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Down-sampling training data has long been shown to improve the generalizationperformance of a wide range of machine learning systems. Recently,down-sampling has proved effective in genetic programming (GP) runs thatutilize the lexicase parent selection technique. Although this down-samplingprocedure has been shown to significantly improve performance across a varietyof problems, it does not seem to do so due to encouraging adaptability throughenvironmental change. We hypothesize that the random sampling that is performedevery generation causes discontinuities that result in the population beingunable to adapt to the shifting environment. We investigate modifications todown-sampled lexicase selection in hopes of promoting incremental environmentalchange to scaffold evolution by reducing the amount of jarring discontinuitiesbetween the environments of successive generations. In our empirical studies,we find that forcing incremental environmental change is not significantlybetter for evolving solutions to program synthesis problems than simple randomdown-sampling. In response to this, we attempt to exacerbate the hypothesizedprevalence of discontinuities by using only disjoint down-samples to see if ithinders performance. We find that this also does not significantly differ fromthe performance of regular random down-sampling. These negative results raisenew questions about the ways in which the composition of sub-samples, which mayinclude synonymous cases, may be expected to influence the performance ofmachine learning systems that use down-sampling.

The Environmental Discontinuity Hypothesis for Down-Sampled Lexicase Selection