I’ve identified a promising stochastic search heuristic, called hyperclimbing, for large-scale optimization over massive attribute product spaces (e.g., the set of all binary strings of some length N, where N is very large) with rugged fitness functions. Hyperclimbing works by progressively limiting sampling to a series of nested subsets with increasing expected fitness. At any given step, this heuristic sifts through vast numbers of coarse partitions of the subset it “inhabits”, and identifies ones that partition this set into subsets whose expected fitness values are significantly variegated. Because hyperclimbing is sensitive, not to the local features of a search space, but to certain more global statistics, it is not susceptible to the kinds of issues that waylay local search heuristics.
The chief barrier to the wide and enthusiastic use of hyperclimbing is that it seems to scale very poorly with the number of attributes. If one heeds the seemingly high cost of applying hyperclimbing to large search spaces, this heuristic quickly looses its shine. A key conclusion of my doctoral work is that this seemingly high cost is illusory. I have uncovered evidence that strongly suggests that genetic algorithms can implement hyperclimbing extraordinarily efficiently.
As readers of this blog probably know, genetic algorithms are search algorithms that mimic natural evolution. These algorithms have been used in a wide range of engineering and scientific fields to quickly procure useful solutions to poorly understood (i.e. black-box) optimization problems. Unfortunately, despite the routine use of genetic algorithms for over three decades, their adaptive capacity has not been adequately accounted for. Given the evidence that genetic algorithms can implement efficient hyperclimbing, I’ve proposed a new explanation for the adaptive capacity of these algorithms. This new account—the generative fixation hypothesis—promises to spark significant advances in the fields of genetic algorithmics and discrete optimization.
The discovery that hyperclimbing is efficiently implementable also promises to have a non-negligible impact on the ecology of machine learning research. Optimization and machine learning are, after all, intimately related. Overlooking a few exceptions, the practice of machine learning research, can be characterized as the effective reduction of difficult learning problems to optimization problems for which efficient algorithms exist. In other words, the machine learning problems that can effectively be tackled are in large part those that can in practice be reduced to optimization problems that can be tackled efficiently. Currently, this largely limits the class of tractable machine learning problems to the class of learning problems that can in practice be reduced to convex optimization problems [1] . The identification of general-purpose non-convex optimization heuristics with efficient implementations (e.g. hyperclimbing), thus, has the potential to significantly extend the reach of machine learning.
For a description of hyperclimbing, and evidence that genetic algorithms can implement this heuristic efficiently, please see my dissertation
[1] Kristin P. Bennett and Emilio Parrado-Hernandez. The interplay of optimization and machine learning research. Journal of Machine Learning Research, 7:1265–1281, 2006.
