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Optimally Improving Cooperative Learning in a Social Setting

Shahrzad Haddadan, Cheng Xin, Jie Gao

TL;DR

This work studies cooperative learning in social networks where networked agents with individual classifiers can improve global accuracy by sharing predictions under linear social-influence dynamics. It formalizes two optimization goals: aggregate improvement and egalitarian improvement, and derives algorithms under varying information access to the joint prediction distribution $\pi$ and the influence matrix $\bar{W}$. The aggregate problem is solvable in polynomial time via selecting the top influencers based on $\mathrm{Inf}(j)=\sum_i \bar{W}_{ij}\mathsf{err}^{(0)}(v_i)$, while the egalitarian problem is NP-hard; the authors propose greedy approximation schemes EgalAlg and EgalAlg^(appx) with guarantees under independence or group-dependence assumptions. Extensive experiments on synthetic and real graphs show that altering a small subset of agents yields substantial network-wide gains, often achieving high accuracy with only $O(\log n)$ interventions. The results advance principled, scalable strategies for improving distributed learning in social networks without sharing models, with implications for cybersecurity, online information integrity, and privacy-preserving collaborative inference.

Abstract

We consider a cooperative learning scenario where a collection of networked agents with individually owned classifiers dynamically update their predictions, for the same classification task, through communication or observations of each other's predictions. Clearly if highly influential vertices use erroneous classifiers, there will be a negative effect on the accuracy of all the agents in the network. We ask the following question: how can we optimally fix the prediction of a few classifiers so as maximize the overall accuracy in the entire network. To this end we consider an aggregate and an egalitarian objective function. We show a polynomial time algorithm for optimizing the aggregate objective function, and show that optimizing the egalitarian objective function is NP-hard. Furthermore, we develop approximation algorithms for the egalitarian improvement. The performance of all of our algorithms are guaranteed by mathematical analysis and backed by experiments on synthetic and real data.

Optimally Improving Cooperative Learning in a Social Setting

TL;DR

This work studies cooperative learning in social networks where networked agents with individual classifiers can improve global accuracy by sharing predictions under linear social-influence dynamics. It formalizes two optimization goals: aggregate improvement and egalitarian improvement, and derives algorithms under varying information access to the joint prediction distribution and the influence matrix . The aggregate problem is solvable in polynomial time via selecting the top influencers based on , while the egalitarian problem is NP-hard; the authors propose greedy approximation schemes EgalAlg and EgalAlg^(appx) with guarantees under independence or group-dependence assumptions. Extensive experiments on synthetic and real graphs show that altering a small subset of agents yields substantial network-wide gains, often achieving high accuracy with only interventions. The results advance principled, scalable strategies for improving distributed learning in social networks without sharing models, with implications for cybersecurity, online information integrity, and privacy-preserving collaborative inference.

Abstract

We consider a cooperative learning scenario where a collection of networked agents with individually owned classifiers dynamically update their predictions, for the same classification task, through communication or observations of each other's predictions. Clearly if highly influential vertices use erroneous classifiers, there will be a negative effect on the accuracy of all the agents in the network. We ask the following question: how can we optimally fix the prediction of a few classifiers so as maximize the overall accuracy in the entire network. To this end we consider an aggregate and an egalitarian objective function. We show a polynomial time algorithm for optimizing the aggregate objective function, and show that optimizing the egalitarian objective function is NP-hard. Furthermore, we develop approximation algorithms for the egalitarian improvement. The performance of all of our algorithms are guaranteed by mathematical analysis and backed by experiments on synthetic and real data.
Paper Structure (54 sections, 31 theorems, 207 equations, 3 figures, 2 tables, 3 algorithms)

This paper contains 54 sections, 31 theorems, 207 equations, 3 figures, 2 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Decentralized learning
  4. Social learning
  5. Summary of Contributions
  6. Models and Problem Definition
  7. DeGroot Model DeGroot1974-ed
  8. Friedkin–Johnsen (FJ) Model Friedkin1990-wl
  9. Finite time Models
  10. Statement of Problems
  11. Improving quality of selected classifiers
  12. Summary of Results
  13. Optimizing the aggregate objective function
  14. Optimizing the egalitarian objective function
  15. Approximate solution with full access to $\mathbf \pi$.
  16. ...and 39 more sections

Key Result

Theorem 3.5

There is an algorithm with run-time complexity $\Theta\left(n^2\right)$ which given $\bar{W}$ and $\{\mathsf{err}(v_i)\}_{i=1}^n$ as input parameters outputs $S$ such that $\mathcal{G}^{({\rm agg})}(S)={\rm OPT^{({\rm agg})}}$.

Figures (3)

  • Figure 1: Comparison of # modified nodes for Accuracy $> 90\%$ on different dataset (lower is better).
  • Figure 2: Algorithms performance on ER (top) and WIKI (bottom).
  • Figure 3: More experimental results on different datasets.

Theorems & Definitions (63)

  • Theorem 3.5
  • Remark 3.6
  • Theorem 3.7
  • Theorem 3.8
  • Theorem 3.9
  • Theorem 3.10
  • Theorem 3.11
  • Remark 3.12
  • Lemma 4.1
  • Lemma 4.2
  • ...and 53 more