Reinforce vs Actor-Critic: Key Reinforcement Learning Algorithms Explained

Understanding Reinforce vs Actor-Critic in Reinforcement Learning

Reinforcement Learning (RL) is one of the most exciting areas of Machine Learning because it focuses on how intelligent agents learn through interaction. Unlike supervised learning, where models learn from labeled datasets, Reinforcement Learning allows an agent to learn by trial and error. The agent explores an environment, takes actions, receives rewards or penalties, and gradually improves its strategy.

Among the many algorithms in Reinforcement Learning, two important approaches are Reinforce and Actor-Critic. Both belong to the family of policy optimization methods, but they differ significantly in how learning updates are performed.

Key Idea:
Reinforce learns only from rewards collected after an episode ends, while Actor-Critic introduces a Critic that provides immediate feedback, making learning faster and more stable.

Table of Contents

• Introduction to Reinforcement Learning
• Core Elements of RL
• What is Reinforce?
• Understanding Policy Gradient
• Problems with Reinforce
• What is Actor-Critic?
• Understanding the Actor
• Understanding the Critic
• Advantage Function
• Mathematics Behind Actor-Critic
• Reinforce vs Actor-Critic Comparison
• Applications
• Final Thoughts

Introduction to Reinforcement Learning

Reinforcement Learning is inspired by behavioral psychology. An agent learns by interacting with an environment and observing the consequences of its actions.

The process follows a simple cycle:

1. The agent observes the current state.
2. The agent selects an action.
3. The environment responds with a reward.
4. The environment transitions into a new state.
5. The agent updates its strategy.

Over time, the agent tries to maximize cumulative rewards.

Expected Return

The total reward collected over time is called the return:

$$ G_t = R_{t+1} + \gamma R_{t+2} + \gamma^2 R_{t+3} + ... $$

Where:

• \(G_t\) = return at time step \(t\)
• \(R_t\) = reward
• \(\gamma\) = discount factor

The discount factor determines how much future rewards matter.

Core Elements of Reinforcement Learning

Concept	Description
Agent	The learner or decision maker
Environment	The world the agent interacts with
State	The current situation of the environment
Action	The decision taken by the agent
Reward	Feedback received from the environment
Policy	The strategy used by the agent

What is Reinforce?

Reinforce is one of the simplest policy gradient algorithms. Instead of learning value tables like Q-Learning, Reinforce directly learns the policy itself.

A policy is usually represented as:

$$ \pi_\theta(a|s) $$

This means:

• \(s\) = state
• \(a\) = action
• \(\theta\) = parameters of the policy network

The policy outputs probabilities for actions.

How Reinforce Works

1. Run a complete episode.
2. Collect rewards.
3. Compute total return.
4. Update the policy toward rewarding actions.

Important:
Reinforce waits until the episode ends before updating the model.

Understanding Policy Gradient

Policy gradient methods optimize policies directly using gradients.

The objective is:

$$ J(\theta) = \mathbb{E}[G_t] $$

We want to maximize expected rewards.

The gradient update becomes:

$$ \nabla J(\theta) = \mathbb{E}[\nabla \log \pi_\theta(a|s) G_t] $$

This equation tells us:

• If rewards are high, increase the probability of chosen actions.
• If rewards are low, reduce the probability.

Intuition Behind Log Probability

Suppose:

$$ \pi_\theta(a|s)=0.8 $$

Then:

$$ \log(0.8) \approx -0.223 $$

The gradient adjusts parameters depending on reward signals.

Problems with Reinforce

Although Reinforce is elegant, it has major limitations.

1. High Variance

Updates can fluctuate significantly because they depend on complete episodic returns.

Two identical actions may appear very different if total episode rewards differ.

2. Slow Learning

The algorithm waits until the episode finishes.

For long episodes, this becomes inefficient.

3. Credit Assignment Problem

It becomes difficult to determine which action caused success or failure.

Variance Formula

Variance measures instability:

$$ Var(X)=\mathbb{E}[(X-\mu)^2] $$

Higher variance means more unstable learning.

What is Actor-Critic?

Actor-Critic combines two ideas:

• Policy learning
• Value estimation

Instead of relying only on rewards at the end of an episode, Actor-Critic introduces a Critic that evaluates actions immediately.

The Two Components

Component	Purpose
Actor	Selects actions
Critic	Evaluates actions

Understanding the Actor

The Actor behaves similarly to Reinforce.

