Inverse Optimization with Prediction Market: A Characterization of Scoring Rules for Elciting System States

Han Bao, Shinsaku Sakaue
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:451-459, 2025.

Abstract

Inverse optimization aims to recover the unknown state in forward optimization after observing a state-outcome pair. This is relevant when we want to identify the underlying state of a system or to design a system with desirable outcomes. Whereas inverse optimization has been investigated in the algorithmic perspective during past two decades, its formulation intimately tied with the principal’s subjective choice of a desirable state—indeed, this is crucial to make the inverse problem well-posed. We go beyond the conventional inverse optimization by building upon prediction market, where multiple agents submit their beliefs until converging to market equilibria. The market equilibria express the crowd consensus on a desirable state, effectively eschewing the subjective design. To this end, we derive a proper scoring rule for prediction market design in the context of inverse optimization.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-bao25a, title = {Inverse Optimization with Prediction Market: A Characterization of Scoring Rules for Elciting System States}, author = {Bao, Han and Sakaue, Shinsaku}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {451--459}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/bao25a/bao25a.pdf}, url = {https://proceedings.mlr.press/v258/bao25a.html}, abstract = {Inverse optimization aims to recover the unknown state in forward optimization after observing a state-outcome pair. This is relevant when we want to identify the underlying state of a system or to design a system with desirable outcomes. Whereas inverse optimization has been investigated in the algorithmic perspective during past two decades, its formulation intimately tied with the principal’s subjective choice of a desirable state—indeed, this is crucial to make the inverse problem well-posed. We go beyond the conventional inverse optimization by building upon prediction market, where multiple agents submit their beliefs until converging to market equilibria. The market equilibria express the crowd consensus on a desirable state, effectively eschewing the subjective design. To this end, we derive a proper scoring rule for prediction market design in the context of inverse optimization.} }
Endnote
%0 Conference Paper %T Inverse Optimization with Prediction Market: A Characterization of Scoring Rules for Elciting System States %A Han Bao %A Shinsaku Sakaue %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-bao25a %I PMLR %P 451--459 %U https://proceedings.mlr.press/v258/bao25a.html %V 258 %X Inverse optimization aims to recover the unknown state in forward optimization after observing a state-outcome pair. This is relevant when we want to identify the underlying state of a system or to design a system with desirable outcomes. Whereas inverse optimization has been investigated in the algorithmic perspective during past two decades, its formulation intimately tied with the principal’s subjective choice of a desirable state—indeed, this is crucial to make the inverse problem well-posed. We go beyond the conventional inverse optimization by building upon prediction market, where multiple agents submit their beliefs until converging to market equilibria. The market equilibria express the crowd consensus on a desirable state, effectively eschewing the subjective design. To this end, we derive a proper scoring rule for prediction market design in the context of inverse optimization.
APA
Bao, H. & Sakaue, S.. (2025). Inverse Optimization with Prediction Market: A Characterization of Scoring Rules for Elciting System States. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:451-459 Available from https://proceedings.mlr.press/v258/bao25a.html.

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