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Self-Correcting Models for Model-Based Reinforcement Learning

Erik Talvitie

arXiv:1612.06018v2cs.LGcs.AI

TL;DR

MBRL can fail when limited models or suboptimal planners compound prediction errors. This paper analyzes hallucinated training and derives a model-quality measure and an algorithm for deterministic MDPs. It concludes that self-correction can better relate to control performance than one-step prediction error under some assumptions.

  • Problem

    MBRL can fail catastrophically when limited model representations or suboptimal planners impair its predictions and plans.

    Source: §1 · p. 1

  • Method

    The paper analyzes hallucinated training, derives bounds based on a model's ability to self-correct, and uses the analysis to develop an MBRL algorithm for deterministic MDPs.

    Source: §1 · pp. 1–2, §2.3 · p. 3

  • Results

    Under some assumptions, a measure of model quality based on self-correction is more tightly related to MBRL performance than standard one-step prediction error.

    Source: §5 · p. 6

  • Takeaways & Limitations

    H-DAgger-MC provides theoretical performance guarantees for control despite flaws in the model and planner.

    Source: §5 · p. 6

    Hallucinated one-step error can be a poor proxy for multi-step error and may be non-zero even for a perfect model.

    Source: §2.3 · pp. 3–4

Abstract

from arXiv · show

When an agent cannot represent a perfectly accurate model of its environment's dynamics, model-based reinforcement learning (MBRL) can fail catastrophically. Planning involves composing the predictions of the model; when flawed predictions are composed, even minor errors can compound and render the model useless for planning. Hallucinated Replay (Talvitie 2014) trains the model to "correct" itself when it produces errors, substantially improving MBRL with flawed models. This paper theoretically analyzes this approach, illuminates settings in which it is likely to be effective or ineffective, and presents a novel error bound, showing that a model's ability to self-correct is more tightly related to MBRL performance than one-step prediction error. These results inspire an MBRL algorithm for deterministic MDPs with performance guarantees that are robust to model class limitations.

1 Introduction

MBRL can fail when model or planner limitations distort composed predictions, despite the appeal of sample efficiency. The paper analyzes Hallucinated Replay and develops error bounds and an algorithm for MBRL with imperfect models.

1 Introduction

  • Model or planner limitations can make MBRL fail catastrophically, even when the model’s inaccuracies seem minor.The paper frames understanding how MBRL can work despite such flaws as vital to gaining its anticipated benefits in large-scale problems.Source: §1 · p. 1
  • One-step prediction accuracy is an inadequate proxy for planning performance; the most accurate model by that measure need not be best for planning.Sorg et al. (2010) and Joseph et al. (2013) proposed optimizing model parameters for control performance, an approach the paper says may discard some benefits of model learning.Source: §1 · p. 1
  • Hallucinated Replay trains on model-sampled states to predict environment states, causing the model to self-correct its rollouts.Talvitie (2014) showed meaningful planning with flawed models in examples where standard training failed, but the approach had no theoretical guarantees.Source: §1 · p. 1, Figure 1 · p. 1
  • The paper presents error bounds, identifies conditions where hallucinated training is ineffective, and derives an MBRL algorithm with guarantees robust to model-class limitations.It also examines a previously underexplored practical concern empirically.Source: §1 · pp. 1–2

1.1 Notation and background

  • The setup is an MDP with initial-state distribution μ and known bounded rewards; the learned model approximates the dynamics but need not be perfect.The agent seeks a policy maximizing expected value from the initial-state distribution.Source: §1.1 · p. 2

2 Bounding value error

The section develops value-error bounds and shows why one-step prediction error can mislead when model limitations compound during planning. In deterministic environments with blind rollout policies, hallucinated one-step error is more tightly related to MBRL performance.

2 Bounding value error

  • The value-error analysis separates planning-algorithm error from model error and focuses model accuracy on state-actions visited by the evaluated and learned policies.The one-step prediction bound can be loose when model-class limitations prevent low error in important states.Source: §2 · p. 2, §2.1 · p. 2

2.1 One-step prediction error

  • In Shooter, the lowest-one-step-error model compounds errors on unfamiliar sampled states until it assigns low probability to persistent targets, while another model self-corrects and remains useful for planning.The two models make the same one-step errors on environment states; their planning usefulness differs in predictions farther into the future.Source: §2.1 · p. 3

2.2 Multi-step prediction error

  • The multi-step bound accounts for recovery after errors by penalizing individual incorrect transitions, unlike a one-step bound that assumes the worst possible value loss after an incorrect state.Directly optimizing multi-step prediction accuracy is difficult, but the bound suggests that algorithms accounting for multi-step error can yield more robust MBRL performance.Source: §2.2 · p. 3

2.3 Hallucinated one-step prediction error

  • Hallucinated one-step error can be nonzero even for a perfect model, making it a misleading proxy when the true dynamics are stochastic.The analysis assumes deterministic environments in the remainder; even there, the bound is loose for arbitrary policies.Source: §2.3 · pp. 3–4

2.4 A Tighter Bound

  • With deterministic dynamics and a blind rollout policy, hallucinated one-step error is more tightly related to MBRL performance than standard one-step error.The paper identifies this relationship as the theoretical basis for Hallucinated Replay and uses it to motivate an MBRL algorithm with performance guarantees.Source: §2.4 · p. 4

3 Hallucinated DAgger-MC

H-DAgger-MC extends DAgger-MC with hallucinated training, using model-generated inputs paired with environment targets to train models to self-correct during rollouts. Its guarantees depend on model error at each rollout depth, planner error, exploration coverage, and an unrolled model; they do not promise the best-performing model set in the class.

