Corruption-Robust Lipschitz Contextual Search
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I study the problem of learning a Lipschitz function with corrupted binary signals. The learner tries to learn a Lipschitz function f that the adversary chooses. In each round, the adversary selects a context vector x_t in the input space, and the learner makes a guess to the true function value f(x_t) and receives a binary signal indicating whether the guess was high or low. In a total of C rounds, the signal may be corrupted, though the value of C is unknown to the learner. The learner's goal is to incur a small cumulative loss. I present a natural yet powerful technique sanity check, which proves useful in designing corruption-robust algorithms. I design algorithms which (treating the Lipschitz parameter L as constant): for the symmetric loss, the learner achieves regret O(Clog T) with d = 1 and O_d(Clog T + T^(d-1)/d) with d > 1; for the pricing loss the learner achieves regret O (T^d/(d+1) + C· T^1/(d+1)).
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