# Scalable and Efficient Comparison-based Search without Features

## TL;DR

This paper introduces a scalable comparison-based search method that efficiently finds target objects using pairwise similarity queries, applicable in both known and hidden feature scenarios, with theoretical guarantees and real-world validation.

## Contribution

It presents a novel Bayesian search algorithm for noisy comparisons and a scalable embedding framework for blind settings, outperforming existing methods in query efficiency.

## Key findings

- The non-blind Bayesian search converges almost surely to the target.
- The combined framework achieves query complexity comparable to non-blind methods.
- Successful real-world user experiment with movie actor search.

## Abstract

We consider the problem of finding a target object $t$ using pairwise comparisons, by asking an oracle questions of the form \emph{"Which object from the pair $(i,j)$ is more similar to $t$?"}. Objects live in a space of latent features, from which the oracle generates noisy answers. First, we consider the {\em non-blind} setting where these features are accessible. We propose a new Bayesian comparison-based search algorithm with noisy answers; it has low computational complexity yet is efficient in the number of queries. We provide theoretical guarantees, deriving the form of the optimal query and proving almost sure convergence to the target $t$. Second, we consider the \emph{blind} setting, where the object features are hidden from the search algorithm. In this setting, we combine our search method and a new distributional triplet embedding algorithm into one scalable learning framework called \textsc{Learn2Search}. We show that the query complexity of our approach on two real-world datasets is on par with the non-blind setting, which is not achievable using any of the current state-of-the-art embedding methods. Finally, we demonstrate the efficacy of our framework by conducting an experiment with users searching for movie actors.