### Web: http://arxiv.org/abs/2206.11546

June 24, 2022, 1:11 a.m. | Kazuto Fukuchi, Jun Sakuma

We investigate the minimax optimal error of a fair regression problem under a
linear model employing the demographic parity as a fairness constraint. As a
tractable demographic parity constraint, we introduce
$(\alpha,\delta)$-fairness consistency, meaning that the quantified unfairness
is decreased at most $n^{-\alpha}$ rate with at least probability $1-\delta$,
where $n$ is the sample size. In other words, the consistently fair algorithm
eventually outputs a regressor satisfying the demographic parity constraint
with high probability as $n$ tends to infinity. As …

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