arXiv subjects

Francesco Archetti

Publications and source records attributed to Francesco Archetti.

At least 19 recordsLinked to original sources

arXiv2026

Diffusion enabled Optimal Transport distances for graph matching

This paper introduces Diffusion Semi-Relaxed Fused Gromov-Wasserstein (DsrFGW), a novel method for graph comparison that unifies node features and structural connectivity through optimal transport. While traditional Gromov-Wasserstein and semi-relaxed variants (srGW, srFGW) capture graph structure, they often struggle with sparse, noisy, or partially observed graphs. Inspired by Graph Diffusion Distance, which posits graphs are similar if they enable similar information transmission patterns, DsrFGW incorporates diffusion processes allowing information propagation across nodes, capturing local and global structural patterns while reducing sensitivity to noise or missing edges. An extensive evaluation on 36 synthetic pairwise graph matching tasks (easy, medium, hard) demonstrates consistent superiority over srFGW, achieving accuracy improvements of 0-20 percentage points and dramatic Adjusted Rand Index (ARI) gains: in medium-difficulty scenarios, srFGW often achieves negative ARI (worse than random) while DsrFGW offers better performance in terms of both internal and external clustering quality measures (i.e., Adjusted Rank Index and Accuracy with respect to the true underlying clusters, respectively). Even under severe noise, DsrFGW improves clustering quality in 92% of the synthetic tasks with optimal diffusion scales adapting to problem difficulty, establishing DsrFGW as a robust framework for graph comparison under structural uncertainty.

cs.LG↗

arXiv2026

Wasserstein-enabled characterization of designs and myopic decisions in Bayesian Optimization

Impractical assumptions, an inherently myopic nature, and the crucial role of the initial design, all together contribute to making theoretical convergence proofs of little value in real-life Bayesian Optimization applications. In this paper, we propose a novel characterization of the design depending on its distributional properties, separately measured with respect to the coverage of the search space and the concentration around the best observed function value. These measures are based on the Wasserstein distance and enable a model-free evaluation of the information value of the design before deciding the next query. Then, embracing the myopic nature of Bayesian Optimization, we take an empirical approach to analyze the relation between the proposed characterization of the design and the quality of the next query. Ultimately, we provide important and useful insights that might inspire the definition of a new generation of acquisition functions in Bayesian Optimization.

math.OC↗

arXiv2026

Weighted Wasserstein Barycenter of Gaussian Processes for exotic Bayesian Optimization tasks

Exploiting the analogy between Gaussian Distributions and Gaussian Processes' posterior, we present how the weighted Wasserstein Barycenter of Gaussian Processes (W2BGP) can be used to unify, under a common framework, different exotic Bayesian Optimization (BO) tasks. Specifically, collaborative/federated BO, (synchronous) batch BO, and multi-fidelity BO are considered in this paper. Our empirical analysis proves that each one of these tasks requires just an appropriate weighting schema for the W2BGP, while the entire framework remains untouched. Moreover, we demonstrate that the most well-known BO acquisition functions can be easily re-interpreted under the proposed framework and also enable a more computationally efficient way to deal with the computation of the Wasserstein Barycenter, compared with state-of-the-art methods from the Machine Learning literature. Finally, research perspectives branching from the proposed approach are presented.

cs.LG↗

arXiv2025

Structural Vulnerability Assessment in Urban Transport Networks: A Network-Wide Geometric Approach Using Gromov-Wasserstein

