code: """
  Original code from John Schulman for CS294 Deep Reinforcement Learning Spring 2017
  Adapted for CS294-112 Fall 2017 by Abhishek Gupta and Joshua Achiam
  Adapted for CS294-112 Fall 2018 by Soroush Nasiriany, Sid Reddy, and Greg Kahn
  """
  import numpy as np
  import tensorflow as tf
  import tensorflow_probability as tfp
  import gym
  import logz
  import os
  import time
  import inspect
  from multiprocessing import Process
  
  #============================================================================================#
  # Utilities
  #============================================================================================#
  
  def build_mlp(input_placeholder, output_size, scope, n_layers, size, activation=tf.tanh, output_activation=None):
      """
          Builds a feedforward neural network
          
          arguments:
              input_placeholder: placeholder variable for the state (batch_size, input_size)
              output_size: size of the output layer
              scope: variable scope of the network
              n_layers: number of hidden layers
              size: dimension of the hidden layer
              activation: activation of the hidden layers
              output_activation: activation of the ouput layers
  
          returns:
              output placeholder of the network (the result of a forward pass) 
  
          Hint: use tf.layers.dense    
      """
      # YOUR CODE HERE
      with tf.variable_scope(scope):
          layer = input_placeholder
          for _ in range(n_layers):
             layer = tf.layers.dense(
                 inputs=layer,
                 units=size,
                 activation=activation
             )
          output_placeholder = tf.layers.dense(
              inputs=layer,
              units=output_size,
              activation=output_activation
          )
  
      return output_placeholder
  
  def pathlength(path):
      return len(path["reward"])
  
  def setup_logger(logdir, locals_):
      # Configure output directory for logging
      logz.configure_output_dir(logdir)
      # Log experimental parameters
      args = inspect.getargspec(train_AC)[0]
      params = {k: locals_[k] if k in locals_ else None for k in args}
      logz.save_params(params)
  
  #============================================================================================#
  # Actor Critic
  #============================================================================================#
  
  class Agent(object):
      def __init__(self, computation_graph_args, sample_trajectory_args, estimate_advantage_args):
          super(Agent, self).__init__()
          self.ob_dim = computation_graph_args['ob_dim']
          self.ac_dim = computation_graph_args['ac_dim']
          self.discrete = computation_graph_args['discrete']
          self.size = computation_graph_args['size']
          self.n_layers = computation_graph_args['n_layers']
          self.learning_rate = computation_graph_args['learning_rate']
          self.num_target_updates = computation_graph_args['num_target_updates']
          self.num_grad_steps_per_target_update = computation_graph_args['num_grad_steps_per_target_update']
  
          self.animate = sample_trajectory_args['animate']
          self.max_path_length = sample_trajectory_args['max_path_length']
          self.min_timesteps_per_batch = sample_trajectory_args['min_timesteps_per_batch']
  
          self.gamma = estimate_advantage_args['gamma']
          self.normalize_advantages = estimate_advantage_args['normalize_advantages']
  
      def init_tf_sess(self):
          tf_config = tf.ConfigProto(inter_op_parallelism_threads=1, intra_op_parallelism_threads=1)
          tf_config.gpu_options.allow_growth = True # may need if using GPU
          self.sess = tf.Session(config=tf_config)
          self.sess.__enter__() # equivalent to `with self.sess:`
          tf.global_variables_initializer().run() #pylint: disable=E1101
  
      def define_placeholders(self):
          """
              Placeholders for batch batch observations / actions / advantages in actor critic
              loss function.
              See Agent.build_computation_graph for notation
  
              returns:
                  sy_ob_no: placeholder for observations
                  sy_ac_na: placeholder for actions
                  sy_adv_n: placeholder for advantages
          """
          sy_ob_no = tf.placeholder(shape=[None, self.ob_dim], name="ob", dtype=tf.float32)
          if self.discrete:
              sy_ac_na = tf.placeholder(shape=[None], name="ac", dtype=tf.int32) 
          else:
              sy_ac_na = tf.placeholder(shape=[None, self.ac_dim], name="ac", dtype=tf.float32) 
          # YOUR CODE HERE
          #TODO: for now single value
          sy_adv_n = tf.placeholder(shape=[None], name="adv", dtype=tf.float32)
          return sy_ob_no, sy_ac_na, sy_adv_n
  
      def policy_forward_pass(self, sy_ob_no):
          """ Constructs the symbolic operation for the policy network outputs,
              which are the parameters of the policy distribution p(a|s)
  
              arguments:
                  sy_ob_no: (batch_size, self.ob_dim)
  
              returns:
                  the parameters of the policy.
  
