python - Actor-Critic 模型永远不会收敛

Question

我正在尝试使用 Keras 和 Tensorflow 实现 Actor-Critic。但是，它永远不会收敛，我不明白为什么。我降低了学习率，但它没有改变。

代码在python3.5.1和tensorflow1.2.1

import gym
import itertools
import matplotlib
import numpy as np
import sys
import tensorflow as tf
import collections

from keras.models import Model
from keras.layers import Input, Dense
from keras.utils import to_categorical
from keras import backend as K

env = gym.make('CartPole-v0')
NUM_STATE = env.env.observation_space.shape[0]
NUM_ACTIONS = env.env.action_space.n

LEARNING_RATE = 0.0005

TARGET_AVG_REWARD = 195

class Actor_Critic():

    def __init__(self):
        l_input = Input(shape=(NUM_STATE, ))
        l_dense = Dense(16, activation='relu')(l_input)

        ## Policy Network
        action_probs = Dense(NUM_ACTIONS, activation='softmax')(l_dense)
        policy_network = Model(input=l_input, output=action_probs)

        ## Value Network
        state_value = Dense(1, activation='linear')(l_dense)
        value_network = Model(input=l_input, output=state_value)

        graph = self._build_graph(policy_network, value_network)
        self.state, self.action, self.target, self.action_probs, self.state_value, self.minimize, self.loss = graph

    def _build_graph(self, policy_network, value_network):
        state = tf.placeholder(tf.float32)
        action = tf.placeholder(tf.float32, shape=(None, NUM_ACTIONS))
        target = tf.placeholder(tf.float32, shape=(None))

        action_probs = policy_network(state)
        state_value = value_network(state)[0]
        advantage = tf.stop_gradient(target) - state_value

        log_prob = tf.log(tf.reduce_sum(action_probs * action, reduction_indices=1))
        p_loss = -log_prob * advantage
        v_loss = tf.reduce_mean(tf.square(advantage))
        loss = p_loss + (0.5 * v_loss)

        # optimizer = tf.train.RMSPropOptimizer(LEARNING_RATE, decay=.99)
        optimizer = tf.train.AdamOptimizer(LEARNING_RATE)
        minimize = optimizer.minimize(loss)

        return state, action, target, action_probs, state_value, minimize, loss,

    def predict_policy(self, sess, state):
        return sess.run(self.action_probs, { self.state: [state] })

    def predict_value(self, sess, state):
        return sess.run(self.state_value, { self.state: [state] })

    def update(self, sess, state, action, target):
        feed_dict = {self.state:[state], self.target:target, self.action:to_categorical(action, NUM_ACTIONS)}
        _, loss = sess.run([self.minimize, self.loss], feed_dict)
        return loss


def train(env, sess, estimator, num_episodes, discount_factor=1.0):

    Transition = collections.namedtuple("Transition", ["state", "action", "reward", "loss"])

    last_100 = np.zeros(100)

    for i_episode in range(num_episodes):
        # Reset the environment and pick the fisrst action
        state = env.reset()

        episode = []

        # One step in the environment
        for t in itertools.count():

            # Take a step
            action_probs = estimator.predict_policy(sess, state)[0]
            action = np.random.choice(np.arange(len(action_probs)), p=action_probs)
            next_state, reward, done, _ = env.step(action)

            target = reward + (0 if done else discount_factor * estimator.predict_value(sess, next_state))

            # Update our policy estimator
            loss = estimator.update(sess, state, action, target)

            # Keep track of the transition
            episode.append(Transition(state=state, action=action, reward=reward, loss=loss))

            if done:
                break

            state = next_state

        total_reward = sum(e.reward for e in episode)
        last_100[i_episode % 100] = total_reward
        last_100_avg = sum(last_100) / 100
        total_loss = sum(e.loss for e in episode)
        print('episode %s loss: %f reward: %f last 100: %f' % (i_episode, total_loss, total_reward, last_100_avg))

        if last_100_avg >= TARGET_AVG_REWARD:
            break

    return

estimator = Actor_Critic()

with tf.Session() as sess:
    sess.run(tf.global_variables_initializer())
    stats = train(env, sess, estimator, 2000, discount_factor=0.99)

