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the budget solve ·
bb_core.js
Watch a race
Sampled paths under the solved wavefront policy, against the value the solver promised.
The solver prices path-time for your budget and returns a wavefront
policy: one kill-below cutoff per time step. Here that policy is applied
to actual sampled paths — a Poisson number of them, stepping
through the same Markov chain the solver planned over. Paths dropping
below the cutoff die (gray); survivors (blue) run to maturity, where the
best of them, or the fallback at zero, is the payoff. Races replay
continuously and the running mean accumulates.
What to look for: the running mean of realized maxima
must converge to the solver's expected maximum, and the running mean of
spent path-time to the solver's expected path-time. The readout monitors
the z-score against a time-uniform confidence band of roughly 3.3–3.6
standard errors: under continuous monitoring a correct simulator crosses a
plain 2-s.e. band infinitely often (the law of the iterated logarithm), so
ordinary excursions past 2 prove nothing. A z-score that leaves the
time-uniform band, or grows without shrinking back, falsifies the forward
pass. The policy is generally a mixture of a few wavefront atoms (the
dashed cutoffs, opacity by weight), and each path independently follows
one of them; by Poisson thinning the sampled cloud then has exactly the
mixture's intensity, so the targets are exact, not approximate.
Paths are sampled from the identical discrete transition kernel the
solver plans over, so the comparison is exact in distribution: any
persistent gap is a bug, not discretization. 50 time steps, 301 state
points.