56 research outputs found
Alternative Restart Strategies for CMA-ES
This paper focuses on the restart strategy of CMA-ES on multi-modal
functions. A first alternative strategy proceeds by decreasing the initial
step-size of the mutation while doubling the population size at each restart. A
second strategy adaptively allocates the computational budget among the restart
settings in the BIPOP scheme. Both restart strategies are validated on the BBOB
benchmark; their generality is also demonstrated on an independent real-world
problem suite related to spacecraft trajectory optimization
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
Benchmarking a Weighted Negative Covariance Matrix Update on the BBOB-2010 Noisy Testbed
In a companion paper, we presented a weighted negative update of the covariance matrix in the CMA-ES—weighted active CMA-ES or, in short, aCMA-ES. In this paper, we benchmark the IPOP-aCMA-ES on the BBOB-2010 noisy testbed in search space dimension between 2 and 40 and compare its performance with the IPOP-CMA-ES. The aCMA suffers from a moderate performance loss, of less than a factor of two, on the sphere function with two different noise models. On the other hand, the aCMA enjoys a (significant) performance gain, up to a factor of four, on 13 unimodal functions in various dimensions, in particular the larger ones. Compared to the best performance observed during BBOB-2009, the IPOP-aCMA-ES sets a new record on overall ten functions. The global picture is in favor of aCMA which might establish a new standard also for noisy problems
Study of the Fractal decomposition based metaheuristic on low-dimensional Black-Box optimization problems
This paper analyzes the performance of the Fractal Decomposition Algorithm
(FDA) metaheuristic applied to low-dimensional continuous optimization
problems. This algorithm was originally developed specifically to deal
efficiently with high-dimensional continuous optimization problems by building
a fractal-based search tree with a branching factor linearly proportional to
the number of dimensions. Here, we aim to answer the question of whether FDA
could be equally effective for low-dimensional problems. For this purpose, we
evaluate the performance of FDA on the Black Box Optimization Benchmark (BBOB)
for dimensions 2, 3, 5, 10, 20, and 40. The experimental results show that
overall the FDA in its current form does not perform well enough. Among
different function groups, FDA shows its best performance on Misc. moderate and
Weak structure functions
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
Black-box Optimization Benchmarking of NIPOP-aCMA-ES and NBIPOP-aCMA-ES on the BBOB-2012 Noiseless Testbed
International audienceIn this paper, we study the performance of NIPOP-aCMA-ES and NBIPOP-aCMA-ES, recently proposed alternative restart strategies for CMA-ES. Both algorithms were tested using restarts till a total number of function evaluations of was reached, where is the dimension of the function search space. We compared new strategies to CMA-ES with IPOP and BIPOP restart schemes, two algorithms with one of the best overall performance observed during the BBOB-2009 and BBOB-2010. We also present the first benchmarking of BIPOP-CMA-ES with the weighted active covariance matrix update (BIPOP-aCMA-ES). The comparison shows that NIPOP-aCMA-ES usually outperforms IPOP-aCMA-ES and has similar performance with BIPOP-aCMA-ES, using only the regime of increasing the population size. The second strategy, NBIPOP-aCMA-ES, outperforms BIPOP-aCMA-ES in dimension 40 on weakly structured multi-modal functions thanks to the adaptive allocation of computation budgets between the regimes of restarts
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 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
, where is the number of decision variables. When is large
(e.g., > 1000), even relatively small values of (e.g., ) 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
Mirrored Variants of the (1,4)-CMA-ES Compared on the Noiseless BBOB-2010 Testbed
International audienceDerandomization by means of mirrored samples has been recently introduced to enhance the performances of -Evolution-Strategies (ESs) with the aim of designing fast and robust stochastic local search algorithms. This paper compares on the BBOB-2010 noiseless benchmark testbed two variants of the (1,4)-CMA-ES where the mirrored samples are used. Independent restarts are conducted up to a total budget of function evaluations, where is the dimension of the search space. The results show that the improved variants are significantly faster than the baseline (1,4)-CMA-ES on 4 functions in 20D (respectively 7 when using sequential selection in addition) by a factor of up to 3 (on the attractive sector function). In no case, the (1,4)-CMA-ES is significantly faster on any tested target function value in 5D and 20D. Moreover, the algorithm employing both mirroring and sequential selection is significantly better than the algorithm without sequentialism on five functions in 20D with expected running times that are about 20% smaller
CMA-ES with Restarts for Solving CEC 2013 Benchmark Problems
This paper investigates the performance of 6 versions of Covariance Matrix Adaptation Evolution Strategy (CMAES) with restarts on a set of 28 noiseless optimization problems (including 23 multi-modal ones) designed for the special session on real-parameter optimization of CEC 2013. The experimental validation of the restart strategies shows that: i). the versions of CMA-ES with weighted active covariance matrix update outperform the original versions of CMA-ES, especially on illconditioned problems; ii). the original restart strategies with increasing population size (IPOP) are usually outperformed by the bi-population restart strategies where the initial mutation stepsize is also varied; iii). the recently proposed alternative restart strategies for CMA-ES demonstrate a competitive performance and are ranked first w.r.t. the proportion of function-target pairs solved after the full run on all 10-, 30- and 50-dimensional problems
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