2023-04-11-cousins23a.md

title	software	abstract	section	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	container-title	volume	genre	issued	pdf	extras
Revisiting Fair-PAC Learning and the Axioms of Cardinal Welfare	https://github.com/aistats2023/1095	Cardinal objectives serve as intuitive targets in fair machine learning by summarizing utility (welfare) or disutility (malfare) $u$ over $g$ groups. Under standard axioms, all welfare and malfare functions are $w$-weighted $p$-power-means, i.e. $M_p(u;w) = \sqrt[p]{\sum_{i=1}^g w_i u_i^p}$, with $p \leq 1$ for welfare, or $p \geq 1$ for malfare. We show the same under weaker axioms, and also identify stronger axioms that naturally restrict $p$. It is known that power-mean malfare functions are Lipschitz continuous, and thus statistically easy to estimate or learn. We show that all power means are locally Holder continuous, i.e., $|M(u; w)-M(u’ ; w)| \leq \lambda \parallel u - u’\parallel^\alpha$ for some $\lambda$, $\alpha$,$\parallel \cdot \parallel$. In particular, $\lambda$ and $1/\alpha$ are bounded except as $p \rightarrow 0$ or $\min_i w_i \rightarrow 0$, and via this analysis we bound the sample complexity of optimizing welfare. This yields a novel concept of fair-PAC learning, wherein welfare functions are only polynomially harder to optimize than malfare functions, except when $p \approx 0$ or $\min_i w_i$ $\approx$ 0, which is exponentially harder.	Regular Papers	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	cousins23a	0	Revisiting Fair-PAC Learning and the Axioms of Cardinal Welfare	6422	6442	6422-6442	6422	false	Cousins, Cyrus	given family Cyrus Cousins	2023-04-11		Proceedings of The 26th International Conference on Artificial Intelligence and Statistics	206	inproceedings	date-parts 2023 4 11	https://proceedings.mlr.press/v206/cousins23a/cousins23a.pdf