Bayesian Optimization (BO) is useful for optimizing functions that are expensive to evaluate, lack an analytical expression and whose evaluations can be contaminated by noise. These methods rely on a probabilistic model of the objective function, typically a Gaussian process (GP), upon which an acquisition function is built. The acquisition function guides the optimization process and measures the expected utility of performing an evaluation of the objective at a new point. GPs assume continuous input variables. When this is not the case, for example when some of the input variables take categorical or integer values, one has to introduce extra approximations. Consider a suggested input location taking values in the real line. Before doing the evaluation of the objective, a common approach is to use a one hot encoding approximation for categorical variables, or to round to the closest integer, in the case of integer-valued variables. We show that this can lead to optimization problems and describe a more principled approach to account for input variables that are categorical or integer-valued. We illustrate in both synthetic and a real experiments the utility of our approach, which significantly improves the results of standard BO methods using Gaussian processes on problems with categorical or integer-valued variables.

Real-world problems often involve the optimization of several objectives under multiple constraints. Furthermore, we may not have an expression for each objective or constraint; they may be expensive to evaluate; and the evaluations can be noisy. These functions are referred to as black-boxes. Bayesian optimization (BO) can efficiently solve the problems described. For this, BO iteratively fits a model to the observations of each black-box. The models are then used to choose where to evaluate the black-boxes next, with the goal of solving the optimization problem in a few iterations. In particular, they guide the search for the problem's solution, and avoid evaluations in regions of little expected utility. A limitation, however, is that current BO methods for these problems choose a point at a time at which to evaluate the black-boxes. If the expensive evaluations can be carried out in parallel (as when a cluster of computers is available), this results in a waste of resources. Here, we introduce PPESMOC, Parallel Predictive Entropy Search for Multi-objective Optimization with Constraints, a BO strategy for solving the problems described. PPESMOC selects, at each iteration, a batch of input locations at which to evaluate the black-boxes, in parallel, to maximally reduce the entropy of the problem's solution. To our knowledge, this is the first batch method for constrained multi-objective BO. We present empirical evidence in the form of synthetic, benchmark and real-world experiments that illustrate the effectiveness of PPESMOC.

During the last two years there has been a plethora of large generative models such as ChatGPT or Stable Diffusion that have been published. Concretely, these models are able to perform tasks such as being a general question and answering system or automatically creating artistic images that are revolutionizing several sectors. Consequently, the implications that these generative models have in the industry and society are enormous, as several job positions may be transformed. For example, Generative AI is capable of transforming effectively and creatively texts to images, like the DALLE-2 model; text to 3D images, like the Dreamfusion model; images to text, like the Flamingo model; texts to video, like the Phenaki model; texts to audio, like the AudioLM model; texts to other texts, like ChatGPT; texts to code, like the Codex model; texts to scientific texts, like the Galactica model or even create algorithms like AlphaTensor. This work consists on an attempt to describe in a concise way the main models are sectors that are affected by generative AI and to provide a taxonomy of the main generative models published recently.

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Optimisation problems are ubiquitous in particle and astrophysics, and involve locating the optimum of a complicated function of many parameters that may be computationally expensive to evaluate. We describe a number of global optimisation algorithms that are not yet widely used in particle astrophysics, benchmark them against random sampling and existing techniques, and perform a detailed comparison of their performance on a range of test functions. These include four analytic test functions of varying dimensionality, and a realistic example derived from a recent global fit of weak-scale supersymmetry. Although the best algorithm to use depends on the function being investigated, we are able to present general conclusions about the relative merits of random sampling, Differential Evolution, Particle Swarm Optimisation, the Covariance Matrix Adaptation Evolution Strategy, Bayesian Optimisation, Grey Wolf Optimisation, and the PyGMO Artificial Bee Colony, Gaussian Particle Filter and Adaptive Memory Programming for Global Optimisation algorithms.