Swap Regret

	Swap Regret Swap regret is a concept from online learning and game theory. It is a generalization of regret in a repeated, ''n''-decision game. Definition In each round t, the learner chooses decision i with probability x^t_i and the utility for decision i is p^t_i. A learner's ''swap-regret'' is defined to be the following: : \mbox= \sum_^n \max_\sum_^T x^t_i \cdot (p^t_j-p^t_i). Intuitively, it is how much a player could improve by switching each occurrence of decision ''i'' to the best decision ''j'' possible in hindsight Hindsight bias, also known as the knew-it-all-along phenomenon or creeping determinism, is the common tendency for people to perceive past events as having been more predictable than they were. After an event has occurred, people often believe .... The swap regret is always nonnegative. Swap regret is useful for computing correlated equilibria. References . Game theory {{gametheory-stub ... [...More Info...] [...Related Items...] OR:* [Wikipedia] [Google] [Baidu]
picture info	Game Theory Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game theory addressed two-person zero-sum games, in which a participant's gains or losses are exactly balanced by the losses and gains of the other participant. In the 1950s, it was extended to the study of non zero-sum games, and was eventually applied to a wide range of Human behavior, behavioral relations. It is now an umbrella term for the science of rational Decision-making, decision making in humans, animals, and computers. Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann. Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics. His paper was f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Regret (decision Theory) In decision theory, regret aversion (or anticipated regret) describes how the human emotional response of regret can influence decision-making under uncertainty. When individuals make choices without complete information, they often experience regret if they later discover that a different choice would have produced a better outcome. This regret can be quantified as the difference in value between the actual decision made and what would have been the optimal decision in hindsight. Unlike traditional models that consider regret as merely a post-decision emotional response, the theory of regret aversion proposes that decision-makers actively anticipate potential future regret and incorporate this anticipation into their current decision-making process. This anticipation can lead individuals to make choices specifically designed to minimize the possibility of experiencing regret later, even if those choices are not optimal from a purely probabilistic expected-value perspective. Regre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Hindsight Hindsight bias, also known as the knew-it-all-along phenomenon or creeping determinism, is the common tendency for people to perceive past events as having been more predictable than they were. After an event has occurred, people often believe that they could have predicted or perhaps even known with a high degree of certainty what the outcome of the event would be before it occurred. Hindsight bias may cause distortions of memories of what was known or believed before an event occurred and is a significant source of overconfidence in one’s ability to predict the outcomes of future events. Examples of hindsight bias can be seen in the writings of historians describing the outcomes of battles, in physicians’ recall of clinical trials, and in criminal or civil trials as people tend to assign responsibility on the basis of the supposed predictability of accidents. In some countries, 20/20 indicates normal visual acuity at 20 feet, from which derives the idiom " hindsight is 20 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Correlated Equilibrium In game theory, a correlated equilibrium is a solution concept that is more general than the well known Nash equilibrium. It was first discussed by mathematician Robert Aumann in 1974. The idea is that each player chooses their action according to their private observation of the value of the same public signal. A strategy assigns an action to every possible observation a player can make. If no player would want to deviate from their strategy (assuming the others also don't deviate), the distribution from which the signals are drawn is called a correlated equilibrium. Formal definition An N-player strategic game \displaystyle (N,\,\) is characterized by an action set A_i and utility function u_i for each player When player i chooses strategy a_i \in A_i and the remaining players choose a strategy profile described by the a_, then player i's utility is \displaystyle u_i(a_i,a_). A ''strategy modification'' for player i is a function \phi_i\colon A_i \to A_i. That is, \phi_i te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]