Beginner Explanation
Imagine you’re trying to teach a dog new tricks. Instead of just giving it treats when it does something right, you also adjust how you show it the trick based on how well it responds. Policy Gradient is like that: it helps an AI learn the best way to make decisions by directly tweaking its strategy based on the rewards it gets, just like you adjust your training based on how well the dog performs.Technical Explanation
Policy Gradient methods are used in reinforcement learning to optimize the policy directly. A policy defines the behavior of an agent by mapping states to actions. The goal is to maximize the expected reward over time. The gradient of the expected reward can be calculated using the likelihood ratio method. For example, in Python, using TensorFlow or PyTorch, you can implement a simple policy gradient algorithm as follows: “`python import numpy as np import torch import torch.nn as nn import torch.optim as optim class PolicyNetwork(nn.Module): def __init__(self, input_dim, output_dim): super(PolicyNetwork, self).__init__() self.fc = nn.Linear(input_dim, output_dim) def forward(self, x): return torch.softmax(self.fc(x), dim=-1) # Assuming states and rewards are collected optimizer = optim.Adam(policy.parameters(), lr=0.01) for state, reward in zip(states, rewards): optimizer.zero_grad() action_probs = policy(state) loss = -torch.log(action_probs[action]) * reward # Calculate loss loss.backward() optimizer.step() “` This code snippet shows how to adjust policy parameters based on the rewards received.Academic Context
Policy Gradient methods are rooted in the framework of reinforcement learning, specifically in the work of Sutton and Barto (1998). They provide a direct approach to policy optimization, contrasting with value-based methods. The key mathematical foundation involves the use of the likelihood ratio to derive the gradient of the expected reward with respect to policy parameters. Notable papers include ‘Policy Gradient Methods for Reinforcement Learning with Function Approximation’ by Sutton et al. (2000) and ‘Trust Region Policy Optimization’ by Schulman et al. (2015), which further advanced the field by addressing issues of stability in policy updates.Code Examples
Example 1:
import numpy as np
import torch
import torch.nn as nn
import torch.optim as optim
class PolicyNetwork(nn.Module):
def __init__(self, input_dim, output_dim):
super(PolicyNetwork, self).__init__()
self.fc = nn.Linear(input_dim, output_dim)
def forward(self, x):
return torch.softmax(self.fc(x), dim=-1)
# Assuming states and rewards are collected
optimizer = optim.Adam(policy.parameters(), lr=0.01)
for state, reward in zip(states, rewards):
optimizer.zero_grad()
action_probs = policy(state)
loss = -torch.log(action_probs[action]) * reward # Calculate loss
loss.backward()
optimizer.step()Example 2:
def __init__(self, input_dim, output_dim):
super(PolicyNetwork, self).__init__()
self.fc = nn.Linear(input_dim, output_dim)Example 3:
def forward(self, x):
return torch.softmax(self.fc(x), dim=-1)Example 4:
optimizer.zero_grad()
action_probs = policy(state)
loss = -torch.log(action_probs[action]) * reward # Calculate loss
loss.backward()
optimizer.step()Example 5:
import numpy as np
import torch
import torch.nn as nn
import torch.optim as optim
Example 6:
import torch
import torch.nn as nn
import torch.optim as optim
class PolicyNetwork(nn.Module):Example 7:
import torch.nn as nn
import torch.optim as optim
class PolicyNetwork(nn.Module):
def __init__(self, input_dim, output_dim):Example 8:
import torch.optim as optim
class PolicyNetwork(nn.Module):
def __init__(self, input_dim, output_dim):
super(PolicyNetwork, self).__init__()Example 9:
class PolicyNetwork(nn.Module):
def __init__(self, input_dim, output_dim):
super(PolicyNetwork, self).__init__()
self.fc = nn.Linear(input_dim, output_dim)
Example 10:
def __init__(self, input_dim, output_dim):
super(PolicyNetwork, self).__init__()
self.fc = nn.Linear(input_dim, output_dim)
def forward(self, x):Example 11:
def forward(self, x):
return torch.softmax(self.fc(x), dim=-1)
# Assuming states and rewards are collected
optimizer = optim.Adam(policy.parameters(), lr=0.01)View Source: https://arxiv.org/abs/2511.16629v1