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Exp 1：原始策略优化（Vanilla Policy Gradient）
Vanilla adj. 一般的，没有新意的；香草的
训练算法总体思路
次要的训练算法集中在 RL_Trainer.run_training_loop 中。通过观察一个循环（iteration）的调用过程，可总结为：
- 收集多个路线,，取得 train_batch_size 个时刻的数据 存在 replay buffer 中
- 上一步齐全完结之后 ，从 buffer 中采样最近 batch_size 个时刻数据
-
用数据训练模型
- 先更新策略
- 再更新 baseline（第一节还不须要）
第一、二步是齐全串行的。且通过观察代码实现可知，尽管有 buffer 作数据直达，但 train_batch_size 与 batch_size 定义为相等，每次训练的数据都是上次模型更新之后的。因而仍然是 On-Policy RL。
第一局部次要须要补全 PGAgent.train，这一函数又牵扯到计算 总收益 Q，以及 policy update
两种 \(\hat{Q} \) 的计算：Reward-to-go or Not
留神这里是 \(\hat{Q} \)（Q-hat），是 单个蒙特卡洛采样门路的收益值，而不是 Q-learning 中神经网络给出的 状态 - 动作对 的预测价值。
Reward-to-go 就是思考因果的 Q 值，t 工夫点的的 Q 不思考 t 之前工夫点的收益。
不思考因果的：求和即可，每个地位的值都和时刻 t 无关，都是一样的。
#####################################################
################## HELPER FUNCTIONS #################
#####################################################
def _discounted_return(self, rewards):
"""
Helper function
Input: list of rewards {r_0, r_1, ..., r_t', ... r_T} from a single rollout of length T
Output: list where each index t contains sum_{t'=0}^T gamma^t' r_{t'}"""
discounted_sum, discount = 0, 1
for rr in rewards:
discounted_sum += discount * rr
discount *= self.gamma
return [discounted_sum for i in range(len(rewards))]思考 Reward-to-go 的：应用迭代的方法
$$
\begin{align}
\hat{Q}_{t}&=\sum_{t’=t}^{T} \gamma^{t’-t} * r_{t’}\\
&=\sum_{t’=t+1}^{T} \gamma^{t’-t} * r_{t’}+r_{t}\\
&=\gamma\sum_{t’=t+1}^{T} \gamma^{t’-t-1} * r_{t’}+r_{t}\\
&=\hat{Q}_{t+1}+r_{t}
\end{align}
$$
而 已知：
$$\hat{Q}_{T}=\sum_{t’=T}^{T} \gamma^{t’-T} * r_{t’}=r_{T}$$
def _discounted_cumsum(self, rewards):
"""
Helper function which
-takes a list of rewards {r_0, r_1, ..., r_t', ... r_T},
-and returns a list where the entry in each index t is sum_{t'=t}^T gamma^(t'-t) * r_{t'}
(For Reward-to-go)
"""
rtg_discounted_q = rewards.copy()
for i in range(len(rtg_discounted_q)-2, -1, -1):
rtg_discounted_q[i] = self.gamma * (rtg_discounted_q[i+1]) + rewards[i]
return rtg_discounted_q策略更新（Policy Updating）
策略优化的数学实质是：通过调整 策略概率模型 的散布， 最大化收益的期望值 。
但通过应用 对数求导 的数学技巧，策略优化指标函数从后果上讲，能够认为是 策略对数概率 的加权均匀 ，而权重是 收益值之和。因而收益越高的决策权重越大。（当然这是感性认识，而不是数学实质）
$$\nabla_{\theta} J(\theta) \approx \frac{1}{N} \sum_{i=1}^{N} \sum_{t=1}^{T} \nabla_{\theta} \log \pi_{\theta}\left(\mathbf{a}_{i, t} \mid \mathbf{s}_{i, t}\right) \hat{Q}_{i, t}^{\pi}$$
class MLPPolicyPG(MLPPolicy):
def __init__(self, ac_dim, ob_dim, n_layers, size, **kwargs):
super().__init__(ac_dim, ob_dim, n_layers, size, **kwargs)
self.baseline_loss = nn.MSELoss()
def update(self, observations, actions, advantages, q_values=None):
observations = ptu.from_numpy(observations)
actions = ptu.from_numpy(actions)
advantages = ptu.from_numpy(advantages)
self.optimizer.zero_grad()
observations, actions, advantages = ptu.from_numpy(observations), ptu.from_numpy(actions), ptu.from_numpy(advantages)
action_distribution = self.forward(observations)
log_probs = action_distribution.log_prob(actions)
loss = -torch.mul(log_probs, advantages).mean()
loss.backward()
self.optimizer.step()
if self.nn_baseline:
pass # omitted
train_log = {'Training Loss': ptu.to_numpy(loss),
}
return train_logExp 2：Neural Network Baselines
Critic 模型用作 Baseline 或者 Critic
这届内容理论是在 Actor-Critic 章节的课程才讲的（）
Critic 模型指的是一个学习器（比方神经网络），输出是状态（或再加上动作），输入是这个状态（或 状态 - 动作 对）的价值。
这一节中尽管存在 Critic 神经网络模型，但它是作为 Baseline 应用，所以仍然是 Policy Gradient，而不是 Actor-Critic。分辨的准则是，PG 在策略更新中 Advantage 值的 被减数 仍然是蒙特卡洛采样 \(\hat{Q} \)
Baseline 模型训练
如上文思路，尽管有 buffer 作数据直达，但 train_batch_size 与 batch_size 定义为相等，每次训练的数据都是上次更新之后的。
因而，buffer 只是表象，实质上还是 On-policy RL。On-Policy 假如成立。
Baseline 模型的训练思路是 函数预计：神经网络的特色抽取和拟合能力，使得它可能辨认出不同但类似的状态，从而采取类似的决策。
这种能够认为是 蒙特卡洛法的延申解释。传统蒙特卡洛法须要在 完全相同 的输出上屡次采样（\(V^{\pi}\left(\mathbf{s}_{t}\right) \approx \frac{1}{N}\sum_{i=1}^{N}\sum_{t^{\prime}=t}^{T} r\left(\mathbf{s}_{t^{\prime}}, \mathbf{a}_{t^{\prime}}\right) \)），这在大部分的 强化学习环境都是不可能的。
当然这里还额定思考了 收益的工夫递加。
class MLPPolicyPG(MLPPolicy):
def __init__(self, ac_dim, ob_dim, n_layers, size, **kwargs):
super().__init__(ac_dim, ob_dim, n_layers, size, **kwargs)
self.baseline_loss = nn.MSELoss()
def update(self, observations, actions, advantages, q_values=None):
# Updating Policy (omitted)
if self.nn_baseline:
