Papers

Papers and notes on few-shot search.

When the Grass Is Greener: Three-Shot Search on Exponentiated Gaussian Landscapes

Peter Cotton · working paper, September 2026; first version April 6, 2022 · PDF · source and numerics · checks · 2022 version

How should a firm spend its last pivot? A searcher knows an incumbent strategy's performance, may run one more trial, and must then commit, on a landscape given by the exponential of a stationary Ornstein–Uhlenbeck path. The final placement is solved exactly, with a closed-form phase diagram for equal observations: abandon a below-median incumbent; after a disappointing trial revert to the better position's own two-shot rule; commit between two good positions; and stay put once a position is strong enough.

Commitment between positions rests on a constant variance-ratio identity: every interior position has the same conditional mean log-performance as an explicit exterior alternative and $(1+\rho)/(1-\rho)$ times its conditional variance. Terminal placement is a projection of the observed values onto a feasible set of correlations, so the geometry solves in every Euclidean dimension.

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