Part 5 · The Maths III: Inside the SOTA Methods
πBO: folding expert beliefs into the acquisition
When a practitioner already believes the optimum lives somewhere (“learning rates around 10−3”), πBO injects that belief π(x) as a decaying multiplicative reweighting of any acquisition α:
αn the ordinary acquisition value · π(x) the expert's prior belief about where the optimum lies · β/n the decaying exponent, so the prior's influence fades as real observations accumulate
At n = β the prior speaks with full voice; as n grows the exponent β/n → 0 and π(x)β/n → 1 — the data always wins eventually, and a wrong prior costs only the early iterations (the paper proves EI’s convergence rate survives). Compare Maths I’s marginal likelihood: that fits the smoothness prior from data; πBO adds a location prior from humans. The two compose.