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Statistical Collusion by Collectives on Learning Platforms

Etienne Gauthier, Francis Bach, Michael I. Jordan

TL;DR

This paper studies how collectives can statistically influence learning platforms by coordinated data modifications, formalizing a model with collective size $\alpha = n/N$ and a data-transforming strategy $h$. It introduces a statistical-inference framework that enables finite-sample computation of strategy-optimization bounds for three goals: signal planting, signal unplanting, and signal erasing, with two planting variants and adaptive-unplanting approaches. The authors derive computable, finite-sample lower bounds that reveal staircase-like behavior across a finite signal set and show that absolute collective size matters alongside relative size; they validate the theory on a synthetic product-evaluation domain and compare with prior infinite-data bounds, finding tighter guarantees. The work contributes practical tools to anticipate a collective's impact on platform behavior, guiding design of more robust and transparent learning systems in the presence of strategic data-injection, and points to future directions in concentration inequalities, regression settings, and population heterogeneity.

Abstract

As platforms increasingly rely on learning algorithms, collectives may form and seek ways to influence these platforms to align with their own interests. This can be achieved by coordinated submission of altered data. To evaluate the potential impact of such behavior, it is essential to understand the computations that collectives must perform to impact platforms in this way. In particular, collectives need to make a priori assessments of the effect of the collective before taking action, as they may face potential risks when modifying their data. Moreover they need to develop implementable coordination algorithms based on quantities that can be inferred from observed data. We develop a framework that provides a theoretical and algorithmic treatment of these issues and present experimental results in a product evaluation domain.

Statistical Collusion by Collectives on Learning Platforms

TL;DR

This paper studies how collectives can statistically influence learning platforms by coordinated data modifications, formalizing a model with collective size and a data-transforming strategy . It introduces a statistical-inference framework that enables finite-sample computation of strategy-optimization bounds for three goals: signal planting, signal unplanting, and signal erasing, with two planting variants and adaptive-unplanting approaches. The authors derive computable, finite-sample lower bounds that reveal staircase-like behavior across a finite signal set and show that absolute collective size matters alongside relative size; they validate the theory on a synthetic product-evaluation domain and compare with prior infinite-data bounds, finding tighter guarantees. The work contributes practical tools to anticipate a collective's impact on platform behavior, guiding design of more robust and transparent learning systems in the presence of strategic data-injection, and points to future directions in concentration inequalities, regression settings, and population heterogeneity.

Abstract

As platforms increasingly rely on learning algorithms, collectives may form and seek ways to influence these platforms to align with their own interests. This can be achieved by coordinated submission of altered data. To evaluate the potential impact of such behavior, it is essential to understand the computations that collectives must perform to impact platforms in this way. In particular, collectives need to make a priori assessments of the effect of the collective before taking action, as they may face potential risks when modifying their data. Moreover they need to develop implementable coordination algorithms based on quantities that can be inferred from observed data. We develop a framework that provides a theoretical and algorithmic treatment of these issues and present experimental results in a product evaluation domain.

Paper Structure

This paper contains 33 sections, 7 theorems, 71 equations, 7 figures, 1 table, 4 algorithms.

Table of Contents

  1. Introduction
  2. Collective Action in Machine Learning.
  3. Contributions.
  4. Related Work
  5. Statistical Algorithmic Collective Action in Classification
  6. Setting
  7. Signal planting
  8. Feature-label signal planting
  9. Feature-only signal planting
  10. Signal unplanting
  11. Naive strategy
  12. Adaptive strategy
  13. Signal erasing
  14. Experimental Evaluation
  15. Signal planting
  16. ...and 18 more sections

Key Result

Theorem 3.3

Let $\delta > 0$, and write $\tilde{\delta} := \delta /(2 + 2\# \tilde{\mathcal{X}} + 2\# \tilde{\mathcal{X}}\# \mathcal{Y})$. Then, by playing the feature-label signal planting strategy against a classifier that is $\varepsilon$-suboptimal on $\tilde{\mathcal{X}}$, the collective achieves with prob where $\Delta_{\tilde{x}}^{(n)} := \underset{y' \in \mathcal{Y}\backslash \{y^* \}}{\max } \underse

Figures (7)

  • Figure 1: Signal planting with feature-label strategy. Comparison of the theoretical lower bound from Theorem \ref{['thm:sp']} and the true success $\hat{S}(n)$ observed at test time for different values of $n$ and a fixed value of $N = 1,000,000$. For all target labels, the lower bound indicates that approximately 10$\%$ of the total number of agents interacting with the platform is necessary to significantly influence it. In reality, the success observed at test time shows that just under 5$\%$ of members is sufficient, except for the target label $y^*$= Excellent, which is already consistently the most frequent and does not require any planting.
  • Figure 2: Signal planting with feature-label strategy. Lower bound from Theorem \ref{['thm:sp']} with $y^*$ = Poor for different values of $n$ with $N=500,000$, $N=1,000,000$, and $N=2,000,000$.
  • Figure 3: Signal unplanting. (a) Comparison of lower bounds from Theorem \ref{['thm:su']} for different values of $n_{\rm e}$. (b) Comparison between the adaptive strategy with $n_{\rm e}= 2,000$ and naive planting strategies targeting labels $y^* \in \{ \text{Good (G), Average (A), Poor (P)}\}$. (c) Comparison of the lower bound achieved by the adaptive strategy with $n_{\rm e}= 2,000$ and the actual success $\hat{S}(n)$ observed at test time.
  • Figure 4: Signal planting. Comparison of signal planting lower bounds with target $y^* =$ Poor using feature-label (F-L) and feature-only (F-O) strategies. Our bounds in the infinite data regime are compared to bounds from hardt2023collectiveaction, when $\varepsilon=0$.
  • Figure 5: Signal planting with feature-only strategy. Comparison of the theoretical lower bound from Theorem \ref{['thm:sp_fo']} and the true success $\hat{S}(n)$ observed at test time for different values of $n$ and a fixed value of $N = 1,000,000$.
  • ...and 2 more figures

Theorems & Definitions (18)

  • Definition 3.1
  • Definition 3.2: Feature-label signal planting strategy
  • Theorem 3.3: Signal planting lower bound, feature-label signal planting strategy
  • Definition 3.4: Feature-only signal planting strategy
  • Theorem 3.5: Signal planting lower bound, feature-only signal planting strategy
  • Definition 3.6: Signal unplanting strategy
  • Theorem 3.7: Signal unplanting lower bound
  • Definition 3.8: Erasure strategy
  • Theorem 3.9: Signal erasing lower bound
  • Lemma 4.1: Hoeffding's Inequality
  • ...and 8 more