Effective Adaptive Mutation Rates for Program Synthesis

TL;DR

This work proposes an adaptive bandit-based scheme that addresses the vanishing mutation rate problem and essentially removes the need to specify a mutation rate, and results on software synthesis and symbolic regression problems validate the effectiveness of the approach.

Abstract

The problem-solving performance of many evolutionary algorithms, including genetic programming systems used for program synthesis, depends on the values of hyperparameters including mutation rates. The mutation method used to produce some of the best results to date on software synthesis benchmark problems, Uniform Mutation by Addition and Deletion (UMAD), adds new genes into a genome at a predetermined rate and then deletes genes at a rate that balances the addition rate, producing no size change on average. While UMAD with a predetermined addition rate outperforms many other mutation and crossover schemes, we do not expect a single rate to be optimal across all problems or all generations within one run of an evolutionary system. However, many current adaptive mutation schemes such as self-adaptive mutation rates suffer from pathologies like the vanishing mutation rate problem, in which the mutation rate quickly decays to zero. We propose an adaptive bandit-based scheme that addresses this problem and essentially removes the need to specify a mutation rate. Although the proposed scheme itself introduces hyperparameters, we either set these to good values or ensemble them in a reasonable range. Results on software synthesis and symbolic regression problems validate the effectiveness of our approach.

Figures (4)

• Figure 1: Performance of four adaptive mutation rate schemes on function minimization problems. 95% confidence intervals obtained by bootstrapping. The bandit controller is competitive with GESMR, with slightly slower adaptation on easy problems like Rosenbrock and Sphere, but better final fitness on rugged domains like Ackley and Rastrigin.
• Figure 2: Rewards obtained by different UMAD rates on software synthesis problems. Naively considering only the expected reward makes the lowest UMAD rate appear to be the best. Considering the expected maximum reward over $len\_history$ samples paints a much more realistic picture.
• Figure 3: Best error and average log-UMAD rate sampled by three different adaptive controllers on Software Synthesis problems. 95% confidence intervals obtained by bootstrapping. The bandit controller is able to effectively avoid the vanishing mutation rate problem.
• Figure 4: Best error and average log-UMAD rate sampled by three different adaptive controllers on SR problems. 95% confidence intervals obtained by bootstrapping. SAMR suffers from a vanishing mutation rate, while GESMR suffers from an exploding mutation rate.