Sure! Below is an example Python script that demonstrates the Trust Region Policy Optimization (TRPO) algorithm using OpenAI Gym's "CartPole-v1" environment: ```python import gym import numpy as np import tensorflow as tf class PolicyNetwork: def __init__(self, state_dim, action_dim, hidden_dim): self.state_dim = state_dim self.action_dim = action_dim self.hidden_dim = hidden_dim self.states = tf.placeholder(tf.float32, [None, state_dim], name="states") self.actions = tf.placeholder(tf.int32, [None], name="actions") self.advantages = tf.placeholder(tf.float32, [None], name="advantages") self.mean_network = self.build_network(scope="mean") self.sample_network = self.build_network(scope="sample") self.sampled_actions = self.sample_network(self.states) self.mean_weights = tf.get_collection(tf.GraphKeys.GLOBAL_VARIABLES, scope="mean") self.sample_weights = tf.get_collection(tf.GraphKeys.GLOBAL_VARIABLES, scope="sample") self.policy_loss = self.compute_policy_loss() self.kl_divergence = self.compute_kl_divergence() self.gradient = self.compute_gradient() def build_network(self, scope): with tf.variable_scope(scope): hidden_layer = tf.layers.dense(self.states, self.hidden_dim, activation=tf.nn.relu) output_layer = tf.layers.dense(hidden_layer, self.action_dim) output_probs = tf.nn.softmax(output_layer) def network(states): feed_dict = {self.states: states} sess = tf.get_default_session() return sess.run(output_probs, feed_dict=feed_dict) return network def compute_policy_loss(self): indices = tf.range(tf.shape(self.sampled_actions)[0]) * tf.shape(self.sampled_actions)[1] + self.actions selected_action_probs = tf.gather(tf.reshape(self.sampled_actions, [-1]), indices) ratio = selected_action_probs / tf.stop_gradient(self.mean_network(self.states)) surrogate_loss = -tf.reduce_mean(ratio * self.advantages) return surrogate_loss def compute_kl_divergence(self): mean_network_probs = self.mean_network(self.states) sample_network_probs = tf.stop_gradient(self.sampled_actions) return tf.reduce_mean(tf.reduce_sum(mean_network_probs * tf.log(mean_network_probs / sample_network_probs), axis=1)) def compute_gradient(self): grads = tf.gradients(self.policy_loss, self.sample_weights) flat_grads = tf.concat([tf.reshape(grad, [-1]) for grad in grads], axis=0) return flat_grads def compute_advantages(rewards, next_value, discount_factor=0.99, gae_lambda=0.95): values = np.append(rewards, next_value) deltas = rewards + discount_factor * values[1:] - values[:-1] advantages = np.zeros_like(rewards) for t in reversed(range(len(rewards))): delta = deltas[t] advantages[t] = delta + discount_factor * gae_lambda * advantages[t+1] return advantages def run_episode(env, policy_network, render=False): states, actions, rewards = [], [], [] state = env.reset() while True: if render: env.render() action_probs = policy_network.sample_network(np.expand_dims(state, axis=0)) action = np.random.choice(len(action_probs[0]), p=action_probs[0]) next_state, reward, done, _ = env.step(action) states.append(state) actions.append(action) rewards.append(reward) state = next_state if done: break return states, actions, rewards def train(env, policy_network, max_iterations=1000, max_episode_length=1000, cg_iterations=10, delta=0.01): optimizer = tf.train.AdamOptimizer(learning_rate=1e-3) trainable_variables = tf.trainable_variables() grads_placeholder = tf.placeholder(tf.float32, shape=[None]) flat_grads_and_vars_placeholder = tf.placeholder(tf.float32, shape=[None]) grads = tf.gradients(policy_network.kl_divergence, trainable_variables) grads_placeholder_and_vars = list(zip(grads_placeholder, trainable_variables)) flat_grads_and_vars_placeholder_and_vars = list(zip(flat_grads_and_vars_placeholder, trainable_variables)) compute_grads = tf.train.AdamOptimizer(learning_rate=1e-3).apply_gradients(grads_placeholder_and_vars) compute_flat_grad = flatten_gradients(grads) apply_flat_grad = unflatten_gradients(flat_grads_and_vars_placeholder, trainable_variables) sess = tf.InteractiveSession() sess.run(tf.global_variables_initializer()) for iteration in range(max_iterations): episode_states, episode_actions, episode_rewards = run_episode(env, policy_network) episode_advantages = compute_advantages(episode_rewards, 0) episode_mean = np.mean(episode_rewards) episode_std = np.std(episode_rewards) feed_dict = { policy_network.states: np.array(episode_states), policy_network.actions: np.array(episode_actions), policy_network.advantages: episode_advantages } # Update policy network sess.run(optimizer.minimize(policy_network.policy_loss), feed_dict=feed_dict) # Update value function (critic network) for _ in range(cg_iterations): sess.run(compute_flat_grad, feed_dict=feed_dict) flat_grads = sess.run(compute_flat_grad, feed_dict=feed_dict) feed_dict[flat_grads_placeholder] = flat_grads step_direction = conjugate_gradients(sess, compute_flat_grad, feed_dict) step_size = np.sqrt(2 * delta / (np.dot(step_direction, hessian_vector_product(sess, state, compute_flat_grad, feed_dict)) + 1e-8)) feed_dict[flat_grads_and_vars_placeholder] = step_size * step_direction sess.run(apply_flat_grad, feed_dict=feed_dict) sess.close() def conjugate_gradients(sess, compute_flat_grad_fn, feed_dict, cg_iterations=10, residual_tol=1e-10): x = np.zeros_like(np.array(feed_dict).flatten()) b = sess.run(compute_flat_grad_fn, feed_dict=feed_dict) r = b.copy() p = b.copy() rsold = np.dot(r, r) for _ in range(cg_iterations): Ap = sess.run(compute_flat_grad_fn, feed_dict={x: p}) alpha = rsold / (np.dot(p, Ap) + 1e-8) x += alpha * p r -= alpha * Ap rsnew = np.dot(r, r) if np.sqrt(rsnew) < residual_tol: break p = r + (rsnew / rsold) * p rsold = rsnew return x def hessian_vector_product(sess, state, compute_flat_grad_fn, feed_dict, damping=0.1): grads = sess.run(compute_flat_grad_fn, feed_dict=feed_dict) constraints = tf.placeholder(tf.float32, shape=[None]) compute_kl_grads = tf.gradients(policy_network.kl_divergence, trainable_variables) gradient_products = tf.reduce_sum(compute_kl_grads * constraints) feed_dict.update({constraints: grads}) return sess.run(gradient_products, feed_dict=feed_dict) def flatten_gradients(grads): flat_grads = [] for grad in grads: flat_grads.append(tf.reshape(grad, [-1])) return tf.concat(flat_grads, axis=0) def unflatten_gradients(grads_placeholder, trainable_variables): grads = [] start = 0 for var in trainable_variables: var_shape = var.shape.as_list() var_size = np.prod(var_shape) grads.append(tf.reshape(grads_placeholder[start:start+var_size], var_shape)) start += var_size return grads def main(): env = gym.make('CartPole-v1') state_dim = env.observation_space.shape[0] action_dim = env.action_space.n hidden_dim = 32 policy_network = PolicyNetwork(state_dim, action_dim, hidden_dim) train(env, policy_network, max_iterations=100) env.close() if __name__ == "__main__": main() ``` In this script, the TRPO algorithm is used to optimize a policy network to solve the CartPole-v1 environment from the Gym library. The `PolicyNetwork` class defines the policy network, and the `train` function implements the TRPO algorithm to train the network. The `compute_advantages`, `run_episode`, `conjugate_gradients`, `hessian_vector_product`, `flatten_gradients`, and `unflatten_gradients` functions are helper functions used in the training process. Note that this implementation assumes you have TensorFlow and Gym libraries installed. You may need to install additional dependencies if necessary.