Urban transportation networks are inherently vulnerable to disruptions that affect connectivity and passenger mobility. Traditional graph_theoretic metrics, such as betweenness and degree centrality, offer insights into local network structure but often fail to capture global structural distortions resulting from link failures. On the other hand, global indices, such as those based on spectral analysis of the networks graph, fail in identifying critical elements. This study proposes to quantify the structural modifications implied by the disruption of single elements in a transportation network through the Gromov-Wasserstein distance. Specifically, we iteratively remove one single edge from the original network to simulate a disruptive event and then compute the Gromov-Wasserstein distance between the original network and the disrupted one. Finally, edges are ranked depending on the observed Gromov-Wasserstein distance: the higher the value of the distance, the more critical the edge is in terms. Two transportation networks from Berlin are considered in the experiments, namely Berlin Friedrichshain Center (BFC) and Berlin Tiergarten (BT). Results reveal that Gromov-Wasserstein is largely uncorrelated with edge betweenness (rho<0.1), proving its ability to capture vulnerability aspects overlooked by local network measures. Moreover, Gromov-Wasserstein exhibits an almost perfect correlation (rho=0.9999) against a proxy measure of the transportation service level, that is, the increase in the maximum shortest path. As a result, the Gromov-Wasserstein distance can be used to rank edges depending on their criticality with respect to their individual impact on the overall infrastructure and level, allowing for prioritizing maintenance, emergency planning, and enhancing the resilience of the urban transport network.

physics.soc-ph↗

arXiv2025

Gromov-Wasserstein and optimal transport: from assignment problems to probabilistic numeric

The assignment problem, a cornerstone of operations research, seeks an optimal one-to-one mapping between agents and tasks to minimize total cost. This work traces its evolution from classical formulations and algorithms to modern optimal transport (OT) theory, positioning the Quadratic Assignment Problem (QAP) and related structural matching tasks within this framework. We connect the linear assignment problem to Monge's transport problem, Kantorovich's relaxation, and Wasserstein distances, then extend to cases where source and target lie in different metric-measure spaces requiring Gromov-Wasserstein (GW) distances. GW formulations, including the fused GW variant that integrates structural and feature information, naturally address QAP-like problems by optimizing alignment based on both intra-domain distances and cross-domain attributes. Applications include graph matching, keypoint correspondence, and feature-based assignments. We present exact solvers, Genetic Algorithms (GA), and multiple GW variants, including a proposed multi-initialization strategy (GW-MultiInit) that mitigates the risk of getting stuck in local optima alongside entropic Sinkhorn-based approximations and fused GW. Computational experiments on capacitated QAP instances show that GW-MultiInit consistently achieves near-optimal solutions and scales efficiently to large problems where exact methods become impractical, while parameterized EGW and FGW variants provide flexible trade-offs between accuracy and runtime. Our findings provide theoretical foundations, computational insights, and practical guidelines for applying OT and GW methods to QAP and other real-world matching problems, such as those in machine learning and logistics.

math.OC↗

arXiv2025

Wasserstein Barycenter Gaussian Process based Bayesian Optimization

Gaussian Process based Bayesian Optimization is a widely applied algorithm to learn and optimize under uncertainty, well-known for its sample efficiency. However, recently -- and more frequently -- research studies have empirically demonstrated that the Gaussian Process fitting procedure at its core could be its most relevant weakness. Fitting a Gaussian Process means tuning its kernel's hyperparameters to a set of observations, but the common Maximum Likelihood Estimation technique, usually appropriate for learning tasks, has shown different criticalities in Bayesian Optimization, making theoretical analysis of this algorithm an open challenge. Exploiting the analogy between Gaussian Processes and Gaussian Distributions, we present a new approach which uses a prefixed set of hyperparameters values to fit as many Gaussian Processes and then combines them into a unique model as a Wasserstein Barycenter of Gaussian Processes. We considered both "easy" test problems and others known to undermine the \textit{vanilla} Bayesian Optimization algorithm. The new method, namely Wasserstein Barycenter Gausssian Process based Bayesian Optimization (WBGP-BO), resulted promising and able to converge to the optimum, contrary to vanilla Bayesian Optimization, also on the most "tricky" test problems.

