, self._distrib, value.TabularValueFunction(self._game), root_state=root_state)
def test_cpp_game(self): """Checks if the value of a policy computation works.""" game = pyspiel.load_game("mfg_crowd_modelling") uniform_policy = policy.UniformRandomPolicy(game) dist = distribution.DistributionPolicy(game, uniform_policy) py_value = policy_value.PolicyValue(game, dist, uniform_policy) py_val = py_value(game.new_initial_state()) self.assertAlmostEqual(py_val, 29.92843602293449)
def test_python_game(self): """Checks if the value of a policy computation works.""" game = crowd_modelling.MFGCrowdModellingGame() uniform_policy = policy.UniformRandomPolicy(game) dist = distribution.DistributionPolicy(game, uniform_policy) py_value = policy_value.PolicyValue(game, dist, uniform_policy) py_val = py_value(game.new_initial_state()) self.assertAlmostEqual(py_val, 27.215850929940448)
def test_average(self): """Test the average of policies. Here we test that the average of values is the value of the average policy. """ game = crowd_modelling.MFGCrowdModellingGame() uniform_policy = policy.UniformRandomPolicy(game) mfg_dist = distribution.DistributionPolicy(game, uniform_policy) br_value = best_response_value.BestResponse(game, mfg_dist) py_value = policy_value.PolicyValue(game, mfg_dist, uniform_policy) greedy_pi = greedy_policy.GreedyPolicy(game, None, br_value) greedy_pi = greedy_pi.to_tabular() merged_pi = fictitious_play.MergedPolicy( game, list(range(game.num_players())), [uniform_policy, greedy_pi], [mfg_dist, distribution.DistributionPolicy(game, greedy_pi)], [0.5, 0.5]) merged_pi_value = policy_value.PolicyValue(game, mfg_dist, merged_pi) self.assertAlmostEqual(merged_pi_value(game.new_initial_state()), (br_value(game.new_initial_state()) + py_value(game.new_initial_state())) / 2)
def test_policy_value(self, name): """Checks if the value of a policy computation works. Args: name: Name of the game. """ game = pyspiel.load_game(name) uniform_policy = policy.UniformRandomPolicy(game) dist = distribution.DistributionPolicy(game, uniform_policy) py_value = policy_value.PolicyValue(game, dist, uniform_policy, value.TabularValueFunction(game)) py_val = py_value(game.new_initial_state()) self.assertAlmostEqual(py_val, 27.215850929940448)
def mean_field_uniform_policy(mfg_game, number_of_iterations, compute_metrics=False): del number_of_iterations uniform_policy = policy_module.UniformRandomPolicy(mfg_game) if compute_metrics: distribution_mfg = distribution_module.DistributionPolicy( mfg_game, uniform_policy) policy_value_ = policy_value.PolicyValue( mfg_game, distribution_mfg, uniform_policy).value(mfg_game.new_initial_state()) return uniform_policy, policy_value_ return uniform_policy
def nash_conv(self): """Returns the nash conv. Returns: A list of size `game.num_players()` representing the nash conv for each population. """ distrib = distribution.DistributionPolicy(self._game, self._policy) pi_value = policy_value.PolicyValue(self._game, distrib, self._policy) br_value = best_response_value.BestResponse(self._game, distrib) return [ br_value.eval_state(state) - pi_value.eval_state(state) for state in self._game.new_initial_states() ]
def test_greedy_cpp(self): """Check if the greedy policy works as expected. The test checks that a greedy policy with respect to an optimal value is an optimal policy. """ game = pyspiel.load_game("mfg_crowd_modelling") uniform_policy = policy.UniformRandomPolicy(game) dist = distribution.DistributionPolicy(game, uniform_policy) br_value = best_response_value.BestResponse(game, dist) br_val = br_value(game.new_initial_state()) greedy_pi = greedy_policy.GreedyPolicy(game, None, br_value) greedy_pi = greedy_pi.to_tabular() pybr_value = policy_value.PolicyValue(game, dist, greedy_pi) pybr_val = pybr_value(game.new_initial_state()) self.assertAlmostEqual(br_val, pybr_val)