                  if discrete, the parameters are the logits of a categorical distribution
                      over the actions
                      sy_logits_na: (batch_size, self.ac_dim)
  
                  if continuous, the parameters are a tuple (mean, log_std) of a Gaussian
                      distribution over actions. log_std should just be a trainable
                      variable, not a network output.
                      sy_mean: (batch_size, self.ac_dim)
                      sy_logstd: (self.ac_dim,)
  
              Hint: use the 'build_mlp' function to output the logits (in the discrete case)
                  and the mean (in the continuous case).
                  Pass in self.n_layers for the 'n_layers' argument, and
                  pass in self.size for the 'size' argument.
          """
          #raise NotImplementedError
          if self.discrete:
              # YOUR_HW2 CODE_HERE
              network = build_mlp(input_placeholder = sy_ob_no,
                  output_size =  self.ac_dim,
                  scope="nn_policy_discrete",
                  n_layers =  self.n_layers,
                  size=self.size
              )
              sy_logits_na = network
              return sy_logits_na
          else:
              # YOUR_HW2 CODE_HERE
              network = build_mlp(input_placeholder = sy_ob_no,
                  output_size =  self.ac_dim,
                  scope="nn_policy_continous_mean",
                  n_layers =  self.n_layers,
                  size=self.size
              )
              sy_mean = network
              sy_logstd = tf.get_variable(
                  "policy_continous_logstd", 
                  shape=[self.ac_dim],
                  trainable=True,
                  dtype=tf.float32,
                  initializer=tf.constant_initializer(np.log(1))
                  #initializer=tf.constant_initializer(np.log(0.01))
                  #initializer=tf.constant_initializer(np.log(np.sqrt(10)))
              )
  
              return (sy_mean, sy_logstd)
  
      def sample_action(self, policy_parameters):
          """ Constructs a symbolic operation for stochastically sampling from the policy
              distribution
  
              arguments:
                  policy_parameters
                      if discrete: logits of a categorical distribution over actions 
                          sy_logits_na: (batch_size, self.ac_dim)
                      if continuous: (mean, log_std) of a Gaussian distribution over actions
                          sy_mean: (batch_size, self.ac_dim)
                          sy_logstd: (self.ac_dim,)
  
              returns:
                  sy_sampled_ac: 
                      if discrete: (batch_size)
                      if continuous: (batch_size, self.ac_dim)
  
              Hint: for the continuous case, use the reparameterization trick:
                   The output from a Gaussian distribution with mean 'mu' and std 'sigma' is
          
                        mu + sigma * z,         z ~ N(0, I)
          
                   This reduces the problem to just sampling z. (Hint: use tf.random_normal!)
          """
          #raise NotImplementedError
          if self.discrete:
              sy_logits_na = policy_parameters
              # YOUR_HW2 CODE_HERE
              action_probs = tf.nn.softmax(sy_logits_na,dim=1)
              self.action_probs = action_probs
              sy_sampled_ac = tf.map_fn(lambda probs: tf.cast(tf.distributions.Categorical(probs=probs).sample(),
                  tf.float32),
                  action_probs,
                  parallel_iterations=False)
              sy_sampled_ac = tf.cast(sy_sampled_ac,tf.int32)
             
   
          else:
              sy_mean, sy_logstd = policy_parameters
              # YOUR_HW2 CODE_HERE
              stds = tf.exp(sy_logstd)
              sy_sampled_ac = tf.map_fn(lambda mean: mean + tf.random.normal([self.ac_dim])*stds,sy_mean)
          return sy_sampled_ac
  
      def get_log_prob(self, policy_parameters, sy_ac_na):
          """ Constructs a symbolic operation for computing the log probability of a set of actions
              that were actually taken according to the policy
  
              arguments:
                  policy_parameters
                      if discrete: logits of a categorical distribution over actions 
                          sy_logits_na: (batch_size, self.ac_dim)
                      if continuous: (mean, log_std) of a Gaussian distribution over actions
                          sy_mean: (batch_size, self.ac_dim)
                          sy_logstd: (self.ac_dim,)
  
                  sy_ac_na: (batch_size, self.ac_dim)
  
              returns:
                  sy_logprob_n: (batch_size)
  
