Corruption-Robust Contextual Search through Density Updates
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We study the problem of contextual search in the adversarial noise model. Let d be the dimension of the problem, T be the time horizon and C be the total amount of noise in the system. For the -ball loss, we give a tight regret bound of O(C + d log(1/)) improving over the O(d^3 log(1/)) log^2(T) + C log(T) log(1/)) bound of Krishnamurthy et al (STOC21). For the symmetric loss, we give an efficient algorithm with regret O(C+d log T). Our techniques are a significant departure from prior approaches. Specifically, we keep track of density functions over the candidate vectors instead of a knowledge set consisting of the candidate vectors consistent with the feedback obtained.
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