一种查询复杂度几乎最优的成对偏好排序主动学习算法
An Active Learning Algorithm for Ranking from Pairwise Preferences with an Almost Optimal Query Complexity
摘要：
我们研究了从成对偏好中学习排序的问题，并解决了一个长期存在的开放问题，该问题导致了许多数学的发展，但对于我们的特定问题没有可证明的结果。给定$n$元素的集合$V$，我们希望在给定成对偏好标签的情况下对它们进行线性排序。成对偏好标签是作为对问题“如果偏好，u还是v？$ for two elements $ u，v \in V $. We assume possible non-transitivity paradoxes which may arise naturally due to human mistakes or irrationality. The goal is to linearly order the elements from the most preferred to the least preferred, while disagreeing with as few pairwise preference labels as possible. Our performance is measured by two parameters: The loss and the query complexity (number of pairwise preference labels we obtain). This is a typical learning problem, with the exception that the space from which the pairwise preferences is drawn is finite, consisting of $ {n \choose 2}$种可能性。我们提出了一个主动学习算法，这个问题，查询边界显着击败一般（非主动）边界相同的错误保证，同时几乎达到信息理论的下限。我们的主要构造是输入s. t的分解。(i)每个块在最佳情况下产生高损失，以及（ii）关于分解的最优解并不比真正的opt差很多。分解是通过适应Kenyon和Schudy最近的结果来完成的，用于相关的组合优化问题以查询有效设置。因此，我们解决了一个由学习排名理论家和实践者提出的开放性问题：什么是可证明正确的偏好标签抽样方法？为了进一步展示我们的解决方案的功能和实用性，我们展示了如何将其与SVM松弛相结合。
英文摘要：
We study the problem of learning to rank from pairwise preferences, and solve a long-standing open problem that has led to development of many heuristics but no provable results for our particular problem. Given a set $V$ of $n$ elements, we wish to linearly order them given pairwise preference labels. A pairwise preference label is obtained as a response, typically from a human, to the question "which if preferred, u or v?$ for two elements $u,v\in V$. We assume possible non-transitivity paradoxes which may arise naturally due to human mistakes or irrationality. The goal is to linearly order the elements from the most preferred to the least preferred, while disagreeing with as few pairwise preference labels as possible. Our performance is measured by two parameters: The loss and the query complexity (number of pairwise preference labels we obtain). This is a typical learning problem, with the exception that the space from which the pairwise preferences is drawn is finite, consisting of ${n\choose 2}$ possibilities only. We present an active learning algorithm for this problem, with query bounds significantly beating general (non active) bounds for the same error guarantee, while almost achieving the information theoretical lower bound. Our main construct is a decomposition of the input s.t. (i) each block incurs high loss at optimum, and (ii) the optimal solution respecting the decomposition is not much worse than the true opt. The decomposition is done by adapting a recent result by Kenyon and Schudy for a related combinatorial optimization problem to the query efficient setting. We thus settle an open problem posed by learning-to-rank theoreticians and practitioners: What is a provably correct way to sample preference labels? To further show the power and practicality of our solution, we show how to use it in concert with an SVM relaxation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
