Taxonomy of Model-Based Methods

Model-based reinforcement learning includes a variety of approaches. These approaches all involve a primary idea: learning a model of the environment and then using that model to aid decision-making. However, how the model is learned and how it's subsequently used can differ significantly. Understanding these distinctions is important for choosing the right approach for a given problem. Model-based methods can be categorized along several axes.

How is the Model Represented and Learned?

The first major distinction lies in whether the model is explicitly given or needs to be learned from experience, and if learned, how it's represented.

1. Given Model: In some scenarios, particularly in classical planning problems or simulations, we might already possess an accurate model of the environment's dynamics ($P(s'|s, a)$) and reward function ($R(s, a)$). If a perfect model is known, the problem reduces to planning. Techniques like Value Iteration or Policy Iteration can directly compute the optimal value function and policy without any further interaction with the (real) environment. While this is often not the case in practical RL settings, planning with a known model serves as a theoretical baseline and is fundamental to understanding methods that use learned models.

2. Learned Model: This is the more common and challenging scenario in RL. The agent must estimate the environment's dynamics and rewards from the data ($s, a, r, s'$) it collects through interaction. The way this learned model is structured varies:

   • Explicit Transition and Reward Models: These methods aim to directly approximate the transition probabilities $P(s'|s, a)$ and the reward function $R(s, a)$ (or $R(s, a, s')$).
     • Tabular Models: For small, discrete state-action spaces, one could simply store counts and estimate probabilities and average rewards empirically. This scales poorly.
     • Function Approximators: For larger or continuous spaces, function approximation is necessary. Common choices include:
       • Linear Models: Simple, but often lack the capacity for complex dynamics.
       • Gaussian Processes: Offer uncertainty estimates but can be computationally expensive.
       • Neural Networks: Highly expressive function approximators capable of modeling complex dynamics. Probabilistic neural networks are often preferred as they can provide uncertainty estimates about their predictions, which can be valuable for planning (e.g., knowing where the model is inaccurate). A significant challenge here is compounding error: small inaccuracies in the one-step model predictions can accumulate over longer simulated trajectories, leading to poor long-term planning.
   • Implicit Models (Latent Models): Instead of explicitly predicting the probability distribution over the next state, some methods learn a model in a latent (compressed) space or learn a generative process. Planning might occur within this latent space, or the model might be used to generate plausible future trajectories without explicitly representing $P(s'|s, a)$. Examples include architectures where an encoder maps states to a latent space, dynamics are predicted in this latent space, and a decoder reconstructs state features or predicts rewards.

How is the Learned Model Used?

Once a model (either given or learned) is available, the next question is how the agent utilizes it.

1. Simulating Experience for Model-Free Updates (Background Planning): The learned model acts as a simulator to generate additional 'imagined' experience $(s, a, r, s')$. This simulated data is then fed into standard model-free RL algorithms (like Q-Learning or SARSA) as if it were real experience. This allows the agent to perform extra updates and potentially learn faster or more sample-efficiently than relying solely on real interactions. The Dyna-Q algorithm, which we'll explore shortly, is the canonical example of this approach. It interleaves real interaction, model learning, and planning (simulated updates).

2. Decision-Time Planning (Lookahead Search): The model is used explicitly for planning at the moment the agent needs to choose an action. The agent simulates potential future trajectories starting from the current state for various action sequences, evaluates the outcomes using the learned model (and potentially a learned value function), and selects the action that leads to the best predicted outcome.

   • Trajectory Sampling: Randomly sample action sequences, simulate them using the model, estimate the return for each sequence, and choose the action that initiated the best sequence.
   • Monte Carlo Tree Search (MCTS): A sophisticated heuristic search algorithm that intelligently explores the tree of possible future trajectories using the learned model. MCTS balances exploration (trying less-visited paths) and exploitation (focusing on promising paths) within the search process. Its successful use in AlphaGo and AlphaZero heavily relied on learned models.
   • Model Predictive Control (MPC): At each step, the agent plans a sequence of actions over a finite horizon using the model, executes only the first action of the sequence, observes the resulting state from the real environment, and then replans from the new state.

3. Direct Policy Optimization via Model Gradients: If the learned model is differentiable (e.g., a neural network), and the reward function is known or learned differentiably, it's possible to compute the gradient of the expected return with respect to the policy parameters by backpropagating through the learned dynamics model. This allows for direct optimization of the policy using gradient ascent, potentially leading to efficient learning if the model is accurate. However, this approach can be sensitive to model errors, as inaccuracies in the model's gradients can lead the policy optimization astray.

4. Hybrid Approaches: Many advanced techniques blend these ideas. For instance, model-based predictions might inform the targets used in a model-free update (like Q-learning), or the value function learned via model-free methods might be used to evaluate states reached during model-based planning (as in AlphaZero).

The following diagram illustrates the general flow in model-based RL, highlighting where the model learning and usage fit in.

This diagram shows the relationship between the agent's components and the environment. Real experience is collected and used both for direct model-free updates (dashed gray lines) and for learning the model (orange line). The learned model is then used by the planning component (green lines) to either generate simulated experience for updating the policy/value function (dotted green lines, Dyna-style) or to directly guide action selection via lookahead search (dashed blue line, MCTS/MPC style).

This taxonomy provides a framework for understanding the different philosophies within model-based RL. In the following sections, we will examine specific algorithms like Dyna-Q and explore the integration of planning methods like MCTS in more detail.