Loss function
In mathematical optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables onto a
Expenditure minimization problem
In microeconomics, the expenditure minimization problem is the dual of the utility maximization problem: "how much money do I need to reach a certain level of happiness?". This question comes in two p
Markov decision process
In mathematics, a Markov decision process (MDP) is a discrete-time stochastic control process. It provides a mathematical framework for modeling decision making in situations where outcomes are partly
Admissible decision rule
In statistical decision theory, an admissible decision rule is a rule for making a decision such that there is no other rule that is always "better" than it (or at least sometimes better and never wor
Expected utility hypothesis
The expected utility hypothesis is a popular concept in economics that serves as a reference guide for decisions when the payoff is uncertain. The theory recommends which option rational individuals s
Utility maximization problem
Utility maximization was first developed by utilitarian philosophers Jeremy Bentham and John Stuart Mill. In microeconomics, the utility maximization problem is the problem consumers face: "How should
AIXI
AIXI ['ai̯k͡siː] is a theoretical mathematical formalism for artificial general intelligence.It combines Solomonoff induction with sequential decision theory.AIXI was first proposed by Marcus Hutter i
Optimal decision
An optimal decision is a decision that leads to at least as good a known or expected outcome as all other available decision options. It is an important concept in decision theory. In order to compare
Regret (decision theory)
In decision theory, on making decisions under uncertainty—should information about the best course of action arrive after taking a fixed decision—the human emotional response of regret is often experi
Kelly criterion
In probability theory, the Kelly criterion (or Kelly strategy or Kelly bet), is a formula that determines the optimal theoretical size for a bet. It is valid when the expected returns are known. The K
Response surface methodology
In statistics, response surface methodology (RSM) explores the relationships between several explanatory variables and one or more response variables. The method was introduced by George E. P. Box and
Odds algorithm
The odds algorithm (or Bruss algorithm) is a mathematical method for computing optimal strategies for a class of problems that belong to the domain of optimal stopping problems. Their solution follows
Feasible region
In mathematical optimization, a feasible region, feasible set, search space, or solution space is the set of all possible points (sets of values of the choice variables) of an optimization problem tha
Automatic basis function construction
In machine learning, automatic basis function construction (or basis discovery) is the mathematical method of looking for a set of task-independent basis functions that map the state space to a lower-
Monte Carlo tree search
In computer science, Monte Carlo tree search (MCTS) is a heuristic search algorithm for some kinds of decision processes, most notably those employed in software that plays board games. In that contex
Bayesian efficiency
Bayesian efficiency is an analog of Pareto efficiency for situations in which there is incomplete information. Under Pareto efficiency, an allocation of a resource is Pareto efficient if there is no o
Disorder problem
In the study of stochastic processes in mathematics, a disorder problem or quickest detection problem (formulated by Kolmogorov) is the problem of using ongoing observations of a stochastic process to
Risk aversion (psychology)
Risk aversion is a preference for a sure outcome over a gamble with higher or equal expected value. Conversely, the rejection of a sure thing in favor of a gamble of lower or equal expected value is k
Bayesian experimental design
Bayesian experimental design provides a general probability-theoretical framework from which other theories on experimental design can be derived. It is based on Bayesian inference to interpret the ob
Mabinogion sheep problem
In probability theory, the Mabinogion sheep problem or Mabinogian urn is a problem in stochastic control introduced by David Williams , who named it after a herd of magic sheep in the Welsh collection
Scenario optimization
The scenario approach or scenario optimization approach is a technique for obtaining solutions to robust optimization and problems based on a sample of the constraints. It also relates to inductive re
Stopping time
In probability theory, in particular in the study of stochastic processes, a stopping time (also Markov time, Markov moment, optional stopping time or optional time) is a specific type of “random time
Cost–utility analysis
Cost–utility analysis (CUA) is a form of economic analysis used to guide procurement decisions.The most common and well-known application of this analysis is in pharmacoeconomics, especially health te
Generalized expected utility
Generalized expected utility is a decision-making metric based on any of a variety of theories that attempt to resolve some discrepancies between expected utility theory and empirical observations, co
Secretary problem
The secretary problem demonstrates a scenario involving optimal stopping theory that is studied extensively in the fields of applied probability, statistics, and decision theory. It is also known as t
Wald's maximin model
In decision theory and game theory, Wald's maximin model is a non-probabilistic decision-making model according to which decisions are ranked on the basis of their worst-case outcomes – the optimal de
Optimal design
In the design of experiments, optimal designs (or optimum designs) are a class of experimental designs that are optimal with respect to some statistical criterion. The creation of this field of statis