A Computationally Efficient Limited Memory CMA-ES for Large Scale Optimization
This work addresses the computational bottleneck in large-scale optimization for researchers and practitioners, representing an incremental improvement over existing methods.
The paper tackles the problem of large-scale optimization by proposing a computationally efficient limited memory CMA-ES algorithm, which reduces time and memory complexity to O(mn) and efficiently solves non-separable problems with n > 1000 using small m values like 20 or 30.
We propose a computationally efficient limited memory Covariance Matrix Adaptation Evolution Strategy for large scale optimization, which we call the LM-CMA-ES. The LM-CMA-ES is a stochastic, derivative-free algorithm for numerical optimization of non-linear, non-convex optimization problems in continuous domain. Inspired by the limited memory BFGS method of Liu and Nocedal (1989), the LM-CMA-ES samples candidate solutions according to a covariance matrix reproduced from $m$ direction vectors selected during the optimization process. The decomposition of the covariance matrix into Cholesky factors allows to reduce the time and memory complexity of the sampling to $O(mn)$, where $n$ is the number of decision variables. When $n$ is large (e.g., $n$ > 1000), even relatively small values of $m$ (e.g., $m=20,30$) are sufficient to efficiently solve fully non-separable problems and to reduce the overall run-time.