One-Step Tabular Q-Learning

A Backup Without New Interaction

One-step tabular Q-planning improves value estimates by using simulated experience from a model. It does not need to wait for another real interaction with the environment for every update. Instead, it randomly selects a state and an available action, asks a sample model for a reward and next state, and then applies one-step tabular Q-learning to change the corresponding Q-function entry.

From Selection to Update

A single planning iteration follows a fixed path. First, the algorithm selects a state S and an available action A at random. Next, it sends that state-action pair to the sample model. The model returns a sample reward R and a sample next state S'. Finally, the four quantities S, A, R, and S' are given to one-step tabular Q-learning, which performs one Q-function backup and changes the entry Q(S, A).

What the Sample Model Supplies

The sample model is responsible for generating the simulated transition. It receives the selected state S and action A, then supplies the sample reward R and sample next state S'. These outputs are not a second planning-specific backup. They are the transition information that one-step tabular Q-learning uses for its ordinary one-step backup.

Planning and Real Experience

Planning and learning differ in where their experience comes from. Planning uses model-generated experience: the sample model supplies the reward and next state after a selected state-action pair. Learning uses experience from the real environment. In both cases, the resulting transition information can be used by a Q-learning update, but planning obtains its transition from the model rather than waiting for another real environmental interaction.

Coverage and Convergence

Random selection alone does not guarantee useful planning. For convergence to the model's optimal policy, every state-action pair must be selected an infinite number of times, and the learning-rate parameter α must decrease appropriately over time. The coverage condition ensures that no state-action pair is permanently neglected. The decreasing-α condition is the other requirement associated with one-step tabular Q-learning in this setting.

• Assuming that random selection automatically provides convergence.

  The convergence condition requires repeated selection of every state-action pair, not merely the use of randomness.

  Fix: Check that the selection process provides the required coverage over time.

• Treating the sample model as the component that updates Q(S, A).

  The model generates the simulated reward and next state; one-step tabular Q-learning performs the backup.

  Fix: Describe the model as the transition generator and Q-learning as the updater.

• Confusing simulated experience with real-environment experience.

  Planning uses model-generated experience, whereas learning uses experience from the real environment.

  Fix: Identify the source of R and S' before describing the update as planning or learning.

• Ignoring the learning-rate condition.

  Convergence requires α to decrease appropriately over time.

  Fix: State both convergence requirements: infinite selection of every state-action pair and appropriately decreasing α.

Check the Flow

Essential Takeaways

1. Random-sample one-step tabular Q-planning selects a state and an available action, then asks a sample model for a reward and next state.
2. The sample model generates the simulated transition; one-step tabular Q-learning performs the Q-function backup.
3. The update changes Q(S, A) using S, A, R, and S'.
4. Planning uses model-generated experience, while learning uses experience from the real environment.
5. Convergence to the model's optimal policy requires every state-action pair to be selected infinitely often and α to decrease appropriately over time.