Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

The Sign Estimator: LLM Alignment in the Face of Choice Heterogeneity

Ali Aouad, Aymane El Gadarri, Vivek F. Farias

TL;DR

The paper tackles learning population-average utilities under user heterogeneity for LLM alignment, highlighting that standard RLHF cross-entropy estimation misweights individuals and distorts social welfare. It introduces the Sign estimator, which achieves ordinal consistency under symmetry and, for linear utility models, recovers the population direction $ar{eta}/ Vertar{eta} Vert$ with a cube-root finite-sample rate $ ilde{O}(n^{-1/3})$. The method avoids full mixture estimation and maintains compatibility with existing RLHF pipelines by replacing cross-entropy with a 0-1 loss proxy, enabling provable consistency and practical gains. Empirical results on digital-twin–driven preference data show substantial reductions in angular error (about $35 ext{%}$) and disagreement (about $40 ext{%}$) compared to RLHF, while outperforming EM-based panel methods in both accuracy and simplicity. The work provides a practical, theoretically justified alternative for robust aggregation of heterogeneous preferences in reward learning for language models.

Abstract

Traditional LLM alignment methods are vulnerable to heterogeneity in human preferences. Fitting a naïve probabilistic model to pairwise comparison data (say over prompt-completion pairs) yields an inconsistent estimate of the population-average utility -a canonical measure of social welfare. We propose a new method, dubbed the sign estimator, that provides a simple, provably consistent, and efficient estimator by replacing cross-entropy with binary classification loss in the aggregation step. This simple modification recovers consistent ordinal alignment under mild assumptions and achieves the first polynomial finite-sample error bounds in this setting. In realistic simulations of LLM alignment using digital twins, the sign estimator substantially reduces preference distortion over a panel of simulated personas, cutting (angular) estimation error by nearly 35% and decreasing disagreement with true population preferences from 12% to 8% compared to standard RLHF. Our method also compares favorably to panel data heuristics that explicitly model user heterogeneity and require tracking individual-level preference data-all while maintaining the implementation simplicity of existing LLM alignment pipelines.

The Sign Estimator: LLM Alignment in the Face of Choice Heterogeneity

TL;DR

The paper tackles learning population-average utilities under user heterogeneity for LLM alignment, highlighting that standard RLHF cross-entropy estimation misweights individuals and distorts social welfare. It introduces the Sign estimator, which achieves ordinal consistency under symmetry and, for linear utility models, recovers the population direction with a cube-root finite-sample rate . The method avoids full mixture estimation and maintains compatibility with existing RLHF pipelines by replacing cross-entropy with a 0-1 loss proxy, enabling provable consistency and practical gains. Empirical results on digital-twin–driven preference data show substantial reductions in angular error (about ) and disagreement (about ) compared to RLHF, while outperforming EM-based panel methods in both accuracy and simplicity. The work provides a practical, theoretically justified alternative for robust aggregation of heterogeneous preferences in reward learning for language models.

Abstract

Traditional LLM alignment methods are vulnerable to heterogeneity in human preferences. Fitting a naïve probabilistic model to pairwise comparison data (say over prompt-completion pairs) yields an inconsistent estimate of the population-average utility -a canonical measure of social welfare. We propose a new method, dubbed the sign estimator, that provides a simple, provably consistent, and efficient estimator by replacing cross-entropy with binary classification loss in the aggregation step. This simple modification recovers consistent ordinal alignment under mild assumptions and achieves the first polynomial finite-sample error bounds in this setting. In realistic simulations of LLM alignment using digital twins, the sign estimator substantially reduces preference distortion over a panel of simulated personas, cutting (angular) estimation error by nearly 35% and decreasing disagreement with true population preferences from 12% to 8% compared to standard RLHF. Our method also compares favorably to panel data heuristics that explicitly model user heterogeneity and require tracking individual-level preference data-all while maintaining the implementation simplicity of existing LLM alignment pipelines.

Paper Structure

This paper contains 31 sections, 15 theorems, 60 equations, 5 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. This paper
  3. Related literature
  4. Problem set-up
  5. Status Quo RLHF Estimator
  6. Utility Aggregation for Gaussian Data via the RLHF Estimator
  7. The Sign Estimator
  8. Ordinal Consistency for General Utilities
  9. Consistency for Linear Utilities up to Positive Scaling
  10. Finite-Sample Convergence
  11. Computational implementation.
  12. Experiments
  13. Results
  14. Comparison with EM:
  15. Additional Experiments
  16. ...and 16 more sections

Key Result

Proposition 1

Suppose that $(X_1,X_2)$ is distributed so that $\phi(X_1) - \phi(X_2) \triangleq X \sim {\cal N}(0,\Sigma)$. Then the RLHF estimator recovers $\hat{\beta}^{\rm RLHF}$ satisfying:

Figures (5)

  • Figure 1: Sign Estimator reduces angular estimaton error and disagreement rates by $\sim 40\%$. Left: Angle error with true mean. Right: Disagreement rate with true mean utility.
  • Figure 2: RLHF, EM vs Sign. Angular Estimation error (left) and disagreement rate (right)
  • Figure 3: (left) Heterogeneity histogram and (right) Persona Demographics .
  • Figure 4: Comparison of 4 levels of scale (1,4,8,12) and the effect of introducing more heterogeneity in estimating the direction of the mean. Predictably, a higher variance amplifies the estimation error of both estimators, while the Sign estimator seems to handle it more gracefully.
  • Figure 5: Representative persona contrasts and RLHF labelling simulation. Top: concise survey summaries. Center: Example of two RLHF alternatives considered. Bottom: raw logits and renormalized choice probabilities.

Theorems & Definitions (24)

  • Proposition 1
  • Proposition 2
  • proof
  • Theorem 1
  • proof
  • Corollary 1
  • Theorem : Informal
  • Proposition 3
  • Theorem 2
  • Proposition 4
  • ...and 14 more