def mean_field_fictitious_play(mfg_game, number_of_iterations, compute_metrics=False): fp = mean_field_fictitious_play_module.FictitiousPlay(mfg_game) tick_time = time.time() for _ in range(number_of_iterations): fp.iteration() timing = time.time() - tick_time fp_policy = fp.get_policy() # print('learning done') if compute_metrics: distribution_mfg = distribution_module.DistributionPolicy( mfg_game, fp_policy) # print('distribution done') policy_value_ = policy_value.PolicyValue( mfg_game, distribution_mfg, fp_policy).value(mfg_game.new_initial_state()) nash_conv_fp = nash_conv_module.NashConv(mfg_game, fp_policy) return timing, fp_policy, nash_conv_fp, policy_value_ return timing, fp_policy
def online_mirror_descent_sioux_falls(mfg_game, number_of_iterations, md_p=None): nash_conv_dict = {} md = md_p if md_p else mirror_descent.MirrorDescent(mfg_game) tick_time = time.time() for i in range(number_of_iterations): md.iteration() md_policy = md.get_policy() nash_conv_md = nash_conv_module.NashConv(mfg_game, md_policy) nash_conv_dict[i] = nash_conv_md.nash_conv() print((f"Iteration {i}, Nash conv: {nash_conv_md.nash_conv()}, " "time: {time.time() - tick_time}")) timing = time.time() - tick_time md_policy = md.get_policy() distribution_mfg = distribution_module.DistributionPolicy( mfg_game, md_policy) policy_value_ = policy_value.PolicyValue(mfg_game, distribution_mfg, md_policy).value( mfg_game.new_initial_state()) nash_conv_md = nash_conv_module.NashConv(mfg_game, md_policy) return timing, md_policy, nash_conv_md, policy_value_, md, nash_conv_dict
def test_greedy(self, name): """Check if the greedy policy works as expected. The test checks that a greedy policy with respect to an optimal value is an optimal policy. Args: name: Name of the game. """ game = pyspiel.load_game(name) uniform_policy = policy.UniformRandomPolicy(game) dist = distribution.DistributionPolicy(game, uniform_policy) br_value = best_response_value.BestResponse( game, dist, value.TabularValueFunction(game)) br_val = br_value(game.new_initial_state()) greedy_pi = greedy_policy.GreedyPolicy(game, None, br_value) greedy_pi = greedy_pi.to_tabular() pybr_value = policy_value.PolicyValue(game, dist, greedy_pi, value.TabularValueFunction(game)) pybr_val = pybr_value(game.new_initial_state()) self.assertAlmostEqual(br_val, pybr_val)
def online_mirror_descent(mfg_game, number_of_iterations, compute_metrics=False, return_policy=False, md_p=None): md = md_p if md_p else mirror_descent.MirrorDescent(mfg_game) tick_time = time.time() for _ in range(number_of_iterations): md.iteration() timing = time.time() - tick_time md_policy = md.get_policy() if compute_metrics: distribution_mfg = distribution_module.DistributionPolicy( mfg_game, md_policy) # print('distribution done') policy_value_ = policy_value.PolicyValue( mfg_game, distribution_mfg, md_policy).value(mfg_game.new_initial_state()) nash_conv_md = nash_conv_module.NashConv(mfg_game, md_policy) if return_policy: return timing, md_policy, nash_conv_md, policy_value_, md return timing, md_policy, nash_conv_md, policy_value_ return timing, md_policy
def main(unused_argv): logging.info("Loading %s", FLAGS.game_name) game = pyspiel.load_game(FLAGS.game_name, GAME_SETTINGS.get(FLAGS.game_name, {})) uniform_policy = policy.UniformRandomPolicy(game) mfg_dist = distribution.DistributionPolicy(game, uniform_policy) envs = [ rl_environment.Environment(game, mfg_distribution=mfg_dist, mfg_population=p) for p in range(game.num_players()) ] info_state_size = envs[0].observation_spec()["info_state"][0] num_actions = envs[0].action_spec()["num_actions"] hidden_layers_sizes = [int(l) for l in FLAGS.hidden_layers_sizes] kwargs = { "replay_buffer_capacity": FLAGS.replay_buffer_capacity, "min_buffer_size_to_learn": FLAGS.min_buffer_size_to_learn, "batch_size": FLAGS.batch_size, "learn_every": FLAGS.learn_every, "learning_rate": FLAGS.rl_learning_rate, "optimizer_str": FLAGS.optimizer_str, "loss_str": FLAGS.loss_str, "update_target_network_every": FLAGS.update_target_network_every, "discount_factor": FLAGS.discount_factor, "epsilon_decay_duration": FLAGS.epsilon_decay_duration, "epsilon_start": FLAGS.epsilon_start, "epsilon_end": FLAGS.epsilon_end, } # pylint: disable=g-complex-comprehension agents = [ dqn.DQN(idx, info_state_size, num_actions, hidden_layers_sizes, **kwargs) for idx in range(game.num_players()) ] joint_avg_policy = rl_agent_policy.JointRLAgentPolicy( game, {idx: agent for idx, agent in enumerate(agents)}, envs[0].use_observation) if FLAGS.use_checkpoints: for agent in agents: if agent.has_checkpoint(FLAGS.checkpoint_dir): agent.restore(FLAGS.checkpoint_dir) # Metrics writer will also log the metrics to stderr. just_logging = FLAGS.logdir is None or jax.host_id() > 0 writer = metric_writers.create_default_writer(FLAGS.logdir, just_logging=just_logging) # Save the parameters. writer.write_hparams(kwargs) for ep in range(1, FLAGS.num_train_episodes + 1): if ep % FLAGS.eval_every == 0: writer.write_scalars( ep, { f"agent{i}/loss": float(agent.loss) for i, agent in enumerate(agents) }) initial_states = game.new_initial_states() # Exact best response to uniform. nash_conv_obj = nash_conv.NashConv(game, uniform_policy) writer.write_scalars( ep, { f"exact_br/{state}": value for state, value in zip(initial_states, nash_conv_obj.br_values()) }) # DQN best response to uniform. pi_value = policy_value.PolicyValue(game, mfg_dist, joint_avg_policy) writer.write_scalars( ep, { f"dqn_br/{state}": pi_value.eval_state(state) for state in initial_states }) if FLAGS.use_checkpoints: for agent in agents: agent.save(FLAGS.checkpoint_dir) for p in range(game.num_players()): time_step = envs[p].reset() while not time_step.last(): agent_output = agents[p].step(time_step) action_list = [agent_output.action] time_step = envs[p].step(action_list) # Episode is over, step all agents with final info state. agents[p].step(time_step) # Make sure all values were written. writer.flush()
def main(argv: Sequence[str]) -> None: # TODO(perolat): move to an example directory. if len(argv) > 1: raise app.UsageError('Too many command-line arguments.') game_settings = { 'only_distribution_reward': True, 'forbidden_states': '[0|0;0|1]', 'initial_distribution': '[0|2;0|3]', 'initial_distribution_value': '[0.5;0.5]', } mfg_game = pyspiel.load_game(FLAGS.game, game_settings) mfg_state = mfg_game.new_initial_state() while not mfg_state.is_terminal(): print(mfg_state.observation_string(0)) if mfg_state.current_player() == pyspiel.PlayerId.CHANCE: action_list, prob_list = zip(*mfg_state.chance_outcomes()) action = np.random.choice(action_list, p=prob_list) mfg_state.apply_action(action) elif mfg_state.current_player() == pyspiel.PlayerId.MEAN_FIELD: dist_to_register = mfg_state.distribution_support() n_states = len(dist_to_register) dist = [1.0 / n_states for _ in range(n_states)] mfg_state.update_distribution(dist) else: legal_list = mfg_state.legal_actions() action = np.random.choice(legal_list) mfg_state.apply_action(action) print('compute nashconv') uniform_policy = policy.UniformRandomPolicy(mfg_game) nash_conv_fp = nash_conv.NashConv(mfg_game, uniform_policy) print(nash_conv_fp.nash_conv()) print('compute distribution') mfg_dist = distribution.DistributionPolicy(mfg_game, uniform_policy) br_value = best_response_value.BestResponse(mfg_game, mfg_dist) py_value = policy_value.PolicyValue(mfg_game, mfg_dist, uniform_policy) print(br_value(mfg_game.new_initial_state())) print(py_value(mfg_game.new_initial_state())) greedy_pi = greedy_policy.GreedyPolicy(mfg_game, None, br_value) greedy_pi = greedy_pi.to_tabular() pybr_value = policy_value.PolicyValue(mfg_game, mfg_dist, greedy_pi) print(pybr_value(mfg_game.new_initial_state())) print('merge') merged_pi = fictitious_play.MergedPolicy( mfg_game, list(range(mfg_game.num_players())), [uniform_policy, greedy_pi], [mfg_dist, distribution.DistributionPolicy(mfg_game, greedy_pi)], [0.5, 0.5]) merged_pi_value = policy_value.PolicyValue(mfg_game, mfg_dist, merged_pi) print(br_value(mfg_game.new_initial_state())) print(py_value(mfg_game.new_initial_state())) print(merged_pi_value(mfg_game.new_initial_state())) print((br_value(mfg_game.new_initial_state()) + py_value(mfg_game.new_initial_state())) / 2) print('fp') fp = fictitious_play.FictitiousPlay(mfg_game) for j in range(100): print(j) fp.iteration() fp_policy = fp.get_policy() nash_conv_fp = nash_conv.NashConv(mfg_game, fp_policy) print(nash_conv_fp.nash_conv())
