SARSA Algorithm vs Q-Learning – biased-algorithms.com

Imagine this: You’re working on an AI system that needs to make decisions in a dynamic environment, like a self-driving car or a video game AI. How does it know which actions to take? That’s where reinforcement learning (RL) comes into play. RL has become the go-to method for training agents to make intelligent decisions, and at the core of RL are two key algorithms—SARSA and Q-Learning. Whether you’re diving into game development, robotics, or automated trading systems, these two algorithms are like the yin and yang of RL, offering different approaches to the same goal: learning optimal behavior through experience.

Purpose:

In this blog, I’m going to break down both SARSA and Q-Learning for you. We’ll explore how these algorithms work, where they differ, and what makes each of them uniquely suited to particular types of problems. By the end of this post, you’ll not only understand how each algorithm works but also know when to use SARSA versus Q-Learning in your own projects.

Reinforcement Learning Overview

What is RL?

You might be wondering, what exactly is reinforcement learning? Think of RL as teaching an agent (like a robot or a software bot) how to behave in an environment by rewarding it for good actions and punishing it for bad ones. The agent’s job is to learn the best actions to take in any given situation to maximize its rewards over time.

At its core, RL involves:

Agent: The decision-maker (your AI system).
Environment: The world the agent interacts with (e.g., a game board, a car driving simulation).
State (S): The current situation the agent is in.
Actions (A): The possible moves the agent can make.
Rewards (R): The feedback the agent receives after taking an action (positive for good actions, negative for bad).
Policy (π): The strategy the agent uses to decide its next action based on the current state.

In RL, the goal is simple: maximize cumulative rewards over time by learning an optimal policy.

Role of SARSA and Q-Learning in RL:

Now, how do SARSA and Q-Learning fit into this? Both are model-free RL algorithms, which means they don’t require a model of the environment. They’re all about learning through experience, rather than trying to predict the future. However, they differ in how they update their knowledge (Q-values) and make decisions.

SARSA stands for State-Action-Reward-State-Action and is an on-policy algorithm, which means it updates based on the actions the agent actually takes.

Q-Learning, on the other hand, is an off-policy algorithm, meaning it updates its values by assuming the agent always takes the best possible action, even if it didn’t.

To understand how these algorithms update their values, let’s look at the mathematical formulas behind them:

# SARSA Update Rule (On-Policy)
# Q(S, A) ← Q(S, A) + α [R + γ * Q(S', A') - Q(S, A)]
# S = Current State
# A = Action Taken
# R = Reward Received
# S' = Next State
# A' = Next Action (determined by the policy, hence "on-policy")
# α = Learning Rate (controls how much new information overrides old information)
# γ = Discount Factor (controls how much future rewards are valued compared to immediate rewards)

# Q-Learning Update Rule (Off-Policy)
# Q(S, A) ← Q(S, A) + α [R + γ * max(Q(S', a)) - Q(S, A)]
# S = Current State
# A = Action Taken
# R = Reward Received
# S' = Next State
# max(Q(S', a)) = Maximum future reward from next state (hence "off-policy")
# α = Learning Rate
# γ = Discount Factor

# Key Differences:
# SARSA updates using the action the agent actually takes, making it more conservative.
# Q-Learning updates using the best possible action (whether the agent takes it or not), making it more aggressive in learning.

In simple terms:

SARSA learns by sticking to the agent’s current behavior and is better for more cautious strategies.
Q-Learning assumes the agent is always choosing the best action, which makes it faster but riskier.

By now, you can see how both SARSA and Q-Learning fit into the reinforcement learning framework, each offering a different approach to balancing exploration (trying new things) and exploitation (making the best-known choice). In the next sections, we’ll dig deeper into how each algorithm works in detail.

Understanding SARSA Algorithm

Definition:

Let’s dive into SARSA, which stands for State-Action-Reward-State-Action. It’s an algorithm within reinforcement learning (RL) that follows an on-policy approach. What does that mean for you? In simple terms, SARSA learns the value of the actions it actually takes, sticking closely to the policy it’s using. It helps you develop policies that ensure safe, cautious exploration in your AI models.

Mathematical Explanation:

Now, here’s the math part. SARSA uses a Bellman equation to update the value of each state-action pair based on the reward it receives. This might sound complex, but trust me, it’s easier than it seems:

# SARSA Bellman Update Equation
# Q(S, A) ← Q(S, A) + α [R + γ * Q(S', A') - Q(S, A)]
# Here's what each term means:
# Q(S, A) = Current estimate of the value of taking action A in state S
# α (alpha) = Learning rate, controls how much new information overrides old information (between 0 and 1)
# R = Reward received after taking action A from state S
# γ (gamma) = Discount factor, determines the importance of future rewards (between 0 and 1)
# Q(S', A') = Estimate of the value of the next state-action pair
# [R + γ * Q(S', A') - Q(S, A)] = TD Error, or the difference between predicted and observed rewards

What’s happening here? SARSA updates the action-value function (Q-value) using TD (Temporal Difference) learning, based on the action actually taken and the subsequent state. This on-policy nature makes SARSA more cautious because it updates based on the current policy’s actions.

