code: from rllab.misc import ext
  from rllab.misc import krylov
  from rllab.misc import logger
  from rllab.core.serializable import Serializable
  import theano.tensor as TT
  import theano
  import itertools
  import numpy as np
  from rllab.misc.ext import sliced_fun
  from ast import Num
  
  
  class PerlmutterHvp(Serializable):
  
      def __init__(self, num_slices=1):
          Serializable.quick_init(self, locals())
          self.target = None
          self.reg_coeff = None
          self.opt_fun = None
          self._num_slices = num_slices
  
      def update_opt(self, f, target, inputs, reg_coeff):
          self.target = target
          self.reg_coeff = reg_coeff
          params = target.get_params(trainable=True)
  
          constraint_grads = theano.grad(
              f, wrt=params, disconnected_inputs='warn')
          xs = tuple([ext.new_tensor_like("%s x" % p.name, p) for p in params])
  
          def Hx_plain():
              Hx_plain_splits = TT.grad(
                  TT.sum([TT.sum(g * x)
                          for g, x in zip(constraint_grads, xs)]),
                  wrt=params,
                  disconnected_inputs='warn'
              )
              return TT.concatenate([TT.flatten(s) for s in Hx_plain_splits])
  
          self.opt_fun = ext.lazydict(
              f_Hx_plain=lambda: ext.compile_function(
                  inputs=inputs + xs,
                  outputs=Hx_plain(),
                  log_name="f_Hx_plain",
              ),
          )
  
      def build_eval(self, inputs):
          def eval(x):
              xs = tuple(self.target.flat_to_params(x, trainable=True))
              ret = sliced_fun(self.opt_fun["f_Hx_plain"], self._num_slices)(
                  inputs, xs) + self.reg_coeff * x
              return ret
  
          return eval
  
  
  class FiniteDifferenceHvp(Serializable):
  
      def __init__(self, base_eps=1e-8, symmetric=True, grad_clip=None, num_slices=1):
          Serializable.quick_init(self, locals())
          self.base_eps = base_eps
          self.symmetric = symmetric
          self.grad_clip = grad_clip
          self._num_slices = num_slices
  
      def update_opt(self, f, target, inputs, reg_coeff):
          self.target = target
          self.reg_coeff = reg_coeff
  
          params = target.get_params(trainable=True)
  
          constraint_grads = theano.grad(
              f, wrt=params, disconnected_inputs='warn')
          flat_grad = ext.flatten_tensor_variables(constraint_grads)
  
          def f_Hx_plain(*args):
              inputs_ = args[:len(inputs)]
              xs = args[len(inputs):]
              flat_xs = np.concatenate([np.reshape(x, (-1,)) for x in xs])
              param_val = self.target.get_param_values(trainable=True)
              eps = np.cast['float32'](
                  self.base_eps / (np.linalg.norm(param_val) + 1e-8))
              self.target.set_param_values(
                  param_val + eps * flat_xs, trainable=True)
              flat_grad_dvplus = self.opt_fun["f_grad"](*inputs_)
              if self.symmetric:
                  self.target.set_param_values(
                      param_val - eps * flat_xs, trainable=True)
                  flat_grad_dvminus = self.opt_fun["f_grad"](*inputs_)
                  hx = (flat_grad_dvplus - flat_grad_dvminus) / (2 * eps)
                  self.target.set_param_values(param_val, trainable=True)
              else:
                  self.target.set_param_values(param_val, trainable=True)
                  flat_grad = self.opt_fun["f_grad"](*inputs_)
                  hx = (flat_grad_dvplus - flat_grad) / eps
              return hx
  
          self.opt_fun = ext.lazydict(
              f_grad=lambda: ext.compile_function(
                  inputs=inputs,
                  outputs=flat_grad,
                  log_name="f_grad",
              ),
              f_Hx_plain=lambda: f_Hx_plain,
          )
  
      def build_eval(self, inputs):
          def eval(x):
              xs = tuple(self.target.flat_to_params(x, trainable=True))
              ret = sliced_fun(self.opt_fun["f_Hx_plain"], self._num_slices)(
                  inputs, xs) + self.reg_coeff * x
              return ret
  
          return eval
  
  
  class ConjugateGradientOptimizer(Serializable):
      """
      Performs constrained optimization via line search. The search direction is computed using a conjugate gradient
      algorithm, which gives x = A^{-1}g, where A is a second order approximation of the constraint and g is the gradient
      of the loss function.
      """
  
      def __init__(
              self,
              cg_iters=10,
              reg_coeff=1e-5,
              subsample_factor=1.,
              backtrack_ratio=0.8,
              max_backtracks=15,
              accept_violation=False,
              hvp_approach=None,
              num_slices=1):
          """
  
          :param cg_iters: The number of CG iterations used to calculate A^-1 g
          :param reg_coeff: A small value so that A -> A + reg*I
          :param subsample_factor: Subsampling factor to reduce samples when using "conjugate gradient. Since the
          computation time for the descent direction dominates, this can greatly reduce the overall computation time.
          :param accept_violation: whether to accept the descent step if it violates the line search condition after
          exhausting all backtracking budgets
          :return:
          """
          Serializable.quick_init(self, locals())
          self._cg_iters = cg_iters
          self._reg_coeff = reg_coeff
          self._subsample_factor = subsample_factor
          self._backtrack_ratio = backtrack_ratio
          self._max_backtracks = max_backtracks
          self._num_slices = num_slices
  
          self._opt_fun = None
          self._target = None
          self._max_constraint_val = None
          self._constraint_name = None
          self._accept_violation = accept_violation
          if hvp_approach is None:
              hvp_approach = PerlmutterHvp(num_slices)
          self._hvp_approach = hvp_approach
  