def main(unused_argv): logging.info("Loading %s", FLAGS.game_name) game = pyspiel.load_game(FLAGS.game_name, GAME_SETTINGS.get(FLAGS.game_name, {})) uniform_policy = policy.UniformRandomPolicy(game) mfg_dist = distribution.DistributionPolicy(game, uniform_policy) envs = [ rl_environment.Environment(game, distribution=mfg_dist, mfg_population=p) for p in range(game.num_players()) ] info_state_size = envs[0].observation_spec()["info_state"][0] num_actions = envs[0].action_spec()["num_actions"] hidden_layers_sizes = [int(l) for l in FLAGS.hidden_layers_sizes] kwargs = { "replay_buffer_capacity": FLAGS.replay_buffer_capacity, "min_buffer_size_to_learn": FLAGS.min_buffer_size_to_learn, "batch_size": FLAGS.batch_size, "learn_every": FLAGS.learn_every, "learning_rate": FLAGS.rl_learning_rate, "optimizer_str": FLAGS.optimizer_str, "loss_str": FLAGS.loss_str, "update_target_network_every": FLAGS.update_target_network_every, "discount_factor": FLAGS.discount_factor, "epsilon_decay_duration": FLAGS.epsilon_decay_duration, "epsilon_start": FLAGS.epsilon_start, "epsilon_end": FLAGS.epsilon_end, } # pylint: disable=g-complex-comprehension agents = [ dqn.DQN(idx, info_state_size, num_actions, hidden_layers_sizes, **kwargs) for idx in range(game.num_players()) ] joint_avg_policy = DQNPolicies(envs, agents) if FLAGS.use_checkpoints: for agent in agents: if agent.has_checkpoint(FLAGS.checkpoint_dir): agent.restore(FLAGS.checkpoint_dir) for ep in range(FLAGS.num_train_episodes): if (ep + 1) % FLAGS.eval_every == 0: losses = [agent.loss for agent in agents] logging.info("Losses: %s", losses) nash_conv_obj = nash_conv.NashConv(game, uniform_policy) print( str(ep + 1) + " Exact Best Response to Uniform " + str(nash_conv_obj.br_values())) pi_value = policy_value.PolicyValue(game, mfg_dist, joint_avg_policy) print( str(ep + 1) + " DQN Best Response to Uniform " + str([ pi_value.eval_state(state) for state in game.new_initial_states() ])) if FLAGS.use_checkpoints: for agent in agents: agent.save(FLAGS.checkpoint_dir) logging.info("_____________________________________________") for p in range(game.num_players()): time_step = envs[p].reset() while not time_step.last(): agent_output = agents[p].step(time_step) action_list = [agent_output.action] time_step = envs[p].step(action_list) # Episode is over, step all agents with final info state. agents[p].step(time_step)
def main(argv: Sequence[str]) -> None: # TODO(perolat): move to an example directory. if len(argv) > 1: raise app.UsageError('Too many command-line arguments.') mfg_game = pyspiel.load_game(FLAGS.game, GAME_SETTINGS.get(FLAGS.game, {})) mfg_state = mfg_game.new_initial_state() print('Playing a single arbitrary trajectory') while not mfg_state.is_terminal(): print('State obs string:', mfg_state.observation_string(0)) if mfg_state.current_player() == pyspiel.PlayerId.CHANCE: action_list, prob_list = zip(*mfg_state.chance_outcomes()) action = np.random.choice(action_list, p=prob_list) mfg_state.apply_action(action) elif mfg_state.current_player() == pyspiel.PlayerId.MEAN_FIELD: dist_to_register = mfg_state.distribution_support() n_states = len(dist_to_register) dist = [1.0 / n_states for _ in range(n_states)] mfg_state.update_distribution(dist) else: legal_list = mfg_state.legal_actions() action = np.random.choice(legal_list) mfg_state.apply_action(action) print('compute nashconv') uniform_policy = policy.UniformRandomPolicy(mfg_game) nash_conv_fp = nash_conv.NashConv(mfg_game, uniform_policy) print('Nashconv:', nash_conv_fp.nash_conv()) print('compute distribution') mfg_dist = distribution.DistributionPolicy(mfg_game, uniform_policy) br_value = best_response_value.BestResponse( mfg_game, mfg_dist, value.TabularValueFunction(mfg_game)) py_value = policy_value.PolicyValue(mfg_game, mfg_dist, uniform_policy, value.TabularValueFunction(mfg_game)) print( 'Value of a best response policy to a uniform policy ' '(computed with best_response_value)', br_value(mfg_game.new_initial_state())) print('Value