Model-based Derivative-free Methods for Optimization
Derivative-free methods can tackle complex optimizations in real domains, such as non-convex, non-differentiable, and non-continuous problems with many local optima.
Derivative-free optimization
:
General analysis
: In the
CEC'14 (PDF)
paper, we proposed the sampling-and-learning (SAL) framework to capture the essence of model-based optimization algorithms, and analyzed its performance using the query complexity for achieving approximate solutions with a probability. We derived a general query complexity bound for SAL algorithms where the learning model is a classifier.
Classification-based optimization
: In the
AAAI'16 (PDF)
(Appendix)
paper, we discovered key factors for classification-based optimization methods, and designed the RACOS algorithm accordingly. RACOS has been shown superior to some state-of-the-art derivative-free optimization algorithms.
Classification-based optimization in discrete domains
: In the
CEC'16 (PDF)
paper, we analyzed the performance of the classification-based optimization in finite discrete spaces.
Sequential classification-based optimization
: In the
AAAI'17 (PDF)
paper, we proposed the sequential version of RACOS, called SRACOS. Unlike the original RACOS that samples and evaluates a batch of solutions at a time, SRACOS samples one solution at a time and update the classifier immediately after the evaluation of this solution. SRACOS shows a significant improvement from RACOS, both theoretically and practically.
High-dimentionality
:
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
:
The derivative-free optimization by classification algorithm:
RACOS
Sequential random embeddings :
SRE