BCMA-ES: A Bayesian approach to CMA-ES
This paper introduces a novel theoretically sound approach for the celebrated CMA-ES algorithm. Assuming the parameters of the multi variate normal distribution for the minimum follow a conjugate prior distribution, we derive their optimal update at each iteration step. Not only provides this Bayesian framework a justification for the update of the CMA-ES algorithm but it also gives two new versions of CMA-ES either assuming normal-Wishart or normal-Inverse Wishart priors, depending whether we parametrize the likelihood by its covariance or precision matrix. We support our theoretical findings by numerical experiments that show fast convergence of these modified versions of CMA-ES.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
BCMA-ES II: revisiting Bayesian CMA-ES
This paper revisits the Bayesian CMA-ES and provides updates for normal Wishart. It emphasizes the difference between a normal and normal inverse Wishart prior. After some computation, we prove that the only difference r…
Combining Bayesian Inference and Reinforcement Learning for Agent Decision Making: A Review
Bayesian inference has many advantages in decision making of agents (e.g. robotics/simulative agent) over a regular data-driven black-box neural network: Data-efficiency, generalization, interpretability, and safety wher…
Active LearningBayesian InferenceBayesian OptimizationDecision Making+4PAC-Bayesian Theory Meets Bayesian Inference
We exhibit a strong link between frequentist PAC-Bayesian risk bounds and the Bayesian marginal likelihood. That is, for the negative log-likelihood loss function, we show that the minimization of PAC-Bayesian generaliza…
Bayesian InferenceregressionBayesian Neural Networks: Essentials
Bayesian neural networks utilize probabilistic layers that capture uncertainty over weights and activations, and are trained using Bayesian inference. Since these probabilistic layers are designed to be drop-in replaceme…
Bayesian InferenceProbabilistic Deep LearningBayesian--AI Fusion for Epidemiological Decision Making: Calibrated Risk, Honest Uncertainty, and Hyperparameter Intelligence
Modern epidemiological analytics increasingly use machine learning models that offer strong prediction but often lack calibrated uncertainty. Bayesian methods provide principled uncertainty quantification, yet are viewed…
Hyperparameter OptimizationDecision Making