The problem of finding an optimum using noisy evaluations of a smooth cost
function arises in many contexts, including economics, business, medicine,
experiment design, and foraging theory. We derive an asymptotic bound E[ (x_t -
x*)^2 ] >= O(1/sqrt(t)) on the rate of convergence of a sequence (x_0, x_1,
>...) generated by an unbiased feedback process observing noisy evaluations of
an unknown quadratic function maximised at x*. The bound is tight, as the proof
leads to a simple algorithm which meets it. We further establish a bound on the
total regret, E[ sum_{i=1..t} (x_i - x*)^2 ] >= O(sqrt(t)) These bounds may
impose practical limitations on an agent's performance, as O(eps^-4) queries
are made before the queries converge to x* with eps accuracy.Comment: 6 pages, 2 figure