      def update_opt(self, loss, target, leq_constraint, inputs, extra_inputs=None, constraint_name="constraint", *args,
                     **kwargs):
          """
          :param loss: Symbolic expression for the loss function.
          :param target: A parameterized object to optimize over. It should implement methods of the
          :class:`rllab.core.paramerized.Parameterized` class.
          :param leq_constraint: A constraint provided as a tuple (f, epsilon), of the form f(*inputs) <= epsilon.
          :param inputs: A list of symbolic variables as inputs, which could be subsampled if needed. It is assumed
          that the first dimension of these inputs should correspond to the number of data points
          :param extra_inputs: A list of symbolic variables as extra inputs which should not be subsampled
          :return: No return value.
          """
  
          inputs = tuple(inputs)
          if extra_inputs is None:
              extra_inputs = tuple()
          else:
              extra_inputs = tuple(extra_inputs)
  
          constraint_term, constraint_value = leq_constraint
  
          params = target.get_params(trainable=True)
          grads = theano.grad(loss, wrt=params, disconnected_inputs='warn')
          flat_grad = ext.flatten_tensor_variables(grads)
  
          self._hvp_approach.update_opt(f=constraint_term, target=target, inputs=inputs + extra_inputs,
                                        reg_coeff=self._reg_coeff)
  
          self._target = target
          self._max_constraint_val = constraint_value
          self._constraint_name = constraint_name
  
          self._opt_fun = ext.lazydict(
              f_loss=lambda: ext.compile_function(
                  inputs=inputs + extra_inputs,
                  outputs=loss,
                  log_name="f_loss",
              ),
              f_grad=lambda: ext.compile_function(
                  inputs=inputs + extra_inputs,
                  outputs=flat_grad,
                  log_name="f_grad",
              ),
              f_constraint=lambda: ext.compile_function(
                  inputs=inputs + extra_inputs,
                  outputs=constraint_term,
                  log_name="constraint",
              ),
              f_loss_constraint=lambda: ext.compile_function(
                  inputs=inputs + extra_inputs,
                  outputs=[loss, constraint_term],
                  log_name="f_loss_constraint",
              ),
          )
  
      def loss(self, inputs, extra_inputs=None):
          inputs = tuple(inputs)
          if extra_inputs is None:
              extra_inputs = tuple()
          return sliced_fun(self._opt_fun["f_loss"], self._num_slices)(inputs, extra_inputs)
  
      def constraint_val(self, inputs, extra_inputs=None):
          inputs = tuple(inputs)
          if extra_inputs is None:
              extra_inputs = tuple()
          return sliced_fun(self._opt_fun["f_constraint"], self._num_slices)(inputs, extra_inputs)
  
      def optimize(self, inputs, extra_inputs=None, subsample_grouped_inputs=None):
  
          inputs = tuple(inputs)
          if extra_inputs is None:
              extra_inputs = tuple()
  
          if self._subsample_factor < 1:
              if subsample_grouped_inputs is None:
                  subsample_grouped_inputs = [inputs]
              subsample_inputs = tuple()
              for inputs_grouped in subsample_grouped_inputs:
                  n_samples = len(inputs_grouped[0])
                  inds = np.random.choice(
                      n_samples, int(n_samples * self._subsample_factor), replace=False)
                  subsample_inputs += tuple([x[inds] for x in inputs_grouped])
          else:
              subsample_inputs = inputs
  
          logger.log("computing loss before")
          loss_before = sliced_fun(self._opt_fun["f_loss"], self._num_slices)(
              inputs, extra_inputs)
          logger.log("performing update")
          logger.log("computing descent direction")
  
          flat_g = sliced_fun(self._opt_fun["f_grad"], self._num_slices)(
              inputs, extra_inputs)
  
          Hx = self._hvp_approach.build_eval(subsample_inputs + extra_inputs)
  
          descent_direction = krylov.cg(Hx, flat_g, cg_iters=self._cg_iters)
  
          initial_step_size = np.sqrt(
              2.0 * self._max_constraint_val *
              (1. / (descent_direction.dot(Hx(descent_direction)) + 1e-8))
          )
          if np.isnan(initial_step_size):
              initial_step_size = 1.
          flat_descent_step = initial_step_size * descent_direction
  
          logger.log("descent direction computed")
  
          prev_param = np.copy(self._target.get_param_values(trainable=True))
          n_iter = 0
          for n_iter, ratio in enumerate(self._backtrack_ratio ** np.arange(self._max_backtracks)):
              cur_step = ratio * flat_descent_step
              cur_param = prev_param - cur_step
              self._target.set_param_values(cur_param, trainable=True)
              loss, constraint_val = sliced_fun(
                  self._opt_fun["f_loss_constraint"], self._num_slices)(inputs, extra_inputs)
              if loss < loss_before and constraint_val <= self._max_constraint_val:
                  break
          if (np.isnan(loss) or np.isnan(constraint_val) or loss >= loss_before or constraint_val >=
                  self._max_constraint_val) and not self._accept_violation:
              logger.log("Line search condition violated. Rejecting the step!")
              if np.isnan(loss):
                  logger.log("Violated because loss is NaN")
              if np.isnan(constraint_val):
                  logger.log("Violated because constraint %s is NaN" %
                             self._constraint_name)
              if loss >= loss_before:
                  logger.log("Violated because loss not improving")
              if constraint_val >= self._max_constraint_val:
                  logger.log(
                      "Violated because constraint %s is violated" % self._constraint_name)
              self._target.set_param_values(prev_param, trainable=True)
          logger.log("backtrack iters: %d" % n_iter)
          logger.log("computing loss after")
          logger.log("optimization finished")
  
apis: numpy.arange numpy.reshape numpy.linalg.norm numpy.isnan