A Functional Optimization Method for Continuous Domains

Smart city solutions are often formulated as adaptive optimization problems in which a cost objective function w.r.t certain constraints is optimized using off-the-shelf optimization libraries. Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is an efficient derivative-free optimization algorithm where a black-box objective function is defined on a parameter space. This modeling makes its performance strongly depends on the quality of chosen features. This paper considers modeling the input space for optimization problems in reproducing kernel Hilbert spaces (RKHS). This modeling amounts to functional optimization whose domain is a function space that enables us to optimize in a very rich function class. Our CMA-ES-RKHS framework performs black-box functional optimization in the RKHS. Adaptive representation of the function and covariance operator is achieved with sparsification techniques. We evaluate CMA-ES-RKHS on simple functional optimization problems which are motivated from many problems of smart cities.