3 Hallucinated DAgger-MC

  • H-DAgger-MC adds hallucinated examples to DAgger-MC, training models on environment targets paired with model-generated inputs during rollouts.The algorithm learns a separate model for each rollout step.Source: §3 · pp. 4–5
  • The performance bound applies to the average policy and assumes exact expected loss; it does not directly establish guarantees for the last policy in the sequence.The analysis also uses L1 loss and infinite samples per iteration.Source: §3 · p. 5
  • When each rollout depth has a low-error model, H-DAgger-MC learns low-error models, and a perfect model in the class can still be learned.Good policy performance also requires low planning error and an exploration distribution that visits important states.Source: §3 · p. 5
  • H-DAgger-MC does not guarantee the best-performing model set, because improving one depth can alter deeper models’ training distributions.Each depth is trained to reduce prediction error on inputs produced by shallower models.Source: §3 · p. 5

4 Empirical Illustration

In Shooter, H-DAgger-MC obtains a good policy despite model-class limitations, while the standard approach fails; with a perfect model available, DAgger-MC performs better. In the unrolled-model experiment, a shared model can degrade on deeper rollouts, while truncating training rollouts may avoid unrolling but offers no principled depth choice or performance guarantee.

4 Empirical Illustration

  • DAgger performs poorly with both fixed and moving bullseyes because its planner is suboptimal.DAgger-MC performs well with fixed bullseyes but suffers compounding errors with moving bullseyes, with both single and unrolled models.Source: §4 · p. 6
  • Early training rollouts were truncated at depth floor(i/10) to avoid incoherent samples; this transient change does not affect H-DAgger-MC’s asymptotic guarantees.Planning rollouts were completed by repeatedly applying the deepest model trained so far.Source: §4 · p. 6
  • H-DAgger-MC obtains a good policy with moving bullseyes despite model-class limits, while the standard approach fails; with fixed bullseyes, DAgger-MC outperforms it.The fixed-bullseye setting contains a perfect model; with moving bullseyes, DAgger-MC is not useful for planning because of compounding errors.Source: §4 · p. 6

4.1 Impact of the unrolled model

  • With one shared model and a perfect model available, performance degraded as longer training rollouts were permitted, despite strong performance under temporary truncation.The proposed mechanism is a feedback loop: attempts to correct large errors can worsen subsequent errors and the training distribution.Source: §4.1 · p. 6
  • Shorter training rollouts performed better in this experiment, suggesting truncation may avoid unrolling, but no principled rollout depth or performance guarantee is provided.The authors note that earlier approaches also limited rollout depth to avoid overly noisy samples.Source: §4.1 · p. 6

5 Conclusions and future work

The paper connects model quality to MBRL performance under model-class limitations and analyzes an algorithm with theoretical guarantees. It also identifies boundaries involving the error criterion, training stability, planning depth, and reward assumptions.

5 Conclusions and future work

  • The paper analyzes model quality measures and an MBRL algorithm that achieves good control performance despite model and planner flaws, with theoretical performance guarantees.Its central focus is effective MBRL under model-class limitations.Source: §5 · p. 6
  • Hallucinated one-step error may be ineffective in the most general setting, leaving open how to handle stochastic dynamics, non-blind policies, or other approaches to multi-step error.Hallucinated training can also raise stability issues because model parameters affect both prediction error and the training distribution.Source: §5 · pp. 6–7
  • The analysis specializes to one-ply Monte Carlo planning, and whether its principles extend to more sophisticated planners remains open.The authors argue that a more sophisticated planner cannot compensate for a poor model when the model class is limited.Source: §5 · p. 7
  • The results assume a known reward function, though the authors state they can be extended to account for reward error.Sampling an incorrect state may have little negative impact when its rewards and transitions resemble those of the correct state.Source: §5 · p. 7

Appendix: Proofs

The appendix presents proof steps for results stated under deterministic-MDP conditions, including recurrence-based arguments and bounds.

Appendix: Proofs

  • For deterministic P, Lemma 7 states a result for any blind policy and state-action distribution.The supplied passage gives the lemma's conditions but not its bound.Source: Appendix: Proofs · p. 9
  • Theorem 8 is stated for deterministic P, any blind policy, and any state-action distribution.The supplied theorem passage does not include its conclusion.Source: Appendix: Proofs · p. 10
  • The proof separates prediction error into cases where the model and environment states match or differ.It then combines the terms into a recurrence and unrolls it.Source: Appendix: Proofs · p. 10

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