A Computationally Efficient Limited Memory CMA-ES for Large Scale Optimization

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.Comment: Genetic and Evolutionary Computation Conference (GECCO'2014) (2014

Information-Geometric Optimization Algorithms: A Unifying Picture via Invariance Principles

We present a canonical way to turn any smooth parametric family of probability distributions on an arbitrary search space $X$ into a continuous-time black-box optimization method on $X$, the \emph{information-geometric optimization} (IGO) method. Invariance as a design principle minimizes the number of arbitrary choices. The resulting \emph{IGO flow} conducts the natural gradient ascent of an adaptive, time-dependent, quantile-based transformation of the objective function. It makes no assumptions on the objective function to be optimized. The IGO method produces explicit IGO algorithms through time discretization. It naturally recovers versions of known algorithms and offers a systematic way to derive new ones. The cross-entropy method is recovered in a particular case, and can be extended into a smoothed, parametrization-independent maximum likelihood update (IGO-ML). For Gaussian distributions on $\mathbb{R}^d$, IGO is related to natural evolution strategies (NES) and recovers a version of the CMA-ES algorithm. For Bernoulli distributions on $\{0,1\}^d$, we recover the PBIL algorithm. From restricted Boltzmann machines, we obtain a novel algorithm for optimization on $\{0,1\}^d$. All these algorithms are unified under a single information-geometric optimization framework. Thanks to its intrinsic formulation, the IGO method achieves invariance under reparametrization of the search space $X$, under a change of parameters of the probability distributions, and under increasing transformations of the objective function. Theory strongly suggests that IGO algorithms have minimal loss in diversity during optimization, provided the initial diversity is high. First experiments using restricted Boltzmann machines confirm this insight. Thus IGO seems to provide, from information theory, an elegant way to spontaneously explore several valleys of a fitness landscape in a single run.Comment: Final published versio

Maximum Likelihood-based Online Adaptation of Hyper-parameters in CMA-ES

The Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is widely accepted as a robust derivative-free continuous optimization algorithm for non-linear and non-convex optimization problems. CMA-ES is well known to be almost parameterless, meaning that only one hyper-parameter, the population size, is proposed to be tuned by the user. In this paper, we propose a principled approach called self-CMA-ES to achieve the online adaptation of CMA-ES hyper-parameters in order to improve its overall performance. Experimental results show that for larger-than-default population size, the default settings of hyper-parameters of CMA-ES are far from being optimal, and that self-CMA-ES allows for dynamically approaching optimal settings.Comment: 13th International Conference on Parallel Problem Solving from Nature (PPSN 2014) (2014

Black-Box Data-efficient Policy Search for Robotics

The most data-efficient algorithms for reinforcement learning (RL) in robotics are based on uncertain dynamical models: after each episode, they first learn a dynamical model of the robot, then they use an optimization algorithm to find a policy that maximizes the expected return given the model and its uncertainties. It is often believed that this optimization can be tractable only if analytical, gradient-based algorithms are used; however, these algorithms require using specific families of reward functions and policies, which greatly limits the flexibility of the overall approach. In this paper, we introduce a novel model-based RL algorithm, called Black-DROPS (Black-box Data-efficient RObot Policy Search) that: (1) does not impose any constraint on the reward function or the policy (they are treated as black-boxes), (2) is as data-efficient as the state-of-the-art algorithm for data-efficient RL in robotics, and (3) is as fast (or faster) than analytical approaches when several cores are available. The key idea is to replace the gradient-based optimization algorithm with a parallel, black-box algorithm that takes into account the model uncertainties. We demonstrate the performance of our new algorithm on two standard control benchmark problems (in simulation) and a low-cost robotic manipulator (with a real robot).Comment: Accepted at the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) 2017; Code at http://github.com/resibots/blackdrops; Video at http://youtu.be/kTEyYiIFGP