DFORD: Directional Feedback based Online Ordinal Regression Learning

TL;DR

This paper presents an online ordinal regression algorithm that learns from directional feedback, using exploration-exploitation and kernel methods, achieving logarithmic regret and competitive performance with full supervision.

Contribution

It introduces a novel online ordinal regression algorithm utilizing directional feedback and kernel methods, with memory-efficient implementation and theoretical regret guarantees.

Findings

Achieves expected regret of O(log T)

Performs comparably or better than full supervision methods

Effective in synthetic and real-world datasets

Abstract

In this paper, we introduce directional feedback in the ordinal regression setting, in which the learner receives feedback on whether the predicted label is on the left or the right side of the actual label. This is a weak supervision setting for ordinal regression compared to the full information setting, where the learner can access the labels. We propose an online algorithm for ordinal regression using directional feedback. The proposed algorithm uses an exploration-exploitation scheme to learn from directional feedback efficiently. Furthermore, we introduce its kernel-based variant to learn non-linear ordinal regression models in an online setting. We use a truncation trick to make the kernel implementation more memory efficient. The proposed algorithm maintains the ordering of the thresholds in the expected sense. Moreover, it achieves the expected regret of $\mathcal{O}(\log T)$. We compare our approach with a full information and a weakly supervised algorithm for ordinal regression on synthetic and real-world datasets. The proposed approach, which learns using directional feedback, performs comparably (sometimes better) to its full information counterpart.