The principle of artificial curiosity directs active exploration towards the most informative or most interesting data. We show its usefulness for global black box optimization when data point evaluations are expensive. Gaussian process regression is used to model the fitness function based on all available observations so far. For each candidate point this model estimates expected Fitness reduction, and yields a novel closed-form expression of expected information gain. A new type of Pareto-front algorithm continually pushes the boundary of candidates not dominated by any other known data according to both criteria, using multi-objective evolutionary search. This makes the exploration-exploitation trade-off explicit, and permits maximally informed data selection. We illustrate the robustness of our approach in a number of experimental scenarios.

The family of natural evolution strategies (NES) offers a principled approach to real-valued evolutionary optimization by following the natural gradient of the expected fitness. Like the well-known CMA-ES, the most competitive algorithm in the field, NES comes with important invariance properties. In this paper, we introduce a number of elegant and efficient improvements of the basic NES algorithm. First, we propose to parameterize the positive definite covariance matrix using the exponential map, which allows the covariance matrix to be updated in a vector space. This new technique makes the algorithm completely invariant under linear transformations of the underlying search space, which was previously achieved only in the limit of small step sizes. Second, we compute all updates in the natural coordinate system, such that the natural gradient coincides with the vanilla gradient. This way we avoid the computation of the inverse Fisher information matrix, which is the main computational bottleneck of the original NES algorithm. Our new algorithm, exponential NES (xNES), is significantly simpler than its predecessors. We show that the various update rules in CMA-ES are closely related to the natural gradient updates of xNES. However, xNES is more principled than CMA-ES, as all the update rules needed for covariance matrix adaptation are derived from a single principle. We empirically assess the performance of the new algorithm on standard benchmark functions

We present a new way of converting a reversible finite Markov chain into a nonreversible one, with a theoretical guarantee that the asymptotic variance of the MCMC estimator based on the non-reversible chain is reduced. The method is applicable to any reversible chain whose states are not connected through a tree, and can be interpreted graphically as inserting vortices into the state transition graph. Our result confirms that non-reversible chains are fundamentally better than reversible ones in terms of asymptotic performance, and suggests interesting directions for further improving MCMC.

Efficient Natural Evolution Strategies (eNES) is a novel alternative to conventional evolutionary algorithms, using the natural gradient to adapt the mutation distribution. Unlike previous methods based on natural gradients, eNES uses a fast algorithm to calculate the inverse of the exact Fisher information matrix, thus increasing both robustness and performance of its evolution gradient estimation, even in higher dimensions. Additional novel aspects of eNES include optimal fitness baselines and importance mixing (a procedure for updating the population with very few fitness evaluations). The algorithm yields competitive results on both unimodal and multimodal benchmarks.

To optimize unknown 'fitness' functions, we present Natural Evolution Strategies, a novel algorithm that constitutes a principled alternative to standard stochastic search methods. It maintains a multinormal distribution on the set of solution candidates. The Natural Gradient is used to update the distribution's parameters in the direction of higher expected fitness, by efficiently calculating the inverse of the exact Fisher information matrix whereas previous methods had to use approximations. Other novel aspects of our method include optimal fitness baselines and importance mixing, a procedure adjusting batches with minimal numbers of fitness evaluations. The algorithm yields competitive results on a number of benchmarks.