In stochastic game theory, Bayesian regret is the expected difference ("

regret Regret is the emotion of wishing one had made a different decision in the past, because the consequences of the decision were unfavorable. Regret is related to perceived opportunity. Its intensity varies over time after the decision, in regard ...

") between the

utility As a topic of economics, utility is used to model worth or value. Its usage has evolved significantly over time. The term was introduced initially as a measure of pleasure or happiness as part of the theory of utilitarianism by moral philosoph ...

of a Bayesian strategy and that of the optimal strategy (the one with the highest expected payoff). The term ''Bayesian'' refers to

Thomas Bayes Thomas Bayes ( ; 1701 7 April 1761) was an English statistician, philosopher and Presbyterian minister who is known for formulating a specific case of the theorem that bears his name: Bayes' theorem. Bayes never published what would become his ...

(1702–1761), who proved a special case of what is now called Bayes' theorem, who provided the first mathematical treatment of a non-trivial problem of statistical data analysis using what is now known as Bayesian inference.

Economics

This term has been used to compare a random buy-and-hold strategy to professional traders' records. This same concept has received numerous different names, as the New York Times notes: "In 1957, for example, a statistician named James Hanna called his theorem Bayesian Regret. He had been preceded by David Blackwell, also a statistician, who called his theorem Controlled Random Walks. Other, later papers had titles like 'On Pseudo Games', 'How to Play an Unknown Game', 'Universal Coding' and 'Universal Portfolios'".

Social Choice (voting methods)

"Bayesian Regret" has also been used as an alternate term for social utility efficiency, that is, a measure of the expected utility of different voting methods under a given probabilistic model of voter utilities and strategies. In this case, the relation to Bayes is unclear, as there is no conditioning or posterior distribution involved.

References

{{Reflist Game theory Bayesian estimation Economic theories Machine learning Bayesian statistics Social choice theory