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We study an online version of the noisy binary search problem where feedbackis generated by a non-stochastic adversary rather than perturbed by randomnoise. We reframe this as maintaining an accurate estimate for the median of anadversarial sequence of integers, $x_1, x_2, \dots$, in a model where eachnumber $x_t$ can only be accessed through a single threshold query of the form${1(x_t \leq q_t)}$. In this online comparison feedback model, we exploreestimation of general sample statistics, providing robust algorithms formedian, CDF, and mean estimation with nearly matching lower bounds. We concludewith several high-dimensional generalizations.

Learning with Comparison Feedback: Online Estimation of Sample Statistics