How does Dyna-Q work?

Dyna-Q is a reinforcement learning algorithm that combines real-world experience with simulated planning to improve learning efficiency. It builds on Q-learning, a model-free method where an agent learns a policy by updating a Q-table that estimates the expected rewards of actions in specific states. Dyna-Q adds a model-based component: the agent simultaneously learns a model of the environment (e.g., state transitions and rewards) while using that model to generate simulated experiences. This hybrid approach allows the agent to update its Q-table both from direct interactions and from planning with the learned model, accelerating learning without requiring additional real-world data.

The algorithm operates in two phases. First, during real interactions, the agent takes actions in the environment, observes outcomes, and updates its Q-table using Q-learning rules (e.g., Q(s,a) += learning_rate * [reward + discount * max(Q(s’,a’)) - Q(s,a)]). Concurrently, it records these experiences in a model—often a simple lookup table storing the most recent observed next state and reward for each (state, action) pair. Second, during planning, the agent samples past states and actions from its experience buffer, uses the model to simulate transitions, and applies the same Q-learning update rules to these synthetic experiences. For example, in a grid-world navigation task, after moving right from cell (1,1) and reaching (1,2) with a reward of 0, the agent would later replay this (state, action, next state, reward) tuple during planning to refine its Q-values, even if it hasn’t physically revisited (1,1) recently.

A key practical consideration is balancing real-world interactions and planning steps. Developers can control how many simulated updates (e.g., 5-50) occur per real interaction. This trade-off impacts both computational cost and learning speed: more planning steps reduce the need for costly real interactions but increase memory and processing. Dyna-Q works best when the environment is relatively stable, as frequent changes can invalidate the learned model. For instance, if a wall appears in a previously open grid cell, the model’s stored transitions for that cell become incorrect until the agent re-experiences the change. Implementing Dyna-Q typically involves maintaining an experience buffer for sampling and periodically validating the model’s accuracy in dynamic environments.