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 one did make were unfavorable. Regret is related to perceived opportunity. Its intensity varies over time after the decisi ...

") between the

utility In economics, utility is a measure of a certain person's satisfaction from a certain state of the world. Over time, the term has been used with at least two meanings. * In a normative context, utility refers to a goal or objective that we wish ...

of a given strategy and the utility of the best possible strategy in hindsight—i.e., the strategy that would have maximized expected payoff if the true underlying model or distribution were known. This notion of regret measures how much is lost, on average, due to uncertainty or imperfect information.

Etymology

The term ''Bayesian'' refers to

Thomas Bayes Thomas Bayes ( , ; 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 m ...

(1702–1761), who proved a special case of what is now called

Bayes' theorem Bayes' theorem (alternatively Bayes' law or Bayes' rule, after Thomas Bayes) gives a mathematical rule for inverting Conditional probability, conditional probabilities, allowing one to find the probability of a cause given its effect. For exampl ...

, who provided the first mathematical treatment of a non-trivial problem of statistical data analysis using what is now known as

Bayesian inference Bayesian inference ( or ) is a method of statistical inference in which Bayes' theorem is used to calculate a probability of a hypothesis, given prior evidence, and update it as more information becomes available. Fundamentally, Bayesian infer ...

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 A statistician is a person who works with Theory, theoretical or applied statistics. The profession exists in both the private sector, private and public sectors. It is common to combine statistical knowledge with expertise in other subjects, a ...

, 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'".

References

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