              Hint:
                  For the discrete case, use the log probability under a categorical distribution.
                  For the continuous case, use the log probability under a multivariate gaussian.
          """
          #raise NotImplementedError
          if self.discrete:
              sy_logits_na = policy_parameters
              # YOUR_HW2 CODE_HERE
              sy_logprob_n = -tf.nn.sparse_softmax_cross_entropy_with_logits(labels=sy_ac_na, logits=sy_logits_na)
          else:
              sy_mean, sy_logstd = policy_parameters
              # YOUR_HW2 CODE_HERE
              std = tf.exp(sy_logstd)
              variance = (std*std)
              inverse_variance = 1/variance
              diff = sy_mean -sy_ac_na
              sy_logprob_n = -(tf.reduce_sum(tf.log(variance))  + tf.reduce_sum(inverse_variance *(diff*diff),axis=1))
          return sy_logprob_n
  
      def build_computation_graph(self):
          """
              Notes on notation:
              
              Symbolic variables have the prefix sy_, to distinguish them from the numerical values
              that are computed later in the function
              
              Prefixes and suffixes:
              ob - observation 
              ac - action
              _no - this tensor should have shape (batch self.size /n/, observation dim)
              _na - this tensor should have shape (batch self.size /n/, action dim)
              _n  - this tensor should have shape (batch self.size /n/)
              
              Note: batch self.size /n/ is defined at runtime, and until then, the shape for that axis
              is None
  
              ----------------------------------------------------------------------------------
              loss: a function of self.sy_logprob_n and self.sy_adv_n that we will differentiate
                  to get the policy gradient.
          """
          self.sy_ob_no, self.sy_ac_na, self.sy_adv_n = self.define_placeholders()
  
          # The policy takes in an observation and produces a distribution over the action space
          self.policy_parameters = self.policy_forward_pass(self.sy_ob_no)
  
          # We can sample actions from this action distribution.
          # This will be called in Agent.sample_trajectory() where we generate a rollout.
          self.sy_sampled_ac = self.sample_action(self.policy_parameters)
  
          # We can also compute the logprob of the actions that were actually taken by the policy
          # This is used in the loss function.
          self.sy_logprob_n = self.get_log_prob(self.policy_parameters, self.sy_ac_na)
  
          self.actor_loss = tf.reduce_sum(-self.sy_logprob_n * self.sy_adv_n)
          self.actor_update_op = tf.train.AdamOptimizer(self.learning_rate).minimize(self.actor_loss)
  
          # define the critic
          self.critic_prediction = tf.squeeze(build_mlp(
                                  self.sy_ob_no,
                                  1,
                                  "nn_critic",
                                  n_layers=self.n_layers,
                                  size=self.size))
          self.sy_target_n = tf.placeholder(shape=[None], name="critic_target", dtype=tf.float32)
          self.critic_loss = tf.losses.mean_squared_error(self.sy_target_n, self.critic_prediction)
          self.critic_update_op = tf.train.AdamOptimizer(self.learning_rate).minimize(self.critic_loss)
  
      def sample_trajectories(self, itr, env):
          # Collect paths until we have enough timesteps
          timesteps_this_batch = 0
          paths = []
          while True:
              animate_this_episode=(len(paths)==0 and (itr % 10 == 0) and self.animate)
              path = self.sample_trajectory(env, animate_this_episode)
              paths.append(path)
              timesteps_this_batch += pathlength(path)
              if timesteps_this_batch > self.min_timesteps_per_batch:
                  break
          return paths, timesteps_this_batch
  
      def sample_trajectory(self, env, animate_this_episode):
          ob = env.reset()
          obs, acs, rewards, next_obs, terminals = [], [], [], [], []
          steps = 0
          while True:
              if animate_this_episode:
                  env.render()
                  time.sleep(0.1)
              obs.append(ob)
              
              ac = self.sess.run(self.sy_sampled_ac, {self.sy_ob_no: [ob]})  # YOUR HW2 CODE HERE
  