Step-by-Step Breakdown:

Let’s break down a SARSA iteration for you:

State S: The agent is in a state, say S, and selects an action, A, based on its current policy.
Action A: The agent takes action A, and as a result, it receives a reward R.
Next State S’: The environment transitions to a new state S', and the agent selects another action A' in this new state (also based on the current policy).
Update Q-value: The agent updates the Q-value for the pair (S, A) using the SARSA update rule from the equation above.
Repeat: The process repeats for the next steps.

The reason this is called SARSA is because the algorithm relies on knowing the following sequence: State (S), Action (A), Reward (R), Next State (S’), Next Action (A’).

On-Policy Learning:

Now, here’s something to think about: SARSA is an on-policy algorithm. That means the agent sticks to the same policy throughout the learning process. It updates its Q-values based on actions it actually takes, not hypothetical ones. This might sound a bit cautious, but in many environments—especially where safety is a priority (like autonomous driving or healthcare)—SARSA’s on-policy learning helps create a safer, more stable policy. It’s like being cautious in a maze, learning by following your actual footsteps rather than imagining shortcuts.

Advantages of SARSA:

You might be wondering: Why should I use SARSA instead of Q-Learning? Great question! SARSA shines in environments where exploration needs to be careful. If your AI agent is navigating an unpredictable, potentially hazardous situation, SARSA’s cautious updates can help prevent risky moves.

For example:

Self-driving cars: You don’t want your AI taking aggressive shortcuts just to learn faster.
Medical AI: Where patient safety comes first, SARSA’s conservative updates ensure safer outcomes.

SARSA adapts well in such situations because it balances exploration with the need for safe actions, sticking to the current policy without making risky assumptions.

Code Example:

Here’s a basic implementation of SARSA in Python. I’ve written it using NumPy and OpenAI Gym to keep things straightforward and clean. The comments will walk you through each step:

import numpy as np
import gym

# Initialize the environment
env = gym.make("FrozenLake-v0")

# Initialize Q-table with zeros
Q = np.zeros([env.observation_space.n, env.action_space.n])

# Hyperparameters
alpha = 0.1  # Learning rate
gamma = 0.99  # Discount factor
epsilon = 0.1  # Epsilon-greedy parameter for exploration
num_episodes = 10000  # Number of episodes to run the algorithm

# SARSA Algorithm
for episode in range(num_episodes):
    state = env.reset()  # Reset environment to initial state
    action = np.argmax(Q[state, :] + np.random.randn(1, env.action_space.n) * (1.0 / (episode + 1)))

    done = False
    while not done:
        # Take action, get new state and reward
        next_state, reward, done, _ = env.step(action)
        
        # Choose next action using epsilon-greedy policy
        if np.random.uniform(0, 1) < epsilon:
            next_action = env.action_space.sample()
        else:
            next_action = np.argmax(Q[next_state, :])
        
        # Update Q-table using SARSA rule
        Q[state, action] = Q[state, action] + alpha * (reward + gamma * Q[next_state, next_action] - Q[state, action])
        
        # Move to next state and action
        state = next_state
        action = next_action

# After training, print the final Q-table
print("Final Q-table:", Q)

In this example, your agent is learning to navigate the FrozenLake environment using SARSA. The algorithm carefully updates its Q-values based on the actions it actually takes, ensuring the learning process stays on-policy. If you tweak the parameters (like alpha, gamma, or epsilon), you’ll see different learning behaviors.

Summary of SARSA:

To sum up, SARSA is your go-to algorithm for cautious, safe exploration in RL. It updates its values based on the actual actions the agent takes, making it more conservative compared to Q-Learning. If your problem demands an AI that doesn’t take too many risks, SARSA’s on-policy nature makes it a reliable choice.

Key Differences Between SARSA and Q-Learning

Policy (On-Policy vs Off-Policy)

Let’s start with a question you might have on your mind: What’s the deal with on-policy and off-policy learning? This is the heart of the difference between SARSA and Q-Learning.

SARSA (On-Policy): SARSA is all about the actions your agent actually takes. It updates based on the current policy in place, meaning the agent learns by doing and sticking to its own chosen path. This makes SARSA a cautious learner, as it adapts and improves based on the behavior it’s already following.
Q-Learning (Off-Policy): Here’s the twist: Q-Learning assumes that, even if the agent didn’t take the best possible action, it could have, and it updates based on that ideal action. This off-policy approach makes Q-Learning more optimistic, assuming that the agent will eventually always take the best step.

