Models like support vector machines or Gaussian process regression often require positive semi-definite kernels. These kernels may be based on distance functions. While definiteness is proven for common distances and kernels, a proof for a new kernel may require too much time and effort for users who simply aim at practical usage. Furthermore, designing definite distances or kernels may be equally intricate. Finally, models can be enabled to use indefinite kernels. This may deteriorate the accuracy or computational cost of the model. Hence, an efficient method to determine definiteness is required. We propose an empirical approach. We show that sampling as well as optimization with an evolutionary algorithm may be employed to determine definiteness. We provide a proof-of-concept with 16 different distance measures for permutations. Our approach allows to disprove definiteness if a respective counter-example is found. It can also provide an estimate of how likely it is to obtain indefinite kernel matrices. This provides a simple, efficient tool to decide whether additional effort should be spent on designing/selecting a more suitable kernel or algorithm.

Cities are some of the clearest and well-used examples of a complex system, and whilst we are certainly better than we have been at managing their growth, they are, to a large extent, unmanageable. A recent study by a team of Spanish researchers at the Universidade da Coruna highlights how AI can be used to better understand how cities grow and evolve, at least in a vertical sense. The researchers use an evolutionary algorithm that's trained on historical and economic data of an urban area to predict how the skyline could look in a few years time. The method was successfully deployed in the Minato Ward, in Tokyo. The team believes that cities grow in a similar way to self-organized biological systems.

Noname manuscript No. (will be inserted by the editor) Abstract Most real-world optimization problems often come with multiple global optima or local optima. Therefore, increasing niching metaheuristic algorithms, which devote to finding multiple optima in a single run, are developed to solve these multimodal optimization problems. However, there are two difficulties urgently to be solved for most existing niching metaheuristic algorithms: how to set the optimal values of niching parameters for different optimization problems, and how to jump out of the local optima efficiently. Based on Whale Swarm Algorithm (WSA) we proposed previously, this paper presents a new multimodal optimizer named WSA with Iterative Counter (WSA-IC) to address these two difficulties. In the one hand, WSA-IC improves the iteration rule of the original WSA for multimodal optimization, which removes the need of specifying different values of attenuation coefficient for different problems to form multiple subpopulations, without introducing any niching parameter. In the other hand, WSA-IC enables the identification of extreme point during iterations relying on two new parameters (i.e., stability threshold T Moreover, the convergence of WSA-IC is proved. Finally, the proposed WSA-IC is compared with several niching metaheuristic algorithms on CEC2015 niching benchmark test functions and five additional classical multimodal functions with high dimensions. The experimental results demonstrate that WSA-IC statistically outperforms other niching metaheuristic algorithms on most test functions. Keywords Whale swarm algorithm · multimodal optimization · metaheuristic algorithm · niching · extreme point 1 Introduction Most of the real-world optimization problems are multimodal [1-6], i.e., their objective functions often contain multiple global optima or local optima. In such a scenario, using metaheuristic algorithms, no matter evolutionary algorithms (EAs) or swarm based algorithms, to solve these problems has become a hot research topic, as they are easy to implement and can converge to as good as possible solutions.

This is one of only a handful couple of writings that consolidates three fundamental postulations in the investigation of rationale programming: the logic that gives logic programs their extraordinary character: the act of programming viably utilizing the logic; and the productive usage of logic software on PCs.

What is the relationship between machine learning and optimization? On the other hand, what happens when machine learning is used to solve optimization problems? Consider this: a UPS driver with 25 packages has 15 trillion possible routes to choose from. And if each driver drives just one more mile each day than necessary, the company would be losing $30 million a year. While UPS would have all the data for their trucks and routes, there is no way they can run 15 trillion computations per each driver with 25 packages.

If nature knows what it's doing, it sure does a good job hiding it. Like, why would evolution produce an elephant with a shovel for a face? For very good reasons, as it turns out. Natural selection is an astoundingly creative phenomenon, molding species to fit their environments, even if that means turning their faces into shovels. It's also created a galaxy of ways for animals to move about, from walking to crawling to flying.

Many applications in machine learning require optimizing a function whose true gradient is unknown, but where surrogate gradient information (directions that may be correlated with, but not necessarily identical to, the true gradient) is available instead. This arises when an approximate gradient is easier to compute than the full gradient (e.g. in meta-learning or unrolled optimization), or when a true gradient is intractable and is replaced with a surrogate (e.g. in certain reinforcement learning applications, or when using synthetic gradients). We propose Guided Evolutionary Strategies, a method for optimally using surrogate gradient directions along with random search. We define a search distribution for evolutionary strategies that is elongated along a guiding subspace spanned by the surrogate gradients. This allows us to estimate a descent direction which can then be passed to a first-order optimizer. We analytically and numerically characterize the tradeoffs that result from tuning how strongly the search distribution is stretched along the guiding subspace, and we use this to derive a setting of the hyperparameters that works well across problems. Finally, we apply our method to example problems including truncated unrolled optimization and a synthetic gradient problem, demonstrating improvement over both standard evolutionary strategies and first-order methods that directly follow the surrogate gradient.

Have you put a bet on the FIFA World Cup? If yes, the chances are you've made a pretty educated guess, right? You know which team has the strongest players or most favourable odds. Or maybe you've put some cash on your country's team, (which normally I'd avoid England, but given their recent performance, I could be wrong to!) Either way, you might be best casting your bets in line with San Francisco based Unanimous AI. They use a technology called Swarm AI - algorithms modelled on swarms in nature that amplifies human intelligence. By using human intelligence and artificial intelligence together, they can predict outcomes better than humans or AI acting alone.

The most data-efficient algorithms for reinforcement learning in robotics are model-based policy search algorithms, which alternate between learning a dynamical model of the robot and optimizing a policy to maximize the expected return given the model and its uncertainties. However, the current algorithms lack an effective exploration strategy to deal with sparse or misleading reward scenarios: if they do not experience any state with a positive reward during the initial random exploration, it is very unlikely to solve the problem. Here, we propose a novel model-based policy search algorithm, Multi-DEX, that leverages a learned dynamical model to efficiently explore the task space and solve tasks with sparse rewards in a few episodes. To achieve this, we frame the policy search problem as a multi-objective, model-based policy optimization problem with three objectives: (1) generate maximally novel state trajectories, (2) maximize the expected return and (3) keep the system in state-space regions for which the model is as accurate as possible. We then optimize these objectives using a Pareto-based multi-objective optimization algorithm. The experiments show that Multi-DEX is able to solve sparse reward scenarios (with a simulated robotic arm) in much lower interaction time than VIME, TRPO, GEP-PG, CMA-ES and Black-DROPS.

The effort devoted to hand-crafting image classifiers has motivated the use of architecture search to discover them automatically. Although evolutionary algorithms have been repeatedly applied to architecture search, the architectures thus discovered have remained inferior to human-crafted ones. Here we show for the first time that artificially-evolved architectures can match or surpass human-crafted and RL-designed image classifiers. In particular, our models---named AmoebaNets---achieved a state-of-the-art accuracy of 97.87% on CIFAR-10 and top-1 accuracy of 83.1% on ImageNet. Among mobile-size models, an AmoebaNet with only 5.1M parameters also achieved a state-of-the-art top-1 accuracy of 75.1% on ImageNet. We also compared this method against strong baselines. Finally, we performed platform-aware architecture search with evolution to find a model that trains quickly on Google Cloud TPUs. This method produced an AmoebaNet that won the Stanford DAWNBench competition for lowest ImageNet training cost.