The Limits of Maxing, Ranking, and Preference Learning

We present a comprehensive understanding of three important problems in PAC preference learning: maximum selection (maxing), ranking, and estimating all pairwise preference probabilities, in the adaptive setting. With just Weak Stochastic Transitivity, we show that maxing requires Ω(n) comparisons and with slightly more restrictive Medium Stochastic Transitivity, we present a linear complexity maxing algorithm. With Strong Stochastic Transitivity and Stochastic Triangle Inequality, we derive a ranking algorithm with optimalO(n log n) complexity and an optimal algorithm that estimates all pairwise preference probabilities.

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