Model-Based Reinforcement Learning

The dynamics model is the core predictive component. It is a function approximator (e.g., a neural network) trained to predict the next state and reward given the current state and action: (s', r) ≈ f_θ(s, a). This model serves as a simulator the agent can query for planning without costly real-world interaction. Training typically uses supervised learning on a dataset of real transitions collected via exploration. Key challenges include model bias and compounding error, where small inaccuracies accumulate over long simulated trajectories.

Once a dynamics model is learned, the agent uses a planning algorithm to select actions. This involves simulating multiple potential action sequences within the model to find those that maximize expected cumulative reward. Common algorithms include:

• Model Predictive Control (MPC): Re-plans at each step over a short horizon.
• Monte Carlo Tree Search (MCTS): Heuristically explores the most promising trajectories.
• Trajectory Optimization: Uses gradient-based methods to optimize action sequences. Planning transforms the model from a passive predictor into an active tool for decision-making.

In MBRL, the policy can be implemented in two primary ways. The first is a planning-based policy, where actions are selected directly by the planning algorithm at runtime (e.g., MPC). The second is a learned policy, where the planning process is used to generate improved action labels or value targets to train a separate, faster policy network π_φ(a|s). This policy distillation step amortizes the cost of planning, allowing for rapid execution after training, a common pattern in algorithms like Expert Iteration.

The replay buffer D is a memory that stores real experience tuples (s, a, r, s') collected from the environment. It serves two critical functions in MBRL:

• Model Training: Provides the supervised dataset for learning the dynamics model f_θ.
• Policy Training: Provides real transitions for training the policy or value functions, often using targets generated via model-based planning. It enables experience replay, breaking temporal correlations and improving data efficiency. Advanced systems may maintain separate buffers for model and policy learning.

Because learned models are imperfect, quantifying predictive uncertainty is essential for robust MBRL. Agents use uncertainty estimates to guide exploration and mitigate model exploitation. Techniques include:

• Ensemble Models: Training multiple dynamics models and using their disagreement as a proxy for uncertainty.
• Bayesian Neural Networks: Representing model weights as distributions to capture epistemic uncertainty.
• Probabilistic Outputs: Having the model output a distribution over next states (e.g., a Gaussian). The agent can then use pessimistic planning (penalizing uncertain states) or curiosity-driven exploration (seeking uncertain states).

This component manages the critical loop between the agent's internal model and the external environment. Its functions include:

• Action Execution: Sending the selected action to the environment.
• State Observation: Receiving and often pre-processing the new observation o (which may be partial).
• State Estimation: In Partially Observable Markov Decision Processes (POMDPs), this involves maintaining a belief state (e.g., via a recurrent network) to infer the latent state s from the observation history.
• Data Logging: Storing the resulting transition (s, a, r, s') into the replay buffer. This interface closes the loop, allowing the model and policy to be continuously refined with real data.

A world model is an internal, learned representation within an AI system that captures the dynamics and regularities of its environment. It enables the agent to simulate and predict future states without direct interaction, serving as the foundational component for planning in MBRL.

• Core Function: Compresses high-dimensional sensory data into a latent state for efficient forward prediction.
• Key Benefit: Allows for 'thinking before acting' through internal simulation, drastically improving sample efficiency compared to model-free methods.

A POMDP is the formal mathematical framework for modeling sequential decision-making under uncertainty and partial observability. It is the standard model for most real-world MBRL problems where the agent cannot directly perceive the full environment state.

• Components: Includes states, actions, observations, transition dynamics, observation function, and rewards.
• Agent Task: Maintains a belief state (a probability distribution over possible true states) and chooses actions to maximize long-term reward.
• Relation to MBRL: The learned dynamics model in MBRL approximates the POMDP's transition and observation functions.

Model Predictive Control is an online planning algorithm that uses a model (learned or known) to optimize a sequence of actions over a finite horizon. It is a primary method for converting a learned world model into actionable policies in MBRL.

• Mechanism: At each step, MPC plans an optimal action sequence using the model, executes only the first action, then re-plans from the new state.
• Advantage: Provides implicit robustness to model inaccuracies through frequent re-planning.
• Application: Widely used in robotics, process control, and autonomous systems where a dynamics model is available.

Monte Carlo Tree Search is a heuristic search algorithm for optimal decision-making in sequential decision processes like games and planning. In MBRL, MCTS uses the learned model to simulate possible futures and evaluate action sequences.

• Four Steps: Selection, Expansion, Simulation (rollout), and Backpropagation.
• Strength: Efficiently balances exploration (trying new actions) and exploitation (refining known good paths) in large state spaces.
• Famous Use Case: Core planning algorithm for DeepMind's AlphaGo and AlphaZero, combined with a learned value and policy model.

The Dyna architecture is a classic hybrid framework that integrates model-free and model-based learning. An agent using Dyna learns a model from real experience, then uses that model to generate simulated experience for additional, more efficient policy learning.

• Key Loop: 1) Take real action, learn from real experience (model-free). 2) Update world model with real experience. 3) Use model to generate 'dreamed' experiences. 4) Learn policy from both real and dreamed data.
• Benefit: Dramatically improves data efficiency by amplifying the learning value of each real-world interaction.

Dreamer is a state-of-the-art model-based reinforcement learning agent that learns a world model from images and learns behaviors entirely by latent imagination. It represents a modern, scalable implementation of the Dyna concept using deep learning.

• Core Idea: Train a latent dynamics model (a Recurrent State-Space Model) from pixels. Then, train a policy and value function entirely on trajectories 'dreamed' or imagined by rolling out the latent model.
• Advantage: Achieves high performance on continuous control tasks from pixels with exceptional sample efficiency, as the policy is trained on millions of simulated latent steps for every real-world step.