# 基于RLLAB的强化学习 REINFORCE 算法解析

## 预备知识

，其中

，通过执行在期望奖励目标函数的梯度上升：

，而

。通过似然比例技巧，目标函数关于

• 初始化参数为

.

• 对迭代

:

• 根据当前策略

，其中

.注意到因为在观察到最后的状态时无行动了已经，所以最后的状态丢弃。

• 计算经验策略梯度：
• 进行一步梯度计算：

## 准备工作

```from __future__ import print_function
from rllab.envs.box2d.cartpole_env import CartpoleEnv
from rllab.policies.gaussian_mlp_policy import GaussianMLPPolicy
from rllab.envs.normalized_env import normalize
import numpy as np
import theano
import theano.tensor as TT
from lasagne.updates import adam

# normalize() makes sure that the actions for the environment lies
# within the range [-1, 1] (only works for environments with continuous actions)
env = normalize(CartpoleEnv())
# Initialize a neural network policy with a single hidden layer of 8 hidden units
policy = GaussianMLPPolicy(env.spec, hidden_sizes=(8,))

# We will collect 100 trajectories per iteration
N = 100
# Each trajectory will have at most 100 time steps
T = 100
# Number of iterations
n_itr = 100
# Set the discount factor for the problem
discount = 0.99
# Learning rate for the gradient update
learning_rate = 0.01```

## 收集样本

```paths = []

for _ in xrange(N):
observations = []
actions = []
rewards = []

observation = env.reset()

for _ in xrange(T):
# policy.get_action() returns a pair of values. The second one returns a dictionary, whose values contains
# sufficient statistics for the action distribution. It should at least contain entries that would be
# returned by calling policy.dist_info(), which is the non-symbolic analog of policy.dist_info_sym().
# Storing these statistics is useful, e.g., when forming importance sampling ratios. In our case it is
# not needed.
action, _ = policy.get_action(observation)
# Recall that the last entry of the tuple stores diagnostic information about the environment. In our
# case it is not needed.
next_observation, reward, terminal, _ = env.step(action)
observations.append(observation)
actions.append(action)
rewards.append(reward)
observation = next_observation
if terminal:
# Finish rollout if terminal state reached
break

# We need to compute the empirical return for each time step along the
# trajectory
returns = []
return_so_far = 0
for t in xrange(len(rewards) - 1, -1, -1):
return_so_far = rewards[t] + discount * return_so_far
returns.append(return_so_far)
# The returns are stored backwards in time, so we need to revert it
returns = returns[::-1]

paths.append(dict(
observations=np.array(observations),
actions=np.array(actions),
rewards=np.array(rewards),
returns=np.array(returns)
))```

```observations = np.concatenate([p["observations"] for p in paths])
actions = np.concatenate([p["actions"] for p in paths])
returns = np.concatenate([p["returns"] for p in paths])```

## 构造计算图

```# Create a Theano variable for storing the observations
# We could have simply written `observations_var = TT.matrix('observations')` instead for this example. However,
# doing it in a slightly more abstract way allows us to delegate to the environment for handling the correct data
# type for the variable. For instance, for an environment with discrete observations, we might want to use integer
# types if the observations are represented as one-hot vectors.
observations_var = env.observation_space.new_tensor_variable(
'observations',
# It should have 1 extra dimension since we want to represent a list of observations
extra_dims=1
)
actions_var = env.action_space.new_tensor_variable(
'actions',
extra_dims=1
)
returns_var = TT.vector('returns')```

```# policy.dist_info_sym returns a dictionary, whose values are symbolic expressions for quantities related to the
# distribution of the actions. For a Gaussian policy, it contains the mean and (log) standard deviation.
dist_info_vars = policy.dist_info_sym(observations_var, actions_var)

# policy.distribution returns a distribution object under rllab.distributions. It contains many utilities for computing
# distribution-related quantities, given the computed dist_info_vars. Below we use dist.log_likelihood_sym to compute
# the symbolic log-likelihood. For this example, the corresponding distribution is an instance of the class
# rllab.distributions.DiagonalGaussian
dist = policy.distribution

# Note that we negate the objective, since most optimizers assume a
# minimization problem
surr = - TT.mean(dist.log_likelihood_sym(actions_var, dist_info_vars) * returns_var)

# Get the list of trainable parameters.
params = policy.get_params(trainable=True)
grads = theano.grad(surr, params)```

## 梯度更新和诊断

```f_train = theano.function(
inputs=[observations_var, actions_var, returns_var],
outputs=None,
updates=adam(grads, params, learning_rate=learning_rate),
allow_input_downcast=True
)
f_train(observations, actions, returns)```

`print('Average Return:', np.mean([sum(path["rewards"]) for path in paths]))`

```# ... initialization code ...
from rllab.baselines.linear_feature_baseline import LinearFeatureBaseline
baseline = LinearFeatureBaseline(env.spec)
# ... inside the loop for each episode, after the samples are collected
path = dict(observations=np.array(observations),actions=np.array(actions),rewards=np.array(rewards),)
path_baseline = baseline.predict(path)
advantages = []
returns = []
return_so_far = 0
for t in xrange(len(rewards) - 1, -1, -1):
return_so_far = rewards[t] + discount * return_so_far
returns.append(return_so_far)
advantage = return_so_far - path_baseline[t]
advantages.append(advantage)
# The advantages are stored backwards in time, so we need to revert it
advantages = np.array(advantages[::-1])
# And we need to do the same thing for the list of returns
returns = np.array(returns[::-1])```

## 规范化回报

`advantages = (advantages - np.mean(advantages)) / (np.std(advantages) + 1e-8)`

## 训练基准函数

`baseline.fit(paths)`

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