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What model does MuZero learn?

Jinke He, Thomas M. Moerland, Joery A. de Vries, Frans A. Oliehoek

TL;DR

It is revealed that MuZero's model struggles to generalize when evaluating unseen policies, which limits its capacity for additional policy improvement, but MuZero's incorporation of the policy prior in MCTS alleviates this problem.

Abstract

Model-based reinforcement learning (MBRL) has drawn considerable interest in recent years, given its promise to improve sample efficiency. Moreover, when using deep-learned models, it is possible to learn compact and generalizable models from data. In this work, we study MuZero, a state-of-the-art deep model-based reinforcement learning algorithm that distinguishes itself from existing algorithms by learning a value-equivalent model. Despite MuZero's success and impact in the field of MBRL, existing literature has not thoroughly addressed why MuZero performs so well in practice. Specifically, there is a lack of in-depth investigation into the value-equivalent model learned by MuZero and its effectiveness in model-based credit assignment and policy improvement, which is vital for achieving sample efficiency in MBRL. To fill this gap, we explore two fundamental questions through our empirical analysis: 1) to what extent does MuZero achieve its learning objective of a value-equivalent model, and 2) how useful are these models for policy improvement? Our findings reveal that MuZero's model struggles to generalize when evaluating unseen policies, which limits its capacity for additional policy improvement. However, MuZero's incorporation of the policy prior in MCTS alleviates this problem, which biases the search towards actions where the model is more accurate.

What model does MuZero learn?

TL;DR

It is revealed that MuZero's model struggles to generalize when evaluating unseen policies, which limits its capacity for additional policy improvement, but MuZero's incorporation of the policy prior in MCTS alleviates this problem.

Abstract

Model-based reinforcement learning (MBRL) has drawn considerable interest in recent years, given its promise to improve sample efficiency. Moreover, when using deep-learned models, it is possible to learn compact and generalizable models from data. In this work, we study MuZero, a state-of-the-art deep model-based reinforcement learning algorithm that distinguishes itself from existing algorithms by learning a value-equivalent model. Despite MuZero's success and impact in the field of MBRL, existing literature has not thoroughly addressed why MuZero performs so well in practice. Specifically, there is a lack of in-depth investigation into the value-equivalent model learned by MuZero and its effectiveness in model-based credit assignment and policy improvement, which is vital for achieving sample efficiency in MBRL. To fill this gap, we explore two fundamental questions through our empirical analysis: 1) to what extent does MuZero achieve its learning objective of a value-equivalent model, and 2) how useful are these models for policy improvement? Our findings reveal that MuZero's model struggles to generalize when evaluating unseen policies, which limits its capacity for additional policy improvement. However, MuZero's incorporation of the policy prior in MCTS alleviates this problem, which biases the search towards actions where the model is more accurate.
Paper Structure (20 sections, 7 equations, 9 figures, 2 tables)

This paper contains 20 sections, 7 equations, 9 figures, 2 tables.

Table of Contents

  1. Background
  2. Markov Decision Processes
  3. MuZero
  4. The value equivalence principle
  5. Policy Evaluation Experiments
  6. Training MuZero agents
  7. Evaluating the learned model
  8. How accurately can MuZero's learned model predict the value of its own behavior policy?
  9. How accurately can MuZero's learned model evaluate policies that are different from the behavior policy?
  10. How accurately can MuZero's learned model from one training step evaluate the behavior policy of the same agent from another training step?
  11. Policy Improvement Experiments
  12. Discussion
  13. Limitations
  14. Outlook
  15. Conclusion
  16. ...and 5 more sections

Figures (9)

  • Figure 1: An illustration of MuZero's loss function.
  • Figure 2: Online performance of MuZero agents in Cart Pole (Left), Lunar Lander (Middle) and Atari Breakout (Right).
  • Figure 3: Value prediction error of using MuZero's learned model to evaluate its own behavior policy.
  • Figure 4: X-axis: action sequences sorted by their probabilities of being taken by the behavior policy (from unlikely to likely reading from left to right). Y-axis: the probabilities (blue, from small to large) and the corresponding value prediction errors (yellow, from small to large). Action sequences with higher probabilities to be taken by MuZero’s behavior policy correlate with lower value prediction errors by MuZero’s learned model. This implies that the learned model is less accurate for policies that are different from the current data collection policy.
  • Figure 5: Cross model policy evaluation. We evaluate MuZero's behavior policy at training step Y (column) with the learned model at training step X (row) and measure the value prediction error. Results are aggregated over states sampled from MuZero's on-policy state distribution at training step X (same as the model).
  • ...and 4 more figures

Theorems & Definitions (2)

  • Definition 1
  • Definition 2