We leverage a dimensionality reduction approach to develop a novel inverse design platform applicable to a wide class of optical nanoantennas. The proposed dimensionality reduction technique uses a high level of correlation (in frequency and space domains) in the propagation of electromagnetic waves to considerably reduce the dimensionality of the response space of the problem. In addition, the correlation that often exists among the effects of design parameters on the response of the structure (i.e., selecting more design parameters than needed for uniquely identifying a structure for a given input-output relation) is used to reduce the dimensionality of the design space. In addition to the considerable mitigation of computation time and complexity, the two key features of dimensionality reduction, i.e., : 1) the ability to train a NN and later use it for a large class of problems, and 2) the possibility of analytically relating the reduced design space to the original design space to obtain valuable intuitive information about the roles of each design parameter in the overall performance of the nanostructure, highlight the superiority of the proposed approach. This is in contrast to existing analysis and optimization techniques, which require an intensive repetition of the simulations for each design problem without providing an intuitive understanding of the roles of design parameters. As a proof of concept, we apply this approach to a nanoscale structural color recently emerged as a promising candidate to organic colors in the printing technology. To circumvent the high absorption loss and efficiency of plasmonic color generators, we harness the fundamental dipolar Mie resonances of an array of asymmetric titanium dioxide elliptical nanopillars. We will further experimentally demonstrate such an optimized polarization-sensitive all-dielectric significantly enhance the resolution, saturation, and hue of color palettes. Such a novel inverse design approach highlights the performance of machine learning based approaches in developing highly-efficient metastructures.