Betting for Sim-to-Real Performance Certificates

This note describes an integration of the sim-to-real performance estimate with betting (from Chen et al.) and the safe anytime-valid inference (from Ramdas et al.). Using the scaled simulators. The method produces efficient, reliable certificates for the mean estimate, an approach that is especially valuable in robot performance testing. This note gives a primary, self-contained account of the construction; preliminaries of the respective methods are kept at a minimum, and one shall refer to the original works for full detail. Some synthetic examples demonstrating the proposed algorithm can be found at https://github.com/ISUSAIL/Bet4Sim2Real-EProcess.

This paper studies the problem of robot performance evaluation, focusing on how to obtain accurate and efficient estimates of real-world behavior under severe constraints on physical experimentation. Such estimates are essential for benchmarking algorithms, comparing design alternatives, validating controllers, and supporting certification or regulatory decision-making, yet real-world testing with physical robots is often expensive, time-consuming, and safety-limited. To mitigate the scarcity of real-world trials, sim-to-real methodologies are commonly employed, using low-cost simulators to inform, supplement, or prioritize physical experiments. Departing from (and complementary to) existing approaches in variance reduction (e.g., importance-sampling variants) or bias-correction (e.g., through prediction-powered inference or learned control variates), we examine this performance-evaluation problem through the lens of betting. We establish theoretical conditions under which a betting mechanism can yield accurate and efficient estimates (provably outperforming the Monte Carlo estimator) and we characterize how such bets should be constructed. We further develop theoretically grounded yet practically implementable approximations of the ideal bet, and we provide concrete decision rules that diagnose when these approximate betting strategies are working as intended. We demonstrate the effectiveness of the proposed methods using both synthetic examples and cross-fidelity computational simulators. Notably, we also showcase an illustrative case in which a group of synthetic distributions are used to infer the real-world pick-and-place accuracy of a robotic manipulator, a seemingly unconventional sim-to-real transfer that becomes natural and feasible under the proposed betting perspective. Programs for reproducing empirical results are available at https://github.com/ISUSAIL/Bet4Sim2Real.

Simulation-to-reality transfer, often called sim-to-real transfer, is a central challenge in robot learning. Yet, the tradeoff between measuring a system more accurately and training over a broader range of simulated dynamics is still poorly understood. In this work, we focused on the allocation of real-robot measurement time between system identification and domain randomization. We studied this tradeoff in a controlled sim-to-sim pendulum setting, where a hidden-parameter model stands in for the physical robot, and the experiment sweeps identification rollouts against the width of the randomization distribution. Across the reality gaps and noise levels we tested, the measurement budget did most of the work. A small number of identification rollouts closed most of the transfer gap, and once any real data was available, policies performed best when trained at the estimated parameters rather than over a widened randomization band. Broad randomization that contained the true system still did not substitute for measurement. These results hold in a benign regime where the dynamics are identifiable and only two parameters are unknown, so structural model mismatch remains the setting where randomization breadth may become more valuable. Overall, our results suggest that sim-to-real pipelines should first measure the parameters they can and reserve randomization for the uncertainty that remains.