Bootstrapping Fisher Market Equilibrium and First-Price Pacing Equilibrium

Luofeng Liao, Christian Kroer
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:29748-29781, 2024.

Abstract

Linear Fisher market (LFM) is an equilibrium model for fair and efficient resource allocation, and first-price pacing equilibrium (FPPE) is a model for budget-management in first-price auctions. One thing they have in common is that both have a corresponding Eisenberg-Gale convex program characterization. In this paper, we introduce and devise several statistically valid bootstrap inference procedures for LFM and FPPE. The most challenging part is to bootstrap general FPPE, which reduces to bootstrapping constrained M-estimators, a largely unexplored problem. We are able to devise a bootstrap procedure for FPPE with structures by using the powerful tool of epi-convergence theory. Experiments with synthetic and semi-real data verify our theory.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-liao24b, title = {Bootstrapping {F}isher Market Equilibrium and First-Price Pacing Equilibrium}, author = {Liao, Luofeng and Kroer, Christian}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {29748--29781}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/liao24b/liao24b.pdf}, url = {https://proceedings.mlr.press/v235/liao24b.html}, abstract = {Linear Fisher market (LFM) is an equilibrium model for fair and efficient resource allocation, and first-price pacing equilibrium (FPPE) is a model for budget-management in first-price auctions. One thing they have in common is that both have a corresponding Eisenberg-Gale convex program characterization. In this paper, we introduce and devise several statistically valid bootstrap inference procedures for LFM and FPPE. The most challenging part is to bootstrap general FPPE, which reduces to bootstrapping constrained M-estimators, a largely unexplored problem. We are able to devise a bootstrap procedure for FPPE with structures by using the powerful tool of epi-convergence theory. Experiments with synthetic and semi-real data verify our theory.} }
Endnote
%0 Conference Paper %T Bootstrapping Fisher Market Equilibrium and First-Price Pacing Equilibrium %A Luofeng Liao %A Christian Kroer %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-liao24b %I PMLR %P 29748--29781 %U https://proceedings.mlr.press/v235/liao24b.html %V 235 %X Linear Fisher market (LFM) is an equilibrium model for fair and efficient resource allocation, and first-price pacing equilibrium (FPPE) is a model for budget-management in first-price auctions. One thing they have in common is that both have a corresponding Eisenberg-Gale convex program characterization. In this paper, we introduce and devise several statistically valid bootstrap inference procedures for LFM and FPPE. The most challenging part is to bootstrap general FPPE, which reduces to bootstrapping constrained M-estimators, a largely unexplored problem. We are able to devise a bootstrap procedure for FPPE with structures by using the powerful tool of epi-convergence theory. Experiments with synthetic and semi-real data verify our theory.
APA
Liao, L. & Kroer, C.. (2024). Bootstrapping Fisher Market Equilibrium and First-Price Pacing Equilibrium. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:29748-29781 Available from https://proceedings.mlr.press/v235/liao24b.html.

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