High-Dimensional Derivative-free Optimization
Derivative-free methods can tackle complex optimizations, however, are hard to scale to high dimensional problems.
Papers
:
Scaling to high-dimension by random embedding
: In the
AAAI'16 (PDF)
paper, we consider solving high-dimensional optimization problems with a low
effective dimension
. We proved that the random embedding algorithm can reduce the regret bound of the simultaneous optimistic optimization (SOO) algorithm, which is a theoretical-grounded derivative-free method, from depending on the size of the high-dimensions to depending on the size of the low effective dimensions.
Sequential random embeddings
: In the
IJCAI'16 (PDF)
paper, we extend the concept of
effective dimension
to be
optimal epsilon-effective dimension
that allows all variable to be effective, but many of them only have a small impact. We then propose the sequential random embedding (SRE) method to break the embedding gap of single random embedding. This method enables us to solve non-convex Ramp loss classification problem up to 100,000 dimensions, and achieve much better results than the concave-convex procedure (CCCP). As a comparison, derivative-free methods are previously used to solve problems with mostly less than 1,000 dimensions.
Codes
:
Sequential random embeddings :
SRE