Exact Passive-Aggressive Algorithms for Learning to Rank Using Interval Labels

TL;DR

This paper introduces exact passive-aggressive online algorithms for learning to rank with interval labels, providing efficient updates, maintaining threshold order, and demonstrating superior performance through theoretical bounds and experiments.

Contribution

It presents novel exact solutions for PA algorithms in ranking with interval labels, including support class algorithms and derived update rules.

Findings

Algorithms maintain threshold order after each update.

Proven mistake bounds in ideal and general settings.

Experimental results show high accuracy with interval labels.

Abstract

In this paper, we propose exact passive-aggressive (PA) online algorithms for learning to rank. The proposed algorithms can be used even when we have interval labels instead of actual labels for examples. The proposed algorithms solve a convex optimization problem at every trial. We find exact solution to those optimization problems to determine the updated parameters. We propose support class algorithm (SCA) which finds the active constraints using the KKT conditions of the optimization problems. These active constrains form support set which determines the set of thresholds that need to be updated. We derive update rules for PA, PA-I and PA-II. We show that the proposed algorithms maintain the ordering of the thresholds after every trial. We provide the mistake bounds of the proposed algorithms in both ideal and general settings. We also show experimentally that the proposed algorithms successfully learn accurate classifiers using interval labels as well as exact labels. Proposed algorithms also do well compared to other approaches.