              ac = ac[0]
              acs.append(ac)
              ob, rew, done, _ = env.step(ac)
              # add the observation after taking a step to next_obs
              # YOUR CODE HERE
              next_obs.append(ob)
              rewards.append(rew)
              steps += 1
              # If the episode ended, the corresponding terminal value is 1
              # otherwise, it is 0
              # YOUR CODE HERE
              if done or steps > self.max_path_length:
                  terminals.append(1)
                  break
              else:
                  terminals.append(0)
          path = {"observation" : np.array(obs, dtype=np.float32), 
                  "reward" : np.array(rewards, dtype=np.float32), 
                  "action" : np.array(acs, dtype=np.float32),
                  "next_observation": np.array(next_obs, dtype=np.float32),
                  "terminal": np.array(terminals, dtype=np.float32)}
          return path
  
      def estimate_advantage(self, ob_no, next_ob_no, re_n, terminal_n):
          """
              Estimates the advantage function value for each timestep.
  
              let sum_of_path_lengths be the sum of the lengths of the paths sampled from 
                  Agent.sample_trajectories
  
              arguments:
                  ob_no: shape: (sum_of_path_lengths, ob_dim)
                  next_ob_no: shape: (sum_of_path_lengths, ob_dim). The observation after taking one step forward
                  re_n: length: sum_of_path_lengths. Each element in re_n is a scalar containing
                      the reward for each timestep
                  terminal_n: length: sum_of_path_lengths. Each element in terminal_n is either 1 if the episode ended
                      at that timestep of 0 if the episode did not end
  
              returns:
                  adv_n: shape: (sum_of_path_lengths). A single vector for the estimated 
                      advantages whose length is the sum of the lengths of the paths
          """
          # First, estimate the Q value as Q(s, a) = r(s, a) + gamma*V(s')
          # To get the advantage, subtract the V(s) to get A(s, a) = Q(s, a) - V(s)
          # This requires calling the critic twice --- to obtain V(s') when calculating Q(s, a),
          # and V(s) when subtracting the baseline
          # Note: don't forget to use terminal_n to cut off the V(s') term when computing Q(s, a)
          # otherwise the values will grow without bound.
          # YOUR CODE HERE
          v_ob_no = self.sess.run(self.critic_prediction, feed_dict={self.sy_ob_no: ob_no})
          v_next_ob_no = self.sess.run(self.critic_prediction, feed_dict={self.sy_ob_no: next_ob_no})
          v_next_ob_no = v_next_ob_no * (1 - terminal_n)
          
          y = re_n + self.gamma * v_next_ob_no
          
          adv_n = y - v_ob_no
          if self.normalize_advantages:
              #raise NotImplementedError
              adv_n = (adv_n - np.mean(adv_n))/np.std(adv_n+1e-8) # YOUR_HW2 CODE_HERE
          return adv_n
  
      def update_critic(self, ob_no, next_ob_no, re_n, terminal_n):
          """
              Update the parameters of the critic.
  
              let sum_of_path_lengths be the sum of the lengths of the paths sampled from
                  Agent.sample_trajectories
              let num_paths be the number of paths sampled from Agent.sample_trajectories
  
              arguments:
                  ob_no: shape: (sum_of_path_lengths, ob_dim)
                  next_ob_no: shape: (sum_of_path_lengths, ob_dim). The observation after taking one step forward
                  re_n: length: sum_of_path_lengths. Each element in re_n is a scalar containing
                      the reward for each timestep
                  terminal_n: length: sum_of_path_lengths. Each element in terminal_n is either 1 if the episode ended
                      at that timestep of 0 if the episode did not end
  
              returns:
                  nothing
          """
          # Use a bootstrapped target values to update the critic
          # Compute the target values r(s, a) + gamma*V(s') by calling the critic to compute V(s')
          # In total, take n=self.num_grad_steps_per_target_update*self.num_target_updates gradient update steps
          # Every self.num_grad_steps_per_target_update steps, recompute the target values
          # by evaluating V(s') on the updated critic
          # Note: don't forget to use terminal_n to cut off the V(s') term when computing the target
  
          # otherwise the values will grow without bound.
          # YOUR CODE HERE
          for _ in range(self.num_target_updates):
              v_next_ob_no = self.sess.run(self.critic_prediction, feed_dict={self.sy_ob_no: next_ob_no})
              v_next_ob_no = v_next_ob_no * (1 - terminal_n)
              y = re_n + self.gamma * v_next_ob_no
              for _ in range(self.num_grad_steps_per_target_update):
                  self.sess.run(self.critic_update_op, feed_dict={self.sy_target_n: y, self.sy_ob_no: ob_no})
  
      def update_actor(self, ob_no, ac_na, adv_n):
          """ 
              Update the parameters of the policy.
  
