Timezone: »

Poster
Sample Complexity Bounds for Active Ranking from Multi-wise Comparisons
Wenbo Ren · Jia Liu · Ness Shroff

Wed Dec 08 04:30 PM -- 06:00 PM (PST) @
We study the sample complexity (i.e., the number of comparisons needed) bounds for actively ranking a set of $n$ items from multi-wise comparisons. Here, a multi-wise comparison takes $m$ items as input and returns a (noisy) result about the best item (the winner feedback) or the order of these items (the full-ranking feedback). We consider two basic ranking problems: top-$k$ items selection and full ranking. Unlike previous works that study ranking from multi-wise comparisons, in this paper, we do not require any parametric model or assumption and work on the fundamental setting where each comparison returns the correct result with probability $1$ or a certain probability larger than $\frac{1}{2}$. This paper helps understand whether and to what degree utilizing multi-wise comparisons can reduce the sample complexity for the ranking problems compared to ranking from pairwise comparisons. Specifically, under the winner feedback setting, one can reduce the sample complexity for top-$k$ selection up to an $m$ factor and that for full ranking up to a $\log{m}$ factor. Under the full-ranking feedback setting, one can reduce the sample complexity for top-$k$ selection up to an $m$ factor and that for full ranking up to an $m\log{m}$ factor. We also conduct numerical simulations to confirm our theoretical results.

#### Author Information

##### Jia Liu (The Ohio State University)

Jia (Kevin) Liu is an Assistant Professor in the Dept. of Electrical and Computer Engineering at The Ohio State University and an Amazon Visiting Academics (AVA). He received his Ph.D. degree from the Dept. of Electrical and Computer Engineering at Virginia Tech in 2010. From Aug. 2017 to Aug. 2020, he was an Assistant Professor in the Dept. of Computer Science at Iowa State University. His research areas include theoretical machine learning, stochastic network optimization and control, and performance analysis for data analytics infrastructure and cyber-physical systems. Dr. Liu is a senior member of IEEE and a member of ACM. He has received numerous awards at top venues, including IEEE INFOCOM'19 Best Paper Award, IEEE INFOCOM'16 Best Paper Award, IEEE INFOCOM'13 Best Paper Runner-up Award, IEEE INFOCOM'11 Best Paper Runner-up Award, IEEE ICC'08 Best Paper Award, and honors of long/spotlight presentations at ICML, NeurIPS, and ICLR. He is an NSF CAREER Award recipient in 2020 and a winner of the Google Faculty Research Award in 2020. He received the LAS Award for Early Achievement in Research at Iowa State University in 2020, and the Bell Labs President Gold Award. His research is supported by NSF, AFOSR, AFRL, and ONR.