Papers
Manuscripts of the budgeted Brownian race program.
Wavefront Pruning in Budgeted Brownian Races
Defines the budgeted Brownian race: a controller observes a cloud of Brownian paths, pays per unit time for each survivor, may irreversibly prune, and allocates a finite path-time budget to maximize the expected terminal maximum. The planned scope is the mean-field limit — the coupled obstacle/Fokker–Planck system whose discrete counterpart this repository already solves — the wavefront characterization of the optimal policy, and the relation to the finite-n pathwise-budget problem. The numerical certificates will be the committed scripts in this repository.
Posterior-Predictive Pass-at-k
The estimation side of the rollout race: pass@k is the expected-maximum payoff of a best-of-k batch, and the standard extrapolation 1 − (1 − p̂)k evaluates it at a noisy point estimate. Jensen's inequality makes that plug-in biased downward for every difficulty, and a prompt with zero observed successes is rated impossible at every k. Replacing the plug-in with the posterior expectation under a two-parameter difficulty prior, fitted once by marginal maximum likelihood, cuts held-out log loss from 3.37 to 0.48 on nine thousand released rollout prompts and brings extrapolated aggregate pass@8 within two points of truth; beta-binomial and probit-normal priors tie to three decimals.
Working notes
The mean-field solver
The Poissonized, expected-budget, discrete-time formulation: the exact layer-cake value of the Poisson terminal maximum, its pivotal-value gradient, the obstacle best response, and the fully-corrective Frank–Wolfe outer loop with dual bisection. The module docstring is the current write-up of record.