Q-learning vs temporal-difference vs model-based reinforcement learning

Reinforcement Learning Algorithms: A Comparison

Reinforcement learning (RL) is a powerful technique for training agents to interact with their environments and achieve specific goals. Various algorithms exist within RL, each with its strengths and weaknesses. This article delves into three prominent approaches: Q-learning, temporal-difference (TD) learning, and model-based RL.

Q-Learning

Fundamentals

Q-learning is a value-based RL algorithm that learns an optimal policy by estimating the expected future reward for each state-action pair. It utilizes a Q-table, which stores the Q-values for all possible combinations of states and actions.

Algorithm

1. Initialize the Q-table with random values.
2. For each episode:
   1. Start in an initial state.
   2. While the episode is not finished:
      1. Choose an action using an exploration strategy (e.g., ε-greedy).
      2. Take the chosen action and observe the next state and reward.
      3. Update the Q-value for the current state-action pair using the following formula:

Code Example (Python)

import numpy as np

# Define the environment
states = [0, 1, 2, 3]
actions = [0, 1]
rewards = {
    (0, 0): 1,
    (0, 1): -1,
    (1, 0): -1,
    (1, 1): 1,
    (2, 0): 1,
    (2, 1): -1,
    (3, 0): -1,
    (3, 1): 1,
}

# Initialize the Q-table
q_table = np.zeros((len(states), len(actions)))

# Q-learning parameters
gamma = 0.9  # Discount factor
alpha = 0.1  # Learning rate
epsilon = 0.1  # Exploration rate

# Run the Q-learning algorithm
for episode in range(1000):
    # ... (code for episode loop)

Temporal-Difference (TD) Learning

Fundamentals

TD learning is another value-based algorithm that estimates the value function directly from experience. Unlike Q-learning, TD learning updates the value function based on the difference between the predicted value and the actual reward received, without needing to wait for the end of the episode.

Algorithm

1. Initialize the value function (V) for all states.
2. For each episode:
   1. Start in an initial state.
   2. While the episode is not finished:
      1. Choose an action based on the current state and value function.
      2. Take the chosen action and observe the next state and reward.
      3. Update the value function for the current state using the following formula:

Code Example (Python)

import numpy as np

# Define the environment
states = [0, 1, 2, 3]
rewards = {
    0: 1,
    1: -1,
    2: 1,
    3: -1,
}

# Initialize the value function
v_table = np.zeros(len(states))

# TD learning parameters
gamma = 0.9  # Discount factor
alpha = 0.1  # Learning rate

# Run the TD learning algorithm
for episode in range(1000):
    # ... (code for episode loop)

Model-Based Reinforcement Learning

Fundamentals

Model-based RL differs from value-based methods by explicitly constructing a model of the environment. This model predicts the transition probabilities and rewards associated with each state-action pair. Once the model is learned, it can be used to plan future actions using techniques like dynamic programming or tree search.

Algorithm

1. Learn a model of the environment by observing transitions and rewards.
2. Use the learned model to plan optimal actions using techniques like:
   1. Dynamic programming: Computing the optimal policy by iteratively updating the value function.
   2. Tree search: Searching the state space to find the best action sequence.

Code Example (Python)

import numpy as np

# Define the environment
states = [0, 1, 2, 3]
actions = [0, 1]
transition_probs = {
    (0, 0): {1: 1.0},
    (0, 1): {2: 1.0},
    (1, 0): {3: 1.0},
    (1, 1): {0: 1.0},
    (2, 0): {1: 1.0},
    (2, 1): {3: 1.0},
    (3, 0): {0: 1.0},
    (3, 1): {2: 1.0},
}
rewards = {
    (0, 0): 1,
    (0, 1): -1,
    (1, 0): -1,
    (1, 1): 1,
    (2, 0): 1,
    (2, 1): -1,
    (3, 0): -1,
    (3, 1): 1,
}

# Initialize the value function
v_table = np.zeros(len(states))

# Model-based RL parameters
gamma = 0.9  # Discount factor

# Run the model-based RL algorithm
# ... (code for model-based RL algorithm)

Comparison

Advantages

Disadvantages

Choice of Algorithm

The choice of RL algorithm depends on the specific task and environment. Q-learning is a good choice for simple tasks with discrete state and action spaces. TD learning is suitable for online learning scenarios. Model-based RL is appropriate when an accurate environment model is available and long-term planning is required.