In stochastic game theory, Bayesian regret is the expected difference ("regret") between the utility of a Bayesian strategy and that of the optimal strategy (the one with the highest expected payoff).
The term Bayesian refers to Thomas Bayes (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.
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.