stat.ML↗

arXiv2023

A Bayesian approach for prompt optimization in pre-trained language models

A prompt is a sequence of symbol or tokens, selected from a vocabulary according to some rule, which is prepended/concatenated to a textual query. A key problem is how to select the sequence of tokens: in this paper we formulate it as a combinatorial optimization problem. The high dimensionality of the token space com-pounded by the length of the prompt sequence requires a very efficient solution. In this paper we propose a Bayesian optimization method, executed in a continuous em-bedding of the combinatorial space. In this paper we focus on hard prompt tuning (HPT) which directly searches for discrete tokens to be added to the text input with-out requiring access to the large language model (LLM) and can be used also when LLM is available only as a black-box. This is critically important if LLMs are made available in the Model as a Service (MaaS) manner as in GPT-4. The current manu-script is focused on the optimization of discrete prompts for classification tasks. The discrete prompts give rise to difficult combinatorial optimization problem which easily become intractable given the dimension of the token space in realistic applications. The optimization method considered in this paper is Bayesian optimization (BO) which has become the dominant approach in black-box optimization for its sample efficiency along with its modular structure and versatility. In this paper we use BoTorch, a library for Bayesian optimization research built on top of pyTorch. Albeit preliminary and obtained using a 'vanilla' version of BO, the experiments on RoB-ERTa on six benchmarks, show a good performance across a variety of tasks and enable an analysis of the tradeoff between size of the search space, accuracy and wall clock time.

cs.LG↗

arXiv2022

Gaussian Process regression over discrete probability measures: on the non-stationarity relation between Euclidean and Wasserstein Squared Exponential Kernels

Gaussian Process regression is a kernel method successfully adopted in many real-life applications. Recently, there is a growing interest on extending this method to non-Euclidean input spaces, like the one considered in this paper, consisting of probability measures. Although a Positive Definite kernel can be defined by using a suitable distance -- the Wasserstein distance -- the common procedure for learning the Gaussian Process model can fail due to numerical issues, arising earlier and more frequently than in the case of an Euclidean input space and, as demonstrated in this paper, that cannot be avoided by adding artificial noise (nugget effect) as usually done. This paper uncovers the main reason of these issues, that is a non-stationarity relationship between the Wasserstein-based squared exponential kernel and its Euclidean-based counterpart. As a relevant result, the Gaussian Process model is learned by assuming the input space as Euclidean and then an algebraic transformation, based on the uncovered relation, is used to transform it into a non-stationary and Wasserstein-based Gaussian Process model over probability measures. This algebraic transformation is simpler than log-exp maps used in the case of data belonging to Riemannian manifolds and recently extended to consider the pseudo-Riemannian structure of an input space equipped with the Wasserstein distance.

cs.LG↗

arXiv2022

BORA: Bayesian Optimization for Resource Allocation

Optimal resource allocation is gaining a renewed interest due its relevance as a core problem in managing, over time, cloud and high-performance computing facilities. Semi-Bandit Feedback (SBF) is the reference method for efficiently solving this problem. In this paper we propose (i) an extension of the optimal resource allocation to a more general class of problems, specifically with resources availability changing over time, and (ii) Bayesian Optimization as a more efficient alternative to SBF. Three algorithms for Bayesian Optimization for Resource Allocation, namely BORA, are presented, working on allocation decisions represented as numerical vectors or distributions. The second option required to consider the Wasserstein distance as a more suitable metric to use into one of the BORA algorithms. Results on (i) the original SBF case study proposed in the literature, and (ii) a real-life application (i.e., the optimization of multi-channel marketing) empirically prove that BORA is a more efficient and effective learning-and-optimization framework than SBF.

cs.LG↗

arXiv2022

Fair and Green Hyperparameter Optimization via Multi-objective and Multiple Information Source Bayesian Optimization

There is a consensus 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 optimize accuracy constrained to some threshold on fairness -- they could drastically increase the energy consumption in the case of large datasets. In this paper we propose FanG-HPO, a Fair and Green Hyperparameter Optimization (HPO) approach based on both multi-objective and multiple information source Bayesian optimization. FanG-HPO uses subsets of the large dataset (aka information sources) to obtain cheap approximations of both accuracy and fairness, and multi-objective Bayesian Optimization to efficiently identify Pareto-efficient machine learning models. Experiments consider two benchmark (fairness) datasets and two machine learning algorithms (XGBoost and Multi-Layer Perceptron), and provide an assessment of FanG-HPO against both fairness-aware machine learning algorithms and hyperparameter optimization via a multi-objective single-source optimization algorithm in BoTorch, a state-of-the-art platform for Bayesian Optimization.

