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🔗 Computing 🔗 Computer science

In computational complexity and optimization the no free lunch theorem is a result that states that for certain types of mathematical problems, the computational cost of finding a solution, averaged over all problems in the class, is the same for any solution method. The name alludes to the saying "no such thing as a free lunch", that is, no method offers a "short cut". This is under the assumption that the search space is a probability density function. It does not apply to the case where the search space has underlying structure (e.g., is a differentiable function) that can be exploited more efficiently (e.g., Newton's method in optimization) than random search or even has closed-form solutions (e.g., the extrema of a quadratic polynomial) that can be determined without search at all. For such probabilistic assumptions, the outputs of all procedures solving a particular type of problem are statistically identical. A colourful way of describing such a circumstance, introduced by David Wolpert and William G. Macready in connection with the problems of search and optimization, is to say that there is no free lunch. Wolpert had previously derived no free lunch theorems for machine learning (statistical inference). Before Wolpert's article was published, Cullen Schaffer independently proved a restricted version of one of Wolpert's theorems and used it to critique the current state of machine learning research on the problem of induction.

In the "no free lunch" metaphor, each "restaurant" (problem-solving procedure) has a "menu" associating each "lunch plate" (problem) with a "price" (the performance of the procedure in solving the problem). The menus of restaurants are identical except in one regard – the prices are shuffled from one restaurant to the next. For an omnivore who is as likely to order each plate as any other, the average cost of lunch does not depend on the choice of restaurant. But a vegan who goes to lunch regularly with a carnivore who seeks economy might pay a high average cost for lunch. To methodically reduce the average cost, one must use advance knowledge of a) what one will order and b) what the order will cost at various restaurants. That is, improvement of performance in problem-solving hinges on using prior information to match procedures to problems.

In formal terms, there is no free lunch when the probability distribution on problem instances is such that all problem solvers have identically distributed results. In the case of search, a problem instance in this context is a particular objective function, and a result is a sequence of values obtained in evaluation of candidate solutions in the domain of the function. For typical interpretations of results, search is an optimization process. There is no free lunch in search if and only if the distribution on objective functions is invariant under permutation of the space of candidate solutions. This condition does not hold precisely in practice, but an "(almost) no free lunch" theorem suggests that it holds approximately.

🔗 Computing 🔗 Telecommunications 🔗 Computing/Networking

Wireless Application Protocol (WAP) is a now obsolete technical standard for accessing information over a mobile wireless network. Introduced in 1999, WAP allowed at launch users with compatible mobile devices to browse content such as news, weather and sports scores provided by mobile network operators, specially designed for the limited capabilities of a mobile device. The Japanese i-mode system offered another major competing wireless data standard.

Before the introduction of WAP, mobile service providers had limited opportunities to offer interactive data services, but needed interactivity to support Internet and Web applications. Although hyped at launch, WAP suffered from much criticism. However the introduction of GPRS networks, offering a faster speed, led to an improvement in the WAP experience. WAP content was accessed using a WAP browser, which is like a standard web browser but designed for reading pages specific for WAP, instead of HTML. By the 2010s it had been largely superseded by more modern standards such as XHTML. Modern phones have proper Web browsers, so they do not need WAP markup for compatibility, and therefore, most are no longer able to render and display pages written in WML, WAP's markup language.