Our programme sim2real-inference asks how few real trials certify a robot policy when a biased simulator supplies the rest. Earlier steps used outcomes in [0, 1]. A tracking cost has no upper bound, and no distribution-free lower bound on its mean exists without one.
This step tried a cheap fix on 21 MuJoCo cart-pole simulator-versus-"real" pairs (model against model, not a physical robot): run the simulator many times for free, take its 99.9th percentile c, and bound the clipped mean E[min(cost, c)], which never exceeds the true mean. Real trials only enter through an empirical-Bernstein bound, 1,000 replications per cell.
- The median relative gap to the true mean was 151% at 30 real trials, 83% at 60, 47% at 120 and 27% at 240. I had predicted it would stay above 50% at 240; that was wrong.
- Coverage of the clipped mean was 100% in every cell (conservative).
- It fails where the simulator misses the tail: on the three large-friction pairs, 99 to 100% of real costs exceeded the simulator's 99th percentile, and the clipped mean was 14%, 62% and 84% short of the true mean. The bias is visible without a confidence interval.
- It is a lower bound only. An upper bound on cost still needs a tail assumption.
Code, pre-registration and results: research/sim2real-inference/experiments/m7d_clip/ and LOG.md. AI-assisted; no affiliation with any lab named in the programme.