Provable Sim-to-Real Transfer via Offline Domain Randomization

Abstract: Reinforcement-learning agents often struggle when deployed from simulation to the real-world. A dominant strategy for reducing the sim-to-real gap is domain randomization (DR) which trains the policy across many simulators produced by sampling dynamics parameters, but standard DR ignores offline data already available from the real system. We study offline domain randomization (ODR), which first fits a distribution over simulator parameters to an offline dataset. While a growing body of empirical work reports substantial gains with algorithms such as DROPO, the theoretical foundations of ODR remain largely unexplored. In this work, we (i) formalize ODR as a maximum-likelihood estimation over a parametric simulator family, (ii) prove consistency of this estimator under mild regularity and identifiability conditions, showing it converges to the true dynamics as the dataset grows, (iii) derive gap bounds demonstrating ODRs sim-to-real error is up to an O(M) factor tighter than uniform DR in the finite-simulator case (and analogous gains in the continuous setting), and (iv) introduce E-DROPO, a new version of DROPO which adds an entropy bonus to prevent variance collapse, yielding broader randomization and more robust zero-shot transfer in practice.

• The paper introduces offline domain randomization as a maximum-likelihood estimation problem to enhance sim-to-real transfer in RL.
• It proves both statistical and almost sure consistency of the ODR estimator, offering sharper performance bounds than uniform domain randomization.
• It proposes entropy-regularized DROPO (E-DROPO) to preserve estimator variance and improve zero-shot transfer in reinforcement learning tasks.

Provable Sim-to-Real Transfer via Offline Domain Randomization

Introduction

The paper "Provable Sim-to-Real Transfer via Offline Domain Randomization" introduces a theoretical framework for offline domain randomization (ODR), a technique aimed at improving the sim-to-real transfer in reinforcement learning (RL) by leveraging offline data. Unlike traditional domain randomization (DR), which samples dynamics parameters uniformly from a pre-defined range to train policies robustly across simulated environments, ODR tunes these parameters based on an offline dataset from the real system. The primary contributions include the formalization of ODR as a maximum-likelihood estimation problem, proving the statistical consistency of the ODR estimator, deriving theoretically tighter sim-to-real performance bounds compared to uniform DR, and introducing entropy-regularized DROPO (E-DROPO) for robust zero-shot transfer.

Theoretical Insights and Consistency

ODR is formulated as a maximum-likelihood estimation problem over a Gaussian distribution of simulator parameters. The paper establishes that, under mild assumptions, the ODR estimator is statistically consistent, meaning it converges in probability to the true system dynamics as the dataset size increases. Particularly, under assumptions of regular parameter space, mixture positivity, and parameter identifiability, it is shown that the ODR estimate $\hat{\phi}_N$ converges with increasing data, providing empirical consistency with theoretical assurance.

Additionally, by strengthening the regularity assumption to uniform Lipschitz continuity, the authors upgrade the consistency results to almost sure convergence, ensuring the distribution learned via ODR accurately reflects the true dynamics in nearly all datasets.

Gap Bound Improvements

The paper demonstrates that ODR offers sharper sim-to-real performance bounds compared to uniform DR. In the finite parameter space case, where each simulator is distinct and fulfilling a separation condition, ODR reduces the worst-case gap by a factor $O(M)$, where $M$ is the number of candidate simulators. This improvement is attributed to the more data-informed parameter distributions derived from offline data, which guide the domain randomization process better than broad uniform ranges.

Entropy-Regularized DROPO

To address potential issues of variance collapse in the covariance estimation during ODR, the authors propose E-DROPO, an extension of DROPO augmented with an entropy bonus. This modification ensures the learned parameter distributions retain sufficient diversity, enhancing zero-shot transfer capabilities. E-DROPO was evaluated on the Robosuite Lift task, showing a reduction in estimation error due to improved variance preservation.

Implementation and Practical Considerations

Implementing the ODR framework requires the translation of theoretical constructs into practical algorithms. This involves fitting a Gaussian distribution to simulator parameters using gradient-free optimization techniques like CMA-ES, focused on maximizing likelihood and entropy. An example pseudocode of E-DROPO, which iteratively updates the parameter distribution to maximize a combined objective of log-likelihood and entropy, is outlined to showcase its application.

For practitioners deploying these methods in RL tasks, ensuring computational efficiency while maintaining sufficient diversity in the learned parameter distributions is crucial. The paper's suggestions, such as the usage of entropy bonuses and optimization strategies that prevent covariance collapse, provide an actionable path towards improving sim-to-real transfer robustness in varied applications, including robotics and autonomous systems.

Conclusion

The paper provides a rigorous framework that strengthens the theoretical foundation for leveraging offline data in domain randomization, achieving better sim-to-real performance. By innovating on both the theoretical and practical fronts, this work bridges the gap between empirical successes in RL and the underlying statistical guarantees, empowering the deployment of RL models in real-world scenarios with increased confidence and reliability. Future research is directed towards relaxing some assumptions to broaden applicability, exploring alternate ODR algorithms, and refining theoretical analyses of variants like E-DROPO.