chapter5.pdf

Notes on Chapter 5: Model-Based Reinforcement Learning 1 Core Concepts Model-Based Reinforcement Learning (MBRL): A method that involves creating a model of the environment’s dynamics and using it for planning and decision-making. This contrasts with model-free methods, w...

Notes on Chapter 5: Model-Based Reinforcement Learning 1 Core Concepts Model-Based Reinforcement Learning (MBRL): A method that involves creating a model of the environment’s dynamics and using it for planning and decision-making. This contrasts with model-free methods, which learn policies or value functions directly from experience. Transition Model: Represents the dynamics of the environment, mapping current states and actions to next states and rewards. Planning: Using the transition model to simulate future states and rewards to determine the best actions to take. Sample Efficiency: The ability of a reinforcement learning algorithm to learn effectively from a limited amount of data. 2 Core Problem Learning the Environment’s Dynamics: The main challenge in MBRL is accurately learning the transition model and effectively using this model for planning. This involves handling high- dimensional state spaces, dealing with uncertainty, and ensuring sample efficiency. 3 Core Algorithms Core Algorithms: Model-based methods typically involve two main steps: 1. Learning the Model: This involves learning the transition model that maps states and actions to next states and rewards. 2. Using the Model for Planning: This involves using the learned model to simulate future states and rewards to plan the best actions. 4 Building a Navigation Map Example: Building a navigation map to illustrate model-based reinforcement learning. This in- volves learning the transitions between different locations and using this knowledge to plan optimal routes. 5 5.1 Dynamics Models of High-Dimensional Problems Transition Model and Knowledge Transfer: The transition model captures the dynamics of the environment, allowing knowledge transfer to new but related tasks, improving learning and planning efficiency. Sample Efficiency: MBRL can be more sample-efficient than model-free methods because it leverages the learned model to simulate and plan, reducing the need for extensive interaction with the real environment. 1 6 5.2 Learning and Planning Agents Tabular Imagination: Using a table-based representation of states and transitions for planning. This method is straightforward but scales poorly with high-dimensional state spaces. Hands On: Imagining Taxi Example: A practical example using the taxi environment to demonstrate model-based planning by simulating trajectories and updating policies based on imag- ined experiences. Reversible Planning and Irreversible Learning: Planning can involve reversible steps (trying different paths and backtracking), whereas learning often involves irreversible updates to the model or policy. Four Types of Model-Based Methods: 1. Learning the Model: Focusing on accurately modeling the environment’s dynamics. 2. Planning with the Model: Using the learned model to plan and make decisions. 3. End-to-End Methods: Combining learning and planning in a single framework. 4. Hybrid Methods: Integrating model-based and model-free approaches. 6.1 5.2.1 Learning the Model Modeling Uncertainty: Addressing the uncertainty in the learned model by incorporating prob- abilistic models or ensembles of models to capture the variability in the environment’s dynamics. Latent Models: Using latent variable models to represent the underlying structure of the envi- ronment. These models can capture complex dependencies and reduce the dimensionality of the state space. 6.2 5.2.2 Planning with the Model Trajectory Rollouts and Model-Predictive Control: Using the model to simulate trajectories and optimize actions over a finite horizon. Model-Predictive Control (MPC): An algorithmic approach where the model is used to predict future states and rewards, optimizing actions over a short horizon and updating the plan as new information becomes available. Algorithm 1 Model-Predictive Control (MPC) 1: Initialize model parameters θ 2: for each time step t do 3: Observe current state st 4: for each action a do 5: Predict future state st+1 ∼ p(st+1 |st , a; θ) 6: Evaluate cost c(st , a) 7: end for 8: Select action at = arg mina c(st , a) 9: Execute action at 10: Update model parameters θ using observed transition (st , at , st+1 ) 11: end for End-to-End Learning and Planning-by-Network: Integrating learning and planning into a single neural network architecture that can learn to predict dynamics and optimize policies simultaneously. 2 7 5.3 High-Dimensional Environments Overview of Model-Based Experiments: Discusses various experiments and applications of MBRL in high-dimensional environments. Small Navigation Tasks: Application of MBRL to simple navigation tasks to illustrate the principles and benefits of model-based approaches. Robotic Applications: Using MBRL for controlling robotic systems, where precise modeling of dynamics and planning is crucial for effective operation. Atari Games Applications: Application of MBRL to Atari games, demonstrating its ability to handle complex, high-dimensional state spaces. Algorithm 2 Model-Based Learning and Planning 1: Initialize model parameters θ 2: Initialize policy parameters ϕ 3: for each episode do 4: Generate trajectories using current policy πϕ 5: Update model parameters θ using observed transitions 6: Plan using the learned model to improve policy πϕ 7: Update policy parameters ϕ based on planned trajectories 8: end for 8 Hands On: PlaNet Example PlaNet Example: A detailed example using the PlaNet algorithm, which combines probabilistic models and planning for effective learning in high-dimensional environments. 9 Summary and Further Reading Summary: A recap of the key points covered in the chapter, emphasizing the benefits and chal- lenges of MBRL. Further Reading: Suggested literature and resources for a deeper understanding of MBRL and its applications in various domains. Quick Questions 1. What is the advantage of model-based over model-free methods? Model-based methods can achieve higher sample efficiency by using a learned model to simu- late and plan actions, reducing the need for extensive interactions with the real environment. 