## TODO: update the neural network baseline using the q_values as
## targets. The q_values should first be normalized to have a mean
## of zero and a standard deviation of one.
## Note: You will need to convert the targets into a tensor using
## ptu.from_numpy before using it in the loss
assert q_values is not None
self.baseline_optimizer.zero_grad()
q_values = ptu.from_numpy(q_values) if isinstance(q_values, np.ndarray) else q_values
q_mean, q_std = torch.mean(q_values), torch.std(q_values)
q_values = (q_values - q_mean).divide(q_std)
values = self.baseline(observations)
print(values.shape, q_values.shape)
b_loss = self.baseline_loss(values, q_values)
b_loss.backward()
self.baseline_optimizer.step()
train_log = {'Training Loss': ptu.to_numpy(loss),
}
return train_log引入 Baselines
很简略：
def estimate_advantage(self, obs: np.ndarray, rews_list: np.ndarray, q_values: np.ndarray, terminals: np.ndarray):
"""Computes advantages by (possibly) using GAE, or subtracting a baseline from the estimated Q values"""
# Estimate the advantage when nn_baseline is True,
# by querying the neural network that you're using to learn the value function
if self.nn_baseline:
values_unnormalized = self.actor.run_baseline_prediction(obs)
## ensure that the value predictions and q_values have the same dimensionality
## to prevent silent broadcasting errors
assert values_unnormalized.ndim == q_values.ndim
## TODO: values were trained with standardized q_values, so ensure
## that the predictions have the same mean and standard deviation as
## the current batch of q_values
values = values_unnormalized * q_values.std() + q_values.mean()
batch_size = obs.shape[0]
if self.gae_lambda is not None:
pass # TODO
else:
## TODO: compute advantage estimates using q_values, and values as baselines
advantages = np.zeros(batch_size)
for i in range(batch_size):
advantages[i] = q_values[i] - values[i]
# Else, just set the advantage to [Q]
else:
advantages = q_values.copy()
# Normalize the resulting advantages to have a mean of zero
# and a standard deviation of one
if self.standardize_advantages:
ad_mean, ad_std = np.average(advantages), np.std(advantages)
advantages = (advantages - ad_mean) / ad_std
return advantagesExp 3：GAE
def estimate_advantage(self, obs: np.ndarray, rews_list: np.ndarray, q_values: np.ndarray, terminals: np.ndarray):
"""Computes advantages by (possibly) using GAE, or subtracting a baseline from the estimated Q values"""
# Estimate the advantage when nn_baseline is True,
# by querying the neural network that you're using to learn the value function
if self.nn_baseline:
values_unnormalized = self.actor.run_baseline_prediction(obs)
assert values_unnormalized.ndim == q_values.ndim
values = values_unnormalized * q_values.std() + q_values.mean()
batch_size = obs.shape[0]
if self.gae_lambda is not None:
## append a dummy T+1 value for simpler recursive calculation
values = np.append(values, [0])
## combine rews_list into a single array
rews = np.concatenate(rews_list)
## create empty numpy array to populate with GAE advantage
## estimates, with dummy T+1 value for simpler recursive calculation
advantages = np.zeros(batch_size + 1)
flatten_rews = np.concatenate(rews_list)
for i in reversed(range(batch_size)):
## TODO: recursively compute advantage estimates starting from
## timestep T.
## HINT: use terminals to handle edge cases. terminals[i]
## is 1 if the state is the last in its trajectory, and
## 0 otherwise.
if terminals[i]:
advantages[i] = flatten_rews[i] - values[i]
else:
delta = flatten_rews[i] + self.gamma * values[i+1] - values[i]
advantages[i] = delta + self.gamma * advantages[i+1]
else:
advantages = np.zeros(batch_size)
for i in range(batch_size):
advantages[i] = q_values[i] - values[i]
else:
advantages = q_values.copy()
# Normalize the resulting advantages to have a mean of zero
# and a standard deviation of one
if self.standardize_advantages:
ad_mean, ad_std = np.average(advantages), np.std(advantages)
advantages = (advantages - ad_mean) / ad_std
return advantages
