Jessica Taylor publishes probability paper characterizing dice enterprises via polynomial approximation
jessi_cata · x · 2026-10-30
Alignment researcher Jessica Taylor posted a probability paper on arXiv, Dice enterprises and polynomial approximation: uniform query tails.
- Problem: a "dice enterprise" uses independent rolls of a die with unknown face probabilities p (plus fair coin flips) to simulate a coin with bias f(p).
- Main result: for continuous f with values in (0,1) and q>0, some enterprise achieves the uniform tail bound sup P(N>n)=O(n^-q) if and only if f can be uniformly approximated by degree-k polynomials with error O(k^-2q).
- Additional findings: the same tail bound is attained by an oblivious enterprise that fixes rolls in advance; the characterization extends to multiple dice via total degree on products of simplices, and for q>1 expected rolls are uniformly bounded.
- 13 pages, purely theoretical probability work.
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