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Most successful stochastic black-box optimizers, such as CMA-ES, use rankingsof the individual samples to obtain a new search distribution. Yet, the use ofrankings also introduces several issues such as the underlying optimizationobjective is often unclear, i.e., we do not optimize the expected fitness.Further, while these algorithms typically produce a high-quality mean estimateof the search distribution, the produced samples can have poor quality as thesealgorithms are ignorant of the regret. Lastly, noisy fitness functionevaluations may result in solutions that are highly sub-optimal on expectation.In contrast, stochastic optimizers that are motivated by policy gradients, suchas the Model-based Relative Entropy Stochastic Search (MORE) algorithm,directly optimize the expected fitness function without the use of rankings.MORE can be derived by applying natural policy gradients and compatiblefunction approximation, and is using information theoretic constraints toensure the stability of the policy update. While MORE does not suffer from thelisted limitations, it often cannot achieve state of the art performance incomparison to ranking based methods. We improve MORE by decoupling the updateof the mean and covariance of the search distribution allowing for moreaggressive updates on the mean while keeping the update on the covarianceconservative, an improved entropy scheduling technique based on an evolutionpath which results in faster convergence and a simplified and more effectivemodel learning approach in comparison to the original paper. We compare ouralgorithm to state of the art black-box optimization algorithms on standardoptimization tasks as well as on episodic RL tasks in robotics where it is alsocrucial to have small regret. We obtain competitive results on benchmarkfunctions and clearly outperform ranking-based methods in terms of regret onthe RL tasks.

Regret-Aware Black-Box Optimization with Natural Gradients, Trust-Regions and Entropy Control