这里是开头的日志:(last 100是最近100集的平均奖励，前100集自动递增，无视)

episode 0 loss: 17.662344 reward: 15.000000 last 100: 0.150000
episode 1 loss: 15.319713 reward: 13.000000 last 100: 0.280000
episode 2 loss: 38.097054 reward: 32.000000 last 100: 0.600000
episode 3 loss: 22.229492 reward: 19.000000 last 100: 0.790000
episode 4 loss: 31.027534 reward: 26.000000 last 100: 1.050000
episode 5 loss: 21.037663 reward: 18.000000 last 100: 1.230000
episode 6 loss: 18.750641 reward: 16.000000 last 100: 1.390000
episode 7 loss: 23.268227 reward: 20.000000 last 100: 1.590000
episode 8 loss: 27.251028 reward: 23.000000 last 100: 1.820000
episode 9 loss: 20.008078 reward: 17.000000 last 100: 1.990000
episode 10 loss: 28.213932 reward: 24.000000 last 100: 2.230000
episode 11 loss: 28.109922 reward: 23.000000 last 100: 2.460000
episode 12 loss: 25.068121 reward: 21.000000 last 100: 2.670000
episode 13 loss: 59.581238 reward: 50.000000 last 100: 3.170000
episode 14 loss: 26.618759 reward: 22.000000 last 100: 3.390000
episode 15 loss: 28.847467 reward: 24.000000 last 100: 3.630000
episode 16 loss: 22.534216 reward: 17.000000 last 100: 3.800000
episode 17 loss: 19.760979 reward: 15.000000 last 100: 3.950000
episode 18 loss: 31.018209 reward: 25.000000 last 100: 4.200000
episode 19 loss: 22.938683 reward: 16.000000 last 100: 4.360000
episode 20 loss: 30.372072 reward: 24.000000 last 100: 4.600000

500集之后，不仅没有进步，反而比开始时还差。

episode 501 loss: 97.043335 reward: 8.000000 last 100: 13.500000
episode 502 loss: 101.957603 reward: 11.000000 last 100: 13.510000
episode 503 loss: 100.277809 reward: 11.000000 last 100: 13.520000
episode 504 loss: 96.754257 reward: 9.000000 last 100: 13.510000
episode 505 loss: 99.436943 reward: 11.000000 last 100: 13.530000
episode 506 loss: 105.161621 reward: 16.000000 last 100: 13.580000
episode 507 loss: 65.993591 reward: 12.000000 last 100: 13.610000
episode 508 loss: 59.837429 reward: 9.000000 last 100: 13.600000
episode 509 loss: 92.478806 reward: 9.000000 last 100: 13.570000
episode 510 loss: 96.697289 reward: 14.000000 last 100: 13.620000
episode 511 loss: 94.611366 reward: 10.000000 last 100: 13.620000
episode 512 loss: 100.259460 reward: 15.000000 last 100: 13.680000
episode 513 loss: 88.776451 reward: 10.000000 last 100: 13.690000
episode 514 loss: 86.659203 reward: 9.000000 last 100: 13.700000
episode 515 loss: 105.494476 reward: 17.000000 last 100: 13.770000
episode 516 loss: 90.662186 reward: 12.000000 last 100: 13.770000
episode 517 loss: 90.777634 reward: 12.000000 last 100: 13.810000
episode 518 loss: 91.290558 reward: 14.000000 last 100: 13.860000
episode 519 loss: 94.902023 reward: 11.000000 last 100: 13.870000
episode 520 loss: 86.746582 reward: 12.000000 last 100: 13.900000

另一方面，普通的 Policy Gradient 确实会收敛。

import gym
import itertools
import matplotlib
import numpy as np
import sys
import tensorflow as tf
import collections

from keras.models import Model
from keras.layers import Input, Dense
from keras.utils import to_categorical
from keras import backend as K

env = gym.make('CartPole-v0')
NUM_STATE = env.env.observation_space.shape[0]
NUM_ACTIONS = env.env.action_space.n

