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A Probabilistic Approach for Model Alignment with Human Comparisons

Junyu Cao, Mohsen Bayati

TL;DR

A two-stage"Supervised Learning+Learning from Human Feedback"(SL+LHF) framework that connects machine learning with human feedback through a probabilistic bisection approach is proposed and the conditions under which the"SL+LHF"framework outperforms the pure SL approach are identified.

Abstract

A growing trend involves integrating human knowledge into learning frameworks, leveraging subtle human feedback to refine AI models. While these approaches have shown promising results in practice, the theoretical understanding of when and why such approaches are effective remains limited. This work takes steps toward developing a theoretical framework for analyzing the conditions under which human comparisons can enhance the traditional supervised learning process. Specifically, this paper studies the effective use of noisy-labeled data and human comparison data to address challenges arising from noisy environment and high-dimensional models. We propose a two-stage "Supervised Learning+Learning from Human Feedback" (SL+LHF) framework that connects machine learning with human feedback through a probabilistic bisection approach. The two-stage framework first learns low-dimensional representations from noisy-labeled data via an SL procedure and then uses human comparisons to improve the model alignment. To examine the efficacy of the alignment phase, we introduce a concept, termed the "label-noise-to-comparison-accuracy" (LNCA) ratio. This paper identifies from a theoretical perspective the conditions under which the "SL+LHF" framework outperforms the pure SL approach; we then leverage this LNCA ratio to highlight the advantage of incorporating human evaluators in reducing sample complexity. We validate that the LNCA ratio meets the proposed conditions for its use through a case study conducted via Amazon Mechanical Turk (MTurk).

A Probabilistic Approach for Model Alignment with Human Comparisons

TL;DR

A two-stage"Supervised Learning+Learning from Human Feedback"(SL+LHF) framework that connects machine learning with human feedback through a probabilistic bisection approach is proposed and the conditions under which the"SL+LHF"framework outperforms the pure SL approach are identified.

Abstract

A growing trend involves integrating human knowledge into learning frameworks, leveraging subtle human feedback to refine AI models. While these approaches have shown promising results in practice, the theoretical understanding of when and why such approaches are effective remains limited. This work takes steps toward developing a theoretical framework for analyzing the conditions under which human comparisons can enhance the traditional supervised learning process. Specifically, this paper studies the effective use of noisy-labeled data and human comparison data to address challenges arising from noisy environment and high-dimensional models. We propose a two-stage "Supervised Learning+Learning from Human Feedback" (SL+LHF) framework that connects machine learning with human feedback through a probabilistic bisection approach. The two-stage framework first learns low-dimensional representations from noisy-labeled data via an SL procedure and then uses human comparisons to improve the model alignment. To examine the efficacy of the alignment phase, we introduce a concept, termed the "label-noise-to-comparison-accuracy" (LNCA) ratio. This paper identifies from a theoretical perspective the conditions under which the "SL+LHF" framework outperforms the pure SL approach; we then leverage this LNCA ratio to highlight the advantage of incorporating human evaluators in reducing sample complexity. We validate that the LNCA ratio meets the proposed conditions for its use through a case study conducted via Amazon Mechanical Turk (MTurk).
Paper Structure (39 sections, 18 theorems, 122 equations, 9 figures, 4 algorithms)

This paper contains 39 sections, 18 theorems, 122 equations, 9 figures, 4 algorithms.

Table of Contents

  1. Introduction
  2. Our Contributions
  3. Modeling.
  4. Theoretical contributions.
  5. Towards practical implementations.
  6. Empirical analysis.
  7. Literature Review
  8. Model
  9. Supervised Learning and Underspecifications
  10. Utility Model of Human Comparisons
  11. One-dimensional Human Comparison
  12. Deterministic Bisection
  13. Probabilistic Bisection
  14. Vertical moves
  15. Horizontal moves
  16. ...and 24 more sections

Key Result

Lemma 1

For any two models $f_{\boldsymbol{\theta}_1}$ and $f_{\boldsymbol{\theta}_2}$, the probability that a human will make the right selection is which is strictly greater than 1/2.

Figures (9)

  • Figure 1: An illustrative example. Among two choices $c_{\Delta}^-(\theta_k)$ and $c_{\Delta}^+(\theta_k)$, $c_{\Delta}^-(\theta_k)$ would be selected because it is closer to the true parameter. In this case, the interval $(\theta_k, \theta^+]$ is eliminated.
  • Figure 2: Roadmap for introducing Algorithm \ref{['Alg: RTB']}.
  • Figure 3: Error ratio of the two-stage framework to the pure SL with different values of $\sigma$.
  • Figure 4: Error ratio of the two-stage framework to the pure SL with different values of $\gamma$.
  • Figure 5: Error ratio of the two-stage framework to the pure SL with different values of $s$.
  • ...and 4 more figures

Theorems & Definitions (45)

  • Example 1: Sparse Linear Models
  • Example 2: Generalized Low-rank Models
  • Example 3
  • Remark 1: Model-level Comparison and Sample-level Comparison
  • Example 4
  • Remark 2
  • Lemma 1: Precision
  • Proposition 1
  • Example 5
  • Definition 1: $(\varepsilon,\delta)$-alignment problem
  • ...and 35 more