Predicting CMA-ES Operators as Inductive Biases for Shape Optimization Problems

Domain-dependent expertise knowledge and high-level abstractions to arbitrate between different problem domains can be considered to be essential components of how human problem-solvers build experience and reuse it over the course of their lifetime. However, replicating it from an algorithmic point of view is a less trivial endeavor. Existing knowledge transfer methods in optimization largely fail to provide more specific guidance on specifying the similarity of different optimization problems and the nature of complementary experiences formed on them. A more rigorously grounded approach can be found alternatively in metalearning. This notion neglects any hurdles on characterizing problem similarity in favor of focusing instead on methodology to form domain-dependent inductive biases and mechanisms to arbitrate between them. In principle, we proposed within our previous research methods for constructing inductive biases and predict these from procedural optimization data. However, while we obtained effective methodology, it does not allow the joint construction of predictive components and biases in a cohesive manner. We therefore show in our following study, that improved configurations can be derived for the CMA-ES algorithm which can serve as inductive biases, and that predictors can be trained to recall them. Particularly noteworthy, this scenario allows the construction of predictive component and bias iteratively in a joint manner. We demonstrate the efficacy of this approach in a shape optimization scenario, in which the inductive bias is predicted through an operator configuration in a problem-specific manner during run-time.