cs.LG↗

arXiv2021

Gamifying optimization: a Wasserstein distance-based analysis of human search

The main objective of this paper is to outline a theoretical framework to characterise humans' decision-making strategies under uncertainty, in particular active learning in a black-box optimization task and trading-off between information gathering (exploration) and reward seeking (exploitation). Humans' decisions making according to these two objectives can be modelled in terms of Pareto rationality. If a decision set contains a Pareto efficient strategy, a rational decision maker should always select the dominant strategy over its dominated alternatives. A distance from the Pareto frontier determines whether a choice is Pareto rational. To collect data about humans' strategies we have used a gaming application that shows the game field, with previous decisions and observations, as well as the score obtained. The key element in this paper is the representation of behavioural patterns of human learners as a discrete probability distribution. This maps the problem of the characterization of humans' behaviour into a space whose elements are probability distributions structured by a distance between histograms, namely the Wasserstein distance (WST). The distributional analysis gives new insights about human search strategies and their deviations from Pareto rationality. Since the uncertainty is one of the two objectives defining the Pareto frontier, the analysis has been performed for three different uncertainty quantification measures to identify which better explains the Pareto compliant behavioural patterns. Beside the analysis of individual patterns WST has also enabled a global analysis computing the barycenters and WST k-means clustering. A further analysis has been performed by a decision tree to relate non-Paretian behaviour, characterized by exasperated exploitation, to the dynamics of the evolution of the reward seeking process.

math.OC↗

arXiv2021

Risk Aware Optimization of Water Sensor Placement

Optimal sensor placement (SP) usually minimizes an impact measure, such as the amount of contaminated water or the number of inhabitants affected before detection. The common choice is to minimize the minimum detection time (MDT) averaged over a set of contamination events, with contaminant injected at a different location. Given a SP, propagation is simulated through a hydraulic software model of the network to obtain spatio-temporal concentrations and the average MDT. Searching for an optimal SP is NP-hard: even for mid-size networks, efficient search methods are required, among which evolutionary approaches are often used. A bi-objective formalization is proposed: minimizing the average MDT and its standard deviation, that is the risk to detect some contamination event too late than the average MDT. We propose a data structure (sort of spatio-temporal heatmap) collecting simulation outcomes for every SP and particularly suitable for evolutionary optimization. Indeed, the proposed data structure enabled a convergence analysis of a population-based algorithm, leading to the identification of indicators for detecting problem-specific converge issues which could be generalized to other similar problems. We used Pymoo, a recent Python framework flexible enough to incorporate our problem specific termination criterion. Results on a benchmark and a real-world network are presented.

eess.SP↗

arXiv2021

MISO-wiLDCosts: Multi Information Source Optimization with Location Dependent Costs

This paper addresses black-box optimization over multiple information sources whose both fidelity and query cost change over the search space, that is they are location dependent. The approach uses: (i) an Augmented Gaussian Process, recently proposed in multi-information source optimization as a single model of the objective function over search space and sources, and (ii) a Gaussian Process to model the location-dependent cost of each source. The former is used into a Confidence Bound based acquisition function to select the next source and location to query, while the latter is used to penalize the value of the acquisition depending on the expected query cost for any source-location pair. The proposed approach is evaluated on a set of Hyperparameters Optimization tasks, consisting of two Machine Learning classifiers and three datasets of different sizes.