LEARNING_RATE = 0.0005

TARGET_AVG_REWARD = 195

class PolicyEstimator():
    """
    Policy Function approximator. 
    """

    def __init__(self):
        l_input = Input(shape=(NUM_STATE, ))
        l_dense = Dense(16, activation='relu')(l_input)
        action_probs = Dense(NUM_ACTIONS, activation='softmax')(l_dense)
        model = Model(inputs=[l_input], outputs=[action_probs])

        self.state, self.action, self.target, self.action_probs, self.minimize, self.loss = self._build_graph(model)

    def _build_graph(self, model):
        state = tf.placeholder(tf.float32)
        action = tf.placeholder(tf.float32, shape=(None, NUM_ACTIONS))
        target = tf.placeholder(tf.float32, shape=(None))

        action_probs = model(state)

        log_prob = tf.log(tf.reduce_sum(action_probs * action, reduction_indices=1))
        loss = -log_prob * target

        # optimizer = tf.train.RMSPropOptimizer(LEARNING_RATE, decay=.99)
        optimizer = tf.train.AdamOptimizer(LEARNING_RATE)
        minimize = optimizer.minimize(loss)

        return state, action, target, action_probs, minimize, loss

    def predict(self, sess, state):
        return sess.run(self.action_probs, { self.state: [state] })

    def update(self, sess, state, action, target):
        feed_dict = {self.state:[state], self.target:[target], self.action:to_categorical(action, NUM_ACTIONS)}
        _, loss = sess.run([self.minimize, self.loss], feed_dict)
        return loss


def train(env, sess, estimator_policy, num_episodes, discount_factor=1.0):

    Transition = collections.namedtuple("Transition", ["state", "action", "reward"])

    last_100 = np.zeros(100)

    for i_episode in range(num_episodes):
        # Reset the environment and pick the fisrst action
        state = env.reset()

        episode = []

        # One step in the environment
        for t in itertools.count():

            # Take a step
            action_probs = estimator_policy.predict(sess, state)[0]
            action = np.random.choice(np.arange(len(action_probs)), p=action_probs)
            next_state, reward, done, _ = env.step(action)

            # Keep track of the transition
            episode.append(Transition(state=state, action=action, reward=reward))

            if done:
                break

            state = next_state

        # Go through the episode and make policy updates
        for t, transition in enumerate(episode):
            # The return after this timestep
            target = sum(discount_factor**i * t2.reward for i, t2 in enumerate(episode[t:]))
            # Update our policy estimator
            loss = estimator_policy.update(sess, transition.state, transition.action, target)

        total_reward = sum(e.reward for e in episode)
        last_100[i_episode % 100] = total_reward
        last_100_avg = sum(last_100) / 100
        print('episode %s reward: %f last 100: %f' % (i_episode, total_reward, last_100_avg))

        if last_100_avg >= TARGET_AVG_REWARD:
            break

    return

policy_estimator = PolicyEstimator()

with tf.Session() as sess:
    sess.run(tf.global_variables_initializer())
    stats = train(env, sess, policy_estimator, 2000, discount_factor=1.0)

引用代码

https://github.com/jaara/AI-blog/blob/master/CartPole-A3C.py

https://github.com/coreylynch/async-rl

感谢任何帮助。

[更新]

我将 _build_graph 中的代码从

advantage = tf.stop_gradient(target) - state_value

log_prob = tf.log(tf.reduce_sum(action_probs * action, reduction_indices=1))
p_loss = -log_prob * advantage
v_loss = tf.reduce_mean(tf.square(advantage))
loss = p_loss + (0.5 * v_loss)

到

advantage = target - state_value

log_prob = tf.log(tf.reduce_sum(action_probs * action, reduction_indices=1))
p_loss = -log_prob * tf.stop_gradient(advantage)
v_loss = 0.5 * tf.reduce_mean(tf.square(advantage))
loss = p_loss + v_loss

它变得更好并获得了 200 个奖励(最大值)。然而，4000集之后，它仍然没有达到195的平均水平。

Answer 1

第一个显而易见的事情是错误的梯度被阻止在优势上:

advantage = tf.stop_gradient(target) - state_value

应该是

advantage = target - tf.stop_gradient(state_value)

因为无论哪种方式都没有目标梯度(它是一个常数)，而你想要实现的是缺少梯度流过值(value)网络(基线)的策略梯度。您有一个单独的基线损失(看起来不错)。

另一个可能的错误是减少损失的方式。您明确地为 v_loss 调用 reduce_mean，但从不为 p_loss 调用。因此，缩放比例关闭，您的值(value)网络可能学习得更慢(因为您首先对 - 可能是时间 - 维度进行平均)。