2. Why may the sample complexity of model-based methods suffer in high-dimensional problems? In high-dimensional problems, accurately learning the transition model requires a large number of samples, which can lead to increased sample complexity. 3. Which functions are part of the dynamics model? The dynamics model typically includes the transition function T (s, a) = s′ and the reward function R(s, a). 4. Mention four deep model-based approaches. Four deep model-based approaches are PlaNet, Model-Predictive Control (MPC), World Mod- els, and Dreamer. 3  5. Do model-based methods achieve better sample complexity than model-free? Yes, model-based methods generally achieve better sample complexity because they can use the learned model to simulate experiences and plan actions efficiently. 6. Do model-based methods achieve better performance than model-free? Model-based methods can achieve better performance in terms of sample efficiency, but model- free methods may achieve better asymptotic performance in some cases due to more accurate direct policy learning. 7. In Dyna-Q the policy is updated by two mechanisms: learning by sampling the envi- ronment and what other mechanism? The policy in Dyna-Q is updated by learning from simulated experiences generated by the model. 8. Why is the variance of ensemble methods lower than of the individual machine learning approaches that are used in the ensemble? Ensemble methods average the predictions of multiple models, which reduces variance and improves robustness compared to individual models. 9. What does model-predictive control do and why is this approach suited for models with lower accuracy? Model-predictive control (MPC) optimizes actions over a short horizon and frequently re- plans based on new observations, making it well-suited for models with lower accuracy by continuously correcting errors. 10. What is the advantage of planning with latent models over planning with actual mod- els? Planning with latent models can reduce computational complexity and capture essential fea- tures of the environment, making planning more efficient and scalable. 11. How are latent models trained? Latent models are typically trained using variational autoencoders (VAEs) or other unsuper- vised learning techniques to learn compact representations of the state space. 12. Mention four typical modules that constitute the latent model. Four typical modules of a latent model are the encoder, decoder, dynamics model, and reward model. 13. What is the advantage of end-to-end planning and learning? End-to-end planning and learning can jointly optimize model learning and policy learning, leading to better integration and performance. 14. Mention two end-to-end planning and learning methods. Two end-to-end planning and learning methods are Dreamer and PlaNet. In class Question 1. Why Model-based? Model-based methods are used because they can achieve higher sample efficiency by learning and utilizing a model of the environment’s dynamics, which allows for better planning and decision-making with fewer interactions with the real environment. 2. What is the “Model”? 4  The “Model” refers to a representation of the environment’s dynamics, typically including a transition function that predicts future states based on current states and actions, and a reward function that predicts the rewards received. 3. What is the difference between model-free and model-based? Model-free methods learn policies or value functions directly from experience without ex- plicitly modeling the environment, whereas model-based methods first learn a model of the environment’s dynamics and use this model for planning and decision-making. 4. Does it work? Yes, model-based methods have been shown to work effectively in various tasks, particularly when sample efficiency is crucial, although they may face challenges in highly complex or high-dimensional environments. 5. Is Dyna Hybrid? How is it Hybrid? Yes, Dyna is a hybrid approach that combines model-free learning (learning from real experi- ences) and model-based learning (learning from simulated experiences generated by a model) to improve sample efficiency and planning. 6. What is the difference between planning and learning? Planning involves using a model to simulate and optimize future actions before execution, while learning involves updating the model or policy based on actual experiences from interacting with the environment. 7. What is the weakness of Model-based? The primary weakness of model-based methods is that they can suffer from model inaccura- cies, especially in complex or high-dimensional environments, which can lead to suboptimal planning and decision-making. 8. Name two ways in which the weakness can be improved Using ensemble models to capture uncertainty and reduce the impact of model inaccuracies. Integrating model-free methods to refine policies based on real experiences, complementing the model-based approach. 9. Name two ways in which the model can be improved Incorporating probabilistic or Bayesian approaches to better handle uncertainty in the model. Using deep learning techniques to create more expressive models that can capture complex dynamics. 10. Name two ways in which the planning can be improved Employing Model-Predictive Control (MPC) to iteratively re-plan actions based on new ob- servations, which helps correct errors in the model. Using trajectory optimization techniques to generate more accurate plans over longer horizons. 11. What is the biggest drawback of MuZero? The biggest drawback of MuZero is its high computational complexity and resource require- ments, which can make it challenging to implement and scale for real-world applications. 12. What is wonderful about MuZero? MuZero’s ability to learn both the model and the policy end-to-end without prior knowledge of the environment’s dynamics is a significant advancement, allowing it to perform exceptionally well across a variety of tasks, including complex games. 5