SOS for Bounded Rationality

Alessio Benavoli, Alessandro Facchini, Dario Piga, Marco Zaffalon
Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications, PMLR 62:25-36, 2017.

Abstract

In the gambling foundation of probability theory, rationality requires that a subject should always (never) find desirable all nonnegative (negative) gambles, because no matter the result of the experiment the subject never (always) decreases her money. Evaluating the nonnegativity of a gamble in infinite spaces is a difficult task. In fact, even if we restrict the gambles to be polynomials in $R^n$, the problem of determining nonnegativity is NP-hard. The aim of this paper is to develop a computable theory of desirable gambles. Instead of requiring the subject to accept all nonnegative gambles, we only require her to accept gambles for which she can efficiently determine the nonnegativity (in particular SOS polynomials). We call this new criterion bounded rationality.

Cite this Paper

BibTeX
@InProceedings{pmlr-v62-benavoli17a, title = {{SOS} for Bounded Rationality}, author = {Benavoli, Alessio and Facchini, Alessandro and Piga, Dario and Zaffalon, Marco}, booktitle = {Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications}, pages = {25--36}, year = {2017}, editor = {Antonucci, Alessandro and Corani, Giorgio and Couso, Inés and Destercke, Sébastien}, volume = {62}, series = {Proceedings of Machine Learning Research}, month = {10--14 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v62/benavoli17a/benavoli17a.pdf}, url = {https://proceedings.mlr.press/v62/benavoli17a.html}, abstract = {In the gambling foundation of probability theory, rationality requires that a subject should always (never) find desirable all nonnegative (negative) gambles, because no matter the result of the experiment the subject never (always) decreases her money. Evaluating the nonnegativity of a gamble in infinite spaces is a difficult task. In fact, even if we restrict the gambles to be polynomials in $R^n$, the problem of determining nonnegativity is NP-hard. The aim of this paper is to develop a computable theory of desirable gambles. Instead of requiring the subject to accept all nonnegative gambles, we only require her to accept gambles for which she can efficiently determine the nonnegativity (in particular SOS polynomials). We call this new criterion bounded rationality.} }
Endnote
%0 Conference Paper %T SOS for Bounded Rationality %A Alessio Benavoli %A Alessandro Facchini %A Dario Piga %A Marco Zaffalon %B Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications %C Proceedings of Machine Learning Research %D 2017 %E Alessandro Antonucci %E Giorgio Corani %E Inés Couso %E Sébastien Destercke %F pmlr-v62-benavoli17a %I PMLR %P 25--36 %U https://proceedings.mlr.press/v62/benavoli17a.html %V 62 %X In the gambling foundation of probability theory, rationality requires that a subject should always (never) find desirable all nonnegative (negative) gambles, because no matter the result of the experiment the subject never (always) decreases her money. Evaluating the nonnegativity of a gamble in infinite spaces is a difficult task. In fact, even if we restrict the gambles to be polynomials in $R^n$, the problem of determining nonnegativity is NP-hard. The aim of this paper is to develop a computable theory of desirable gambles. Instead of requiring the subject to accept all nonnegative gambles, we only require her to accept gambles for which she can efficiently determine the nonnegativity (in particular SOS polynomials). We call this new criterion bounded rationality.
APA
Benavoli, A., Facchini, A., Piga, D. & Zaffalon, M.. (2017). SOS for Bounded Rationality. Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 62:25-36 Available from https://proceedings.mlr.press/v62/benavoli17a.html.

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