Residual-as-Teacher: Mitigating Bias Propagation in Student--Teacher Estimation

TL;DR

This paper introduces Residual-as-Teacher (RaT), a novel method that reduces bias propagation in student--teacher models by estimating residuals, with theoretical guarantees and superior performance over traditional soft matching.

Contribution

The paper proposes and analyzes RaT, a new residual-based approach that mitigates teacher bias in student--teacher estimation, supported by theoretical analysis and empirical validation.

Findings

RaT reduces teacher bias effects in student predictions.

RaT achieves minimax-optimal rates in kernel settings.

Experimental results confirm theoretical advantages on synthetic and real data.

Abstract

We study statistical estimation in a student--teacher setting, where predictions from a pre-trained teacher are used to guide a student model. A standard approach is to train the student to directly match the teacher's outputs, which we refer to as student soft matching (SM). This approach directly propagates any systematic bias or mis-specification present in the teacher, thereby degrading the student's predictions. We propose and analyze an alternative scheme, known as residual-as-teacher (RaT), in which the teacher is used to estimate residuals in the student's predictions. Our analysis shows how the student can thereby emulate a proximal gradient scheme for solving an oracle optimization problem, and this provably reduces the effect of teacher bias. For general student--teacher pairs, we establish non-asymptotic excess risk bounds for any RaT fixed point, along with convergence guarantees for the student-teacher iterative scheme. For kernel-based student--teacher pairs, we prove a sharp separation: the RaT method achieves the minimax-optimal rate, while the SM method incurs constant prediction error for any sample size. Experiments on both synthetic data and ImageNette classification under covariate shift corroborate our theoretical findings.