              arguments:
                  ob_no: shape: (sum_of_path_lengths, ob_dim)
                  ac_na: shape: (sum_of_path_lengths).
                  adv_n: shape: (sum_of_path_lengths). A single vector for the estimated
                      advantages whose length is the sum of the lengths of the paths
  
              returns:
                  nothing
  
          """
          self.sess.run(self.actor_update_op,
              feed_dict={self.sy_ob_no: ob_no, self.sy_ac_na: ac_na, self.sy_adv_n: adv_n})
  
  
  def train_AC(
          exp_name,
          env_name,
          n_iter, 
          gamma, 
          min_timesteps_per_batch, 
          max_path_length,
          learning_rate,
          num_target_updates,
          num_grad_steps_per_target_update,
          animate, 
          logdir, 
          normalize_advantages,
          seed,
          n_layers,
          size):
  
      start = time.time()
  
      #========================================================================================#
      # Set Up Logger
      #========================================================================================#
      setup_logger(logdir, locals())
  
      #========================================================================================#
      # Set Up Env
      #========================================================================================#
  
      # Make the gym environment
      env = gym.make(env_name)
  
      # Set random seeds
      tf.set_random_seed(seed)
      np.random.seed(seed)
      env.seed(seed)
  
      # Maximum length for episodes
      max_path_length = max_path_length or env.spec.max_episode_steps
  
      # Is this env continuous, or self.discrete?
      discrete = isinstance(env.action_space, gym.spaces.Discrete)
  
      # Observation and action sizes
      ob_dim = env.observation_space.shape[0]
      ac_dim = env.action_space.n if discrete else env.action_space.shape[0]
  
      #========================================================================================#
      # Initialize Agent
      #========================================================================================#
      computation_graph_args = {
          'n_layers': n_layers,
          'ob_dim': ob_dim,
          'ac_dim': ac_dim,
          'discrete': discrete,
          'size': size,
          'learning_rate': learning_rate,
          'num_target_updates': num_target_updates,
          'num_grad_steps_per_target_update': num_grad_steps_per_target_update,
          }
  
      sample_trajectory_args = {
          'animate': animate,
          'max_path_length': max_path_length,
          'min_timesteps_per_batch': min_timesteps_per_batch,
      }
  
      estimate_advantage_args = {
          'gamma': gamma,
          'normalize_advantages': normalize_advantages,
      }
  
      agent = Agent(computation_graph_args, sample_trajectory_args, estimate_advantage_args) #estimate_return_args
  
      # build computation graph
      agent.build_computation_graph()
  
      # tensorflow: config, session, variable initialization
      agent.init_tf_sess()
  
      #========================================================================================#
      # Training Loop
      #========================================================================================#
  
      total_timesteps = 0
      for itr in range(n_iter):
          print("********** Iteration %i ************"%itr)
          paths, timesteps_this_batch = agent.sample_trajectories(itr, env)
          total_timesteps += timesteps_this_batch
  
          # Build arrays for observation, action for the policy gradient update by concatenating 
          # across paths
          ob_no = np.concatenate([path["observation"] for path in paths])
          ac_na = np.concatenate([path["action"] for path in paths])
          re_n = np.concatenate([path["reward"] for path in paths])
          next_ob_no = np.concatenate([path["next_observation"] for path in paths])
          terminal_n = np.concatenate([path["terminal"] for path in paths])
  
          # Call tensorflow operations to:
          # (1) update the critic, by calling agent.update_critic
          # (2) use the updated critic to compute the advantage by, calling agent.estimate_advantage
          # (3) use the estimated advantage values to update the actor, by calling agent.update_actor
          # YOUR CODE HERE
          agent.update_critic(ob_no, next_ob_no, re_n, terminal_n)
          adv_n = agent.estimate_advantage(ob_no, next_ob_no, re_n, terminal_n)
          agent.update_actor(ob_no,ac_na,adv_n)
          #raise NotImplementedError
  
