Our programme sim2real-inference asks how few real robot trials certify a policy when a biased simulator supplies the rest. This step tested the sequential version: stop collecting real trials as soon as a confidence sequence (hedged-capital betting, valid at any stopping time) shows the mean success is above a bar.
On 21 MuJoCo twin-versus-"real" pairs, 1,000 replications each, up to 300 trials:
- All three sequences stayed valid under optional stopping: the truth left the sequence in at most 2.5% of runs (limit 5%).
- Using the simulator as a control variate was slower, not faster: a median of 74 real trials to rule out a bar 0.10 below the truth, against 50 without the simulator, on all 12 pairs where simulator and "real" outcomes correlate at 0.8 or more.
- Fitting the control-variate weight on a 20-trial pilot made it slower again (133).
The reason is range: the paired difference spans twice the interval, and a plug-in bet does not recover that even when the variance is half. So the simulator's value remains point-estimate precision, not faster decisions. This is model-versus-model on one task; a mixture bet is the next thing to try.
Code, pre-registration and outcome: research/sim2real-inference/ (milestone 5b).