Evolution with Drifting Targets

We consider the question of the stability of evolutionary algorithms to gradual changes,or drift, in the target concept. We define an algorithm to be resistant to drift if, forsome inverse polynomial drift rate in the target function, it converges to accuracy 1 − ǫwith polynomial resources, and then stays within that accuracy indefinitely, except withprobability ǫ at any one time. We show that every evolution algorithm, in the sense ofValiant [19], can be converted using the Correlational Query technique of Feldman [9], intosuch a drift resistant algorithm. For certain evolutionary algorithms, such as for Booleanconjunctions, we give bounds on the rates of drift that they can resist. We develop somenew evolution algorithms that are resistant to significant drift. In particular, we give analgorithm for evolving linear separators over the spherically symmetric distribution that isresistant to a drift rate of O(ǫ/n), and another algorithm over the more general productnormal distributions that resists a smaller drift rate. The above translation result can be also interpreted as one on the robustness of the notion ofevolvability itself under changes of definition. As a second result in that direction we showthat every evolution algorithm can be converted to a quasi-monotonic one that can evolvefrom any starting point without the performance ever dipping significantly below that ofthe starting point. This permits the somewhat unnatural feature of arbitrary performancedegradations to be removed from several known robustness translations.