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Simple and near-optimal algorithms for hidden stratification and multi-group learning

Christopher Tosh, Daniel Hsu

TL;DR

The structure of solutions to the multi-group learning problem is studied, and simple and near-optimal algorithms for the learning problem are provided.

Abstract

Multi-group agnostic learning is a formal learning criterion that is concerned with the conditional risks of predictors within subgroups of a population. The criterion addresses recent practical concerns such as subgroup fairness and hidden stratification. This paper studies the structure of solutions to the multi-group learning problem, and provides simple and near-optimal algorithms for the learning problem.

Simple and near-optimal algorithms for hidden stratification and multi-group learning

TL;DR

The structure of solutions to the multi-group learning problem is studied, and simple and near-optimal algorithms for the learning problem are provided.

Abstract

Multi-group agnostic learning is a formal learning criterion that is concerned with the conditional risks of predictors within subgroups of a population. The criterion addresses recent practical concerns such as subgroup fairness and hidden stratification. This paper studies the structure of solutions to the multi-group learning problem, and provides simple and near-optimal algorithms for the learning problem.
Paper Structure (34 sections, 18 theorems, 101 equations, 3 algorithms)

This paper contains 34 sections, 18 theorems, 101 equations, 3 algorithms.

Table of Contents

  1. Introduction
  2. Summary of results
  3. Related work
  4. Distributionally robust optimization.
  5. Group and individual fairness.
  6. Online fairness.
  7. Multicalibration, multiaccuracy, and outcome distinguishability.
  8. Hidden stratification.
  9. Transfer learning and covariate shift.
  10. Boosting.
  11. Paper outline
  12. Setting and notation
  13. Multi-group agnostic learning
  14. Convergence of conditional risks
  15. A simple multi-group learning algorithm
  16. ...and 19 more sections

Key Result

Theorem 1

Let $\mathcal{H}$ be a hypothesis class, let $\mathcal{G}$ be a set of groups, and let $\ell \colon \mathcal{Z} \times \mathcal{Y} \to [0,1]$ be a loss function. With probability at least $1-\delta$, where $D = 2\log \left(\Pi_{2n}((\ell \circ \mathcal{H})_{\textnormal{thresh}}) \Pi_{2n}(\mathcal{G}) \right) + \log(8/\delta)$.

Theorems & Definitions (18)

  • Theorem 1
  • Lemma 2
  • Proposition 3
  • Theorem 4
  • Corollary 5
  • Theorem 6
  • Proposition 7
  • Theorem 8
  • Corollary 9
  • Theorem 10
  • ...and 8 more