In short, SARSA follows its policy, while Q-Learning imagines a better future. If you need a learner that sticks to the current strategy (like for cautious systems), SARSA is your go-to. If you want an aggressive, forward-thinking agent, Q-Learning leads the charge.

Exploration vs Exploitation

You might be wondering, how do these algorithms balance exploration and exploitation?

SARSA tends to be more conservative. Since it’s updating based on the actions it actually takes, it cautiously explores the environment, sticking closely to what it knows. This helps ensure that risky actions don’t throw the agent off course.
Q-Learning, on the other hand, goes all-in on exploration. Because it assumes that the agent always takes the best action (even if it didn’t), it encourages more aggressive exploration, seeking out new paths to maximize future rewards. This makes Q-Learning more suitable for environments where you want the agent to take risks.

In essence, SARSA is like a careful navigator, while Q-Learning is the explorer who’s not afraid to try new routes, even if they seem risky.

Update Rule

Now let’s get technical for a second and compare the Bellman updates for SARSA and Q-Learning. Here’s the deal:

# SARSA Update Rule (On-Policy)
# Q(S, A) ← Q(S, A) + α [R + γ * Q(S', A') - Q(S, A)]
# The agent updates based on the next action A' it takes from the next state S'.

# Q-Learning Update Rule (Off-Policy)
# Q(S, A) ← Q(S, A) + α [R + γ * max(Q(S', a)) - Q(S, A)]
# Q-Learning updates using the maximum Q-value possible for the next state S', assuming the agent will take the best action.

The key difference? SARSA updates based on the actual next action the agent takes, while Q-Learning updates based on the best possible action, even if the agent doesn’t actually take it.

Convergence and Stability

Here’s something that might surprise you: SARSA often converges more slowly than Q-Learning. Why? Because SARSA’s updates depend on the actual behavior of the agent, meaning it might take longer to find the optimal policy. However, it’s also more stable in environments where safety and consistency matter.

Q-Learning, on the flip side, can converge faster because it’s more aggressive in updating based on the best possible future actions. But—there’s a catch—it can also be less stable in environments where risky exploration leads to inconsistent results.

So, if you’re working in a controlled, stable environment, SARSA might take longer but be more reliable. In fast-paced, dynamic environments, Q-Learning’s quick convergence could be more useful.

Risk Sensitivity

Let’s talk about risk: SARSA is risk-averse. It’s updating based on the actual actions taken, making it cautious and less prone to overestimating future rewards. If you want an AI that sticks to the safe path, SARSA is your friend.

Q-Learning, in contrast, is more risk-tolerant. By updating based on the best possible actions, it’s optimistic about future rewards. This can make Q-Learning faster but also more prone to risky, sometimes unstable decisions.

Use Cases and Applications

SARSA Use Cases:

Now you might be wondering: When should I use SARSA?

SARSA excels in situations where you need safe exploration. Think of environments where taking the wrong step can have severe consequences. Some real-world examples:

Self-Driving Cars: SARSA ensures that your autonomous car doesn’t take overly risky paths. It’s crucial for navigating safely in unpredictable environments where cautious exploration matters.
Medical AI: If you’re building an AI to help doctors with decision-making, SARSA’s conservative updates prevent overly risky recommendations, ensuring patient safety.

In short, SARSA is your go-to when cautious, risk-averse behavior is critical.

Q-Learning Use Cases:

But what if you’re dealing with large, complex environments where aggressive exploration is a good thing? Here’s where Q-Learning comes in:

Game AI Development: Q-Learning shines in video games, where aggressive exploration helps the AI discover new strategies and improve quickly. It’s perfect for environments where taking risks leads to finding the most rewarding actions.
Large-Scale Simulations: In complex simulations, like urban planning or large-scale logistics, Q-Learning’s ability to explore aggressively makes it ideal for optimizing systems efficiently.

In other words, Q-Learning is for those environments where taking risks can lead to big rewards.

Conclusion:

So, here’s the bottom line: both SARSA and Q-Learning have their strengths, but they’re suited to different kinds of tasks.

SARSA: If you’re building a system that needs to explore cautiously, safely, and steadily, SARSA’s on-policy nature will ensure stability and long-term learning. It’s perfect for controlled, safety-critical environments.
Q-Learning: When speed, exploration, and aggressive risk-taking are key, Q-Learning’s off-policy learning is what you need. It’s perfect for dynamic, fast-paced environments where quick convergence is a priority.

At the end of the day, it’s all about choosing the right tool for the right problem. Now that you’ve learned the ins and outs of both SARSA and Q-Learning, you can confidently apply the best approach to your AI project!