Temporal Difference

Temporal Difference Learning

Temporal Difference (TD) learning is a fundamental concept in reinforcement learning that combines ideas from dynamic programming and Monte Carlo methods. It enables an agent to learn directly from raw experience without needing a model of the environment.

Key Concepts of Temporal Difference Learning

1. Bootstrapping: TD learning updates its estimates based on other learned estimates, rather than waiting for the final outcome (as in Monte Carlo methods). This allows for faster learning and convergence.

2. Value Function: TD methods focus on estimating the value function, which predicts the expected return (or future reward) for states or state-action pairs.

3. Learning from Experience: The agent learns from the environment through interactions, updating its value estimates as it receives rewards and transitions between states.

TD Learning Algorithm

The TD learning process can be summarized in the following steps:

1. Initialization: Initialize the value function arbitrarily for all states (or state-action pairs).

2. Episode Loop: For each episode:

   • Start in an initial state.
   • While the state is not terminal:

     • Choose an action based on a policy (e.g., ε-greedy).

     • Take the action, observe the reward, and the new state.

     • Update the value estimate using the TD update rule:

       $V(s) \leftarrow V(s) + \alpha \left( r + \gamma V(s') - V(s) \right)$

     • Set the new state as the current state.

3. Repeat until convergence.

Key Advantages of TD Learning

• Efficiency: It can learn online, updating values after each step rather than waiting for an entire episode.
• Flexibility: It can be used in both model-based and model-free settings.
• Convergence: Under certain conditions, TD learning can converge to the optimal value function.

Example of TD Learning

One common example of TD learning is the TD(0) algorithm, where updates are made after each action based on immediate rewards and the estimated value of the next state.

Conclusion

Temporal Difference learning is a powerful method that allows agents to learn from their experiences in a way that is both efficient and flexible. It forms the basis for many advanced reinforcement learning algorithms, including Q-learning and SARSA.

Aditional Reading

• Learning to predict by the MEthods of Temporal Diffrences - By Richard Sutton (1988)