of the uniform policy:', py_value(mfg_game.new_initial_state())) greedy_pi = greedy_policy.GreedyPolicy(mfg_game, None, br_value) greedy_pi = greedy_pi.to_tabular() pybr_value = policy_value.PolicyValue(mfg_game, mfg_dist, greedy_pi, value.TabularValueFunction(mfg_game)) print( 'Value of a best response policy to a uniform policy (computed at the ' 'value of the greedy policy of the best response value)', pybr_value(mfg_game.new_initial_state())) print('merge') merged_pi = fictitious_play.MergedPolicy( mfg_game, list(range(mfg_game.num_players())), [uniform_policy, greedy_pi], [mfg_dist, distribution.DistributionPolicy(mfg_game, greedy_pi)], [0.5, 0.5]) merged_pi_value = policy_value.PolicyValue( mfg_game, mfg_dist, merged_pi, value.TabularValueFunction(mfg_game)) print(br_value(mfg_game.new_initial_state())) print(py_value(mfg_game.new_initial_state())) print(merged_pi_value(mfg_game.new_initial_state())) print((br_value(mfg_game.new_initial_state()) + py_value(mfg_game.new_initial_state())) / 2) print('fp') fp = fictitious_play.FictitiousPlay(mfg_game) for j in range(100): print('Iteration', j, 'of fictitious play') fp.iteration() fp_policy = fp.get_policy() nash_conv_fp = nash_conv.NashConv(mfg_game, fp_policy) print('Nashconv of the current FP policy', nash_conv_fp.nash_conv()) print('md') md = mirror_descent.MirrorDescent(mfg_game, value.TabularValueFunction(mfg_game)) for j in range(10): print('Iteration', j, 'of mirror descent') md.iteration() md_policy = md.get_policy() nash_conv_md = nash_conv.NashConv(mfg_game, md_policy) print('Nashconv of the current MD policy', nash_conv_md.nash_conv())
def test_softmax(self, name): """Check if the softmax policy works as expected. The test checks that: - uniform prior policy gives the same results than no prior. - very high temperature gives almost a uniform policy. - very low temperature gives almost a deterministic policy for the best action. Args: name: Name of the game. """ game = pyspiel.load_game(name) uniform_policy = policy.UniformRandomPolicy(game) dist = distribution.DistributionPolicy(game, uniform_policy) br_value = best_response_value.BestResponse( game, dist, value.TabularValueFunction(game)) br_init_val = br_value(game.new_initial_state()) # uniform prior policy gives the same results than no prior. softmax_pi_uniform_prior = softmax_policy.SoftmaxPolicy( game, None, 1.0, br_value, uniform_policy).to_tabular() softmax_pi_uniform_prior_value = policy_value.PolicyValue( game, dist, softmax_pi_uniform_prior, value.TabularValueFunction(game)) softmax_pi_uniform_prior_init_val = softmax_pi_uniform_prior_value( game.new_initial_state()) softmax_pi_no_prior = softmax_policy.SoftmaxPolicy( game, None, 1.0, br_value, None) softmax_pi_no_prior_value = policy_value.PolicyValue( game, dist, softmax_pi_no_prior, value.TabularValueFunction(game)) softmax_pi_no_prior_init_val = softmax_pi_no_prior_value( game.new_initial_state()) self.assertAlmostEqual(softmax_pi_uniform_prior_init_val, softmax_pi_no_prior_init_val) # very high temperature gives almost a uniform policy. uniform_policy = uniform_policy.to_tabular() uniform_value = policy_value.PolicyValue( game, dist, uniform_policy, value.TabularValueFunction(game)) uniform_init_val = uniform_value(game.new_initial_state()) softmax_pi_no_prior = softmax_policy.SoftmaxPolicy( game, None, 100000000, br_value, None) softmax_pi_no_prior_value = policy_value.PolicyValue( game, dist, softmax_pi_no_prior, value.TabularValueFunction(game)) softmax_pi_no_prior_init_val = softmax_pi_no_prior_value( game.new_initial_state()) self.assertAlmostEqual(uniform_init_val, softmax_pi_no_prior_init_val) # very low temperature gives almost a best response policy. softmax_pi_no_prior = softmax_policy.SoftmaxPolicy( game, None, 0.0001, br_value, None) softmax_pi_no_prior_value = policy_value.PolicyValue( game, dist, softmax_pi_no_prior, value.TabularValueFunction(game)) softmax_pi_no_prior_init_val = softmax_pi_no_prior_value( game.new_initial_state()) self.assertAlmostEqual(br_init_val, softmax_pi_no_prior_init_val)