Ranking with Multiple Oracles: From Weak to Strong Stochastic Transitivity

摘要

We study the problem of efficiently aggregating the preferences of items from multiple information sources (oracles) and infer the ranking under both the weak stochastic transitivity (WST) and the strong stochastic transitivity (SST) conditions. When the underlying preference model satisfies the WST condition, we propose an algorithm named RMO-WST, which has a bi-level design: at the higher level, it actively allocates comparison budgets to all undetermined pairs until the full ranking is recovered; at the lower level, it attempts to compare the pair of items and selects the more accurate oracles simultaneously. We prove that the sample complexity of RMO-WST is $ \tilde O( N\sum_{i=2}^{N}H_{\sigma^{-1}(i),{\sigma^{-1}(i-1)}} )$, where $N$ is the number of items to rank, $H$ is a problem-dependent hardness factor, and $\sigma^{-1}(i)$ represents the $i$-th best item. We also provide a tight lower bound that matches the upper bound of approximate ranking under the WST condition, answering a previously open problem. In addition, when the SST condition is satisfied, we propose an algorithm named RMO-SST, which can achieve an $\tilde{O}(\sum_{i=1}^{N} H_i \log(N))$ sample complexity. This outperforms the best-known sample complexity by a factor of $\log(N)$. The theoretical advantages of our algorithms are verified by empirical experiments in a simulated environment.