It maintains a policy:

$$ \pi_\theta(a|s) $$

The Actor decides which action to take.

Its goal is to maximize rewards.

Understanding the Critic

The Critic estimates how good the current state is.

This is done using the value function:

$$ V^\pi(s) $$

The value function estimates expected future rewards from a state.

Instead of waiting until the end of the episode, the Critic gives immediate feedback.

Core Improvement:
The Critic reduces uncertainty by estimating future rewards continuously.

Advantage Function

Actor-Critic often uses the Advantage Function.

The advantage tells us whether an action was better or worse than expected.

$$ A(s,a)=Q(s,a)-V(s) $$

Where:

• \(Q(s,a)\) = action-value function
• \(V(s)\) = state-value function

Positive advantage means the action was better than expected.

Negative advantage means the action was worse.

Mathematics Behind Actor-Critic

The Critic updates value estimates using Temporal Difference learning.

TD Error

$$ \delta = r + \gamma V(s') - V(s) $$

Where:

• \(r\) = immediate reward
• \(s'\) = next state
• \(\gamma\) = discount factor

The TD error measures how surprising the outcome was.

Example Calculation

Suppose:

• Reward = 5
• \(\gamma = 0.9\)
• \(V(s') = 8\)
• \(V(s)=10\)

Then:

$$ \delta = 5 + 0.9(8) - 10 $$ $$ \delta = 5 + 7.2 -10 $$ $$ \delta = 2.2 $$

A positive TD error means the outcome was better than expected.

Actor Update Rule

The Actor updates using:

$$ \nabla J(\theta)=\nabla \log \pi_\theta(a|s)\delta $$

Instead of using full episode returns, Actor-Critic uses TD error for immediate learning.

Critic Update Rule

The Critic minimizes prediction error:

$$ V(s) \leftarrow V(s)+\alpha\delta $$

Where:

• \(\alpha\) = learning rate
• \(\delta\) = TD error

Reinforce vs Actor-Critic Comparison

Feature	Reinforce	Actor-Critic
Learning Type	Policy Gradient	Policy + Value Learning
Variance	High	Lower
Learning Speed	Slow	Faster
Episode Dependency	Needs full episode	Step-by-step updates
Complexity	Simpler	More advanced
Scalability	Limited	Better for large problems

Why Lower Variance Matters

Stable learning is crucial in Reinforcement Learning.

High variance can cause:

• Oscillating performance
• Slow convergence
• Unstable policies
• Poor exploration

Actor-Critic reduces variance by using value estimates.

Bias-Variance Tradeoff

Machine learning often balances:

$$ Error = Bias^2 + Variance + Noise $$

Reinforce has low bias but high variance.

Actor-Critic introduces slightly more bias but greatly reduces variance.

Applications of Actor-Critic

Actor-Critic methods are widely used in modern AI systems.

• Robotics
• Autonomous driving
• Game playing
• Recommendation systems
• Financial trading
• Industrial optimization
• Resource allocation
• Smart control systems

Popular Actor-Critic Variants

Algorithm	Description
A2C	Advantage Actor-Critic
A3C	Asynchronous Advantage Actor-Critic
PPO	Proximal Policy Optimization
DDPG	Deep Deterministic Policy Gradient
SAC	Soft Actor-Critic

Why PPO Became Popular

PPO stabilizes Actor-Critic updates by limiting how drastically policies can change during training.

This prevents destructive updates and improves reliability.

Code Intuition (Pseudo Workflow)

for each step:

    action = actor(state)

    next_state, reward = environment(action)

    td_error = reward + gamma * V(next_state) - V(state)

    actor.update(td_error)

    critic.update(td_error)

    state = next_state

This demonstrates how Actor-Critic learns continuously after every step.

Final Thoughts

Reinforce is one of the best algorithms for understanding the foundations of policy optimization. It introduces the core concept of directly learning policies from rewards.

However, its reliance on complete episodic returns makes learning unstable and inefficient in complex environments.

Actor-Critic improves upon Reinforce by introducing a Critic that estimates value functions and provides immediate feedback. This reduces variance, speeds up learning, and makes the algorithm practical for real-world applications.

Final Takeaway:
Reinforce teaches the fundamentals of policy gradients, while Actor-Critic demonstrates how combining policy learning with value estimation creates faster and more stable reinforcement learning systems.