High-level program optimizations, such as loop transformations, are critical for high performance on multi-core targets. However, complex sequences of loop transformations are often required to expose parallelism (both coarse-grain and fine-grain) and improve data locality. The polyhedral compilation framework has proved to be very effective at representing these complex sequences and restructuring compute-intensive applications, seamlessly handling perfectly and imperfectly nested loops. Nevertheless identifying the most effective loop transformations remains a major challenge. We address the problem of selecting the best polyhedral optimizations with dedicated machine learning models, trained specifically on the target machine. We show that these models can quickly select high-performance optimizations with very limited iterative search. Our end-to-end framework is validated using numerous benchmarks on two modern multi-core platforms. We investigate a variety of different machine learning algorithms and hardware counters, and we obtain performance improvements over productions compilers ranging on average from 3.2x to 8.7x, by running not more than 6 program variants from a polyhedral optimization space.