cs.LG↗

arXiv2021

Uncertainty quantification and exploration-exploitation trade-off in humans

The main objective of this paper is to outline a theoretical framework to analyse how humans' decision-making strategies under uncertainty manage the trade-off between information gathering (exploration) and reward seeking (exploitation). A key observation, motivating this line of research, is the awareness that human learners are amazingly fast and effective at adapting to unfamiliar environments and incorporating upcoming knowledge: this is an intriguing behaviour for cognitive sciences as well as an important challenge for Machine Learning. The target problem considered is active learning in a black-box optimization task and more specifically how the exploration/exploitation dilemma can be modelled within Gaussian Process based Bayesian Optimization framework, which is in turn based on uncertainty quantification. The main contribution is to analyse humans' decisions with respect to Pareto rationality where the two objectives are improvement expected and uncertainty quantification. According to this Pareto rationality model, if a decision set contains a Pareto efficient (dominant) strategy, a rational decision maker should always select the dominant strategy over its dominated alternatives. The distance from the Pareto frontier determines whether a choice is (Pareto) rational (i.e., lays on the frontier) or is associated to "exasperate" exploration. However, since the uncertainty is one of the two objectives defining the Pareto frontier, we have investigated three different uncertainty quantification measures and selected the one resulting more compliant with the Pareto rationality model proposed. The key result is an analytical framework to characterize how deviations from "rationality" depend on uncertainty quantifications and the evolution of the reward seeking process.

cs.AI↗

arXiv2020

Green Machine Learning via Augmented Gaussian Processes and Multi-Information Source Optimization

Searching for accurate Machine and Deep Learning models is a computationally expensive and awfully energivorous process. A strategy which has been gaining recently 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.

cs.LG↗

arXiv2020

Resilience in urban networked infrastructure: the case of Water Distribution Systems

Resilience is meant as the capability of a networked infrastructure to provide its service even if some components fail: in this paper we focus on how resilience depends both on net-wide measures of connectivity and the role of a single component. This paper has two objectives: first to show how a set of global measures can be obtained using techniques from network theory, in particular how the spectral analysis of the adjacency and Laplacian matrices and a similarity measure based on Jensen-Shannon divergence allows us to obtain a characteriza-tion of global connectivity which is both mathematically sound and operational. Second, how a clustering method in the subspace spanned by the l smallest eigen-vectors of the Laplacian matrix allows us to identify the edges of the network whose failure breaks down the network. Even if most of the analysis can be applied to a generic networked infrastructure, specific references will be made to Water Distribution Networks (WDN).

cs.SI↗

arXiv2020

Composition of kernel and acquisition functions for High Dimensional Bayesian Optimization

Bayesian Optimization has become the reference method for the global optimization of black box, expensive and possibly noisy functions. Bayesian Op-timization learns a probabilistic model about the objective function, usually a Gaussian Process, and builds, depending on its mean and variance, an acquisition function whose optimizer yields the new evaluation point, leading to update the probabilistic surrogate model. Despite its sample efficiency, Bayesian Optimiza-tion does not scale well with the dimensions of the problem. The optimization of the acquisition function has received less attention because its computational cost is usually considered negligible compared to that of the evaluation of the objec-tive function. Its efficient optimization is often inhibited, particularly in high di-mensional problems, by multiple extrema. In this paper we leverage the addition-ality of the objective function into mapping both the kernel and the acquisition function of the Bayesian Optimization in lower dimensional subspaces. This ap-proach makes more efficient the learning/updating of the probabilistic surrogate model and allows an efficient optimization of the acquisition function. Experi-mental results are presented for real-life application, that is the control of pumps in urban water distribution systems.

stat.ML↗

arXiv2020

Learning Optimal Control of Water Distribution Networks through Sequential Model-based Optimization

Sequential Model-based Bayesian Optimization has been successful-ly applied to several application domains, characterized by complex search spaces, such as Automated Machine Learning and Neural Architecture Search. This paper focuses on optimal control problems, proposing a Sequential Model-based Bayesian Optimization framework to learn optimal control strategies. A quite general formalization of the problem is provided, along with a specific instance related to optimization of pumping operations in an urban Water Distri-bution Network. Relevant results on a real-life Water Distribution Network are reported, comparing different possible choices for the proposed framework.

eess.SY↗