          # Log diagnostics
          returns = [path["reward"].sum() for path in paths]
          ep_lengths = [pathlength(path) for path in paths]
          logz.log_tabular("Time", time.time() - start)
          logz.log_tabular("Iteration", itr)
          logz.log_tabular("AverageReturn", np.mean(returns))
          logz.log_tabular("StdReturn", np.std(returns))
          logz.log_tabular("MaxReturn", np.max(returns))
          logz.log_tabular("MinReturn", np.min(returns))
          logz.log_tabular("EpLenMean", np.mean(ep_lengths))
          logz.log_tabular("EpLenStd", np.std(ep_lengths))
          logz.log_tabular("TimestepsThisBatch", timesteps_this_batch)
          logz.log_tabular("TimestepsSoFar", total_timesteps)
          logz.dump_tabular()
          logz.pickle_tf_vars()
  
  
  def main():
      import argparse
      parser = argparse.ArgumentParser()
      parser.add_argument('env_name', type=str)
      parser.add_argument('--exp_name', type=str, default='vac')
      parser.add_argument('--render', action='store_true')
      parser.add_argument('--discount', type=float, default=1.0)
      parser.add_argument('--n_iter', '-n', type=int, default=100)
      parser.add_argument('--batch_size', '-b', type=int, default=1000)
      parser.add_argument('--ep_len', '-ep', type=float, default=-1.)
      parser.add_argument('--learning_rate', '-lr', type=float, default=5e-3)
      parser.add_argument('--dont_normalize_advantages', '-dna', action='store_true')
      parser.add_argument('--num_target_updates', '-ntu', type=int, default=10)
      parser.add_argument('--num_grad_steps_per_target_update', '-ngsptu', type=int, default=10)
      parser.add_argument('--seed', type=int, default=1)
      parser.add_argument('--n_experiments', '-e', type=int, default=1)
      parser.add_argument('--n_layers', '-l', type=int, default=2)
      parser.add_argument('--size', '-s', type=int, default=64)
      args = parser.parse_args()
  
      data_path = os.path.join(os.path.dirname(os.path.realpath(__file__)), 'data')
  
      if not (os.path.exists(data_path)):
          os.makedirs(data_path)
      logdir = 'ac_' + args.exp_name + '_' + args.env_name + '_' + time.strftime("%d-%m-%Y_%H-%M-%S")
      logdir = os.path.join(data_path, logdir)
      if not(os.path.exists(logdir)):
          os.makedirs(logdir)
  
      max_path_length = args.ep_len if args.ep_len > 0 else None
  
      processes = []
  
      for e in range(args.n_experiments):
          seed = args.seed + 10*e
          print('Running experiment with seed %d'%seed)
  
          def train_func():
              train_AC(
                  exp_name=args.exp_name,
                  env_name=args.env_name,
                  n_iter=args.n_iter,
                  gamma=args.discount,
                  min_timesteps_per_batch=args.batch_size,
                  max_path_length=max_path_length,
                  learning_rate=args.learning_rate,
                  num_target_updates=args.num_target_updates,
                  num_grad_steps_per_target_update=args.num_grad_steps_per_target_update,
                  animate=args.render,
                  logdir=os.path.join(logdir,'%d'%seed),
                  normalize_advantages=not(args.dont_normalize_advantages),
                  seed=seed,
                  n_layers=args.n_layers,
                  size=args.size
                  )
          # # Awkward hacky process runs, because Tensorflow does not like
          # # repeatedly calling train_AC in the same thread.
          p = Process(target=train_func, args=tuple())
          p.start()
          processes.append(p)
          # if you comment in the line below, then the loop will block 
          # until this process finishes
          # p.join()
  
      for p in processes:
          p.join()
          
  
  if __name__ == "__main__":
      main()
  
apis: numpy.random.seed tensorflow.variable_scope numpy.log tensorflow.nn.sparse_softmax_cross_entropy_with_logits tensorflow.nn.softmax tensorflow.reduce_sum tensorflow.global_variables_initializer numpy.mean tensorflow.cast numpy.max tensorflow.set_random_seed numpy.min tensorflow.Session tensorflow.losses.mean_squared_error numpy.std tensorflow.layers.dense tensorflow.ConfigProto tensorflow.placeholder tensorflow.distributions.Categorical tensorflow.train.AdamOptimizer tensorflow.exp tensorflow.random.normal numpy.array tensorflow.log numpy.concatenate