A pilot-checked bound on halving regret is safe but loose

Testing, pilot by pilot, whether a 16-point routed pilot can bound the regret of successive halving over cheap chip-flow estimates.

Research findings · 1 min read · Source
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verified-dse asks whether cheap estimates of a chip design's quality can be trusted to prune a search, with a guarantee. An earlier step proved that successive halving loses at most the sum of each cut rung's worst ranking mistake. That worst mistake cannot be read off a small pilot, so the next step tested two things a pilot can compute.

On the cached table (20 design-and-clock groups, about 50 flow runs each), using 16 routed pilot points at a time:

  • Random-pair quantiles (the previous step's statistic) cover the realised regret in under 80% of pilots in 6 of 40 cells. The worst is 0.28, on the ripple adder, whose scores take only four distinct values.
  • The pilot's best three points against all other pilot points cover in all 40 cells (minimum 0.81). But the bound is a median 4.6 times the realised regret, and under 0.1 log units only when halving starts from the mapped rung at the relaxed clock (7 of 10 groups).

So the bound is safe where it was tested and useful only where the cheap rung is already good. Limits: one table, a pilot that is a third of the pool, and no proof for the second statistic yet. Details are in the research log.

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