The Necessity of Meta Bias in Search Algorithms

Bias is necessary for learning, and is a probability over a search space. This is usually introduced implicitly by the designer of a search algorithm, for example by designing a new search operator. This bias is does not change; each time a stochastic search algorithm is executed it will give a different answer. However, if executed repeated it will give the same solution on average. In other words, the bias is static (even if we include a self adaptive component to the search algorithm). One desirable property of search algorithms is that they converge (i.e. given enough time they will eventually reach the global optima). In terms of bias, this means that there is a non-zero probability of visiting each item in the search space. Search algorithms are intended to be reused on many instances of a problem. These instances can be consider to be drawn from a probability distribution. In other words, a search algorithm and problem class can both be viewed as probability distributions over the search space. If the bias of a search algorithm does not match the bias of a problem class, it will under perform, if however, they do match, it will perform well. Therefore we need some mechanism of altering the initial bias of the search algorithm to coincide with that of the problem class. This mechanism can be realized by a meta level which alters the bias of the base level. In other words, if a search algorithm is to be applied to many instances of a problem, then meta bias is necessary. This implies that convergence at the meta level means a search algorithm shift its bias to any probability distribution. Additionally, shifting bias is equivalent to automating the design of search algorithms.