Prompt optimization is a crucial task for improving the performance of large language models for downstream tasks. In this paper, a prompt is a sequence of n-grams selected from a vocabulary. Consequently, the aim is to select the optimal prompt concerning a certain performance metric. Prompt optimization can be considered as a combinatorial optimization problem, with the number of possible prompts (i.e., the combinatorial search space) given by the size of the vocabulary (i.e., all the possible n-grams) raised to the power of the length of the prompt. Exhaustive search is impractical; thus, an efficient search strategy is needed. We propose a Bayesian Optimization method performed over a continuous relaxation of the combinatorial search space. Bayesian Optimization is the dominant approach in black-box optimization for its sample efficiency, along with its modular structure and versatility. We use BoTorch, a library for Bayesian Optimization research built on top of PyTorch. Specifically, we focus on Hard Prompt Tuning, which directly searches for an optimal prompt to be added to the text input without requiring access to the Large Language Model, using it as a black-box (such as for GPT-4 which is available as a Model as a Service). Albeit preliminary and based on “vanilla” Bayesian Optimization algorithms, our experiments with RoBERTa as a large language model, on six benchmark datasets, show good performances when compared against other state-of-the-art black-box prompt optimization methods and enable an analysis of the trade-off between the size of the search space, accuracy, and wall-clock time.

It has been recently remarked that focusing only on accuracy in searching for optimal Machine Learning models amplifies biases contained in the data, leading to unfair predictions and decision supports. Recently, multi-objective hyperparameter optimization has been proposed to search for Machine Learning models which offer equally Pareto-efficient trade-offs between accuracy and fairness. Although these approaches proved to be more versatile than fairness-aware Machine Learning algorithms—which instead optimize accuracy constrained to some threshold on fairness—their carbon footprint could be dramatic, due to the large amount of energy required in the case of large datasets. We propose an approach named FanG-HPO: fair and green hyperparameter optimization (HPO), based on both multi-objective and multiple information source Bayesian optimization. FanG-HPO uses subsets of the large dataset to obtain cheap approximations (aka information sources) of both accuracy and fairness, and multi-objective Bayesian optimization to efficiently identify Pareto-efficient (accurate and fair) Machine Learning models. Experiments consider four benchmark (fairness) datasets and four Machine Learning algorithms, and provide an assessment of FanG-HPO against both fairness-aware Machine Learning approaches and two state-of-the-art Bayesian optimization tools addressing multi-objective and energy-aware optimization.

Searching for accurate machine and deep learning models is a computationally expensive and awfully energivorous process. A strategy which has been recently gaining importance to drastically reduce computational time and energy consumed is to exploit the availability of different information sources, with different computational costs and different “fidelity,” typically smaller portions of a large dataset. The multi-source optimization strategy fits into the scheme of Gaussian Process-based Bayesian Optimization. An Augmented Gaussian Process method exploiting multiple information sources (namely, AGP-MISO) is proposed. The Augmented Gaussian Process is trained using only “reliable” information among available sources. A novel acquisition function is defined according to the Augmented Gaussian Process. Computational results are reported related to the optimization of the hyperparameters of a Support Vector Machine (SVM) classifier using two sources: a large dataset—the most expensive one—and a smaller portion of it. A comparison with a traditional Bayesian Optimization approach to optimize the hyperparameters of the SVM classifier on the large dataset only is reported.

This article proposes a new general approach in short-term water demand forecasting based on a two-stage learning process that couples time-series clustering with gene expression programming (GEP). The approach was tested on the real life water demand data of the city of Milan, in Italy. Moreover, multi-scale modeling using a series of head-time was deployed to investigate the optimum temporal resolution under study. Multi-scale modeling was performed based on rearranging hourly based patterns of water demand into 3, 6, 12, and 24 h lead times. Results showed that GEP should receive more attention among the emerging nonlinear modelling techniques if coupled with unsupervised learning algorithms in detailed spherical k-means.

The sensor placement problem is modeled as a multi-objective optimization problem with Boolean decision variables. A new multi objective evolutionary algorithm (MOEA) is proposed for approximating and analyzing the set of Pareto optimal solutions. The evaluation of the objective functions requires the execution of a hydraulic simulation model of the network. To organize the simulation results a data structure is proposed which enables the dynamic representation of a sensor placement and its fitness as a heatmap. This allows the definition of information spaces, in which the fitness of a placement can be represented as a matrix or, in probabilistic terms as a histogram. The key element in the new algorithm is this probabilistic representation which is embedded in a space endowed with a metric based on a specific notion of distance. Among several distances between probability distributions the Wasserstein (WST) distance has been selected: WST has enabled to derive new genetic operators, indicators of the quality of the Pareto set and criteria to choose among the Pareto solutions. The new algorithm has been tested on a benchmark water distribution network with two objective functions showing an improvement over NSGA-II, in particular for low generation counts, making it a good candidate for expensive black-box multi-objective optimization