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Survival analysis is a critical tool for analyzing time-to-event data and extracting valuable clinical insights. Recently, numerous machine learning techniques leveraging neural networks and decision trees have been developed for this task. Among these, the most successful approaches often rely on specific assumptions about the shape of the modeled hazard function. These assumptions include proportional hazard, accelerated failure time, or discrete estimation at a predefined set of time points. In this study, we propose a novel paradigm for survival model design based on the weighted sum of individual fully parametric hazard contributions. We build upon well-known ensemble techniques to deliver a novel contribution to the field by applying additive hazard functions, improving over approaches based on survival or cumulative hazard functions. Furthermore, the proposed model, which we call FPBoost, is the first algorithm to directly optimize the survival likelihood via gradient boosting. We evaluated our approach across a diverse set of datasets, comparing it against a variety of state-of-the-art models. The results demonstrate that FPBoost improves risk estimation, according to both concordance and calibration metrics.

We tackle three optimization problems in which a colored graph, where each node is assigned a color, must be partitioned into colorful connected components. A component is defined as colorful if each color appears at most once. The problems differ in the objective function, which determines which partition is the best one. These problems have applications in community detection, cybersecurity, and bioinformatics. We present integer non-linear formulations, which are then linearized using standard techniques. To solve these formulations, we develop exact branch-and-cut algorithms, embedding various improving techniques, such as valid inequalities, bounds limiting the number of variables, and warm-start and preprocessing techniques. Extensive computational tests on benchmark instances demonstrate the effectiveness of the proposed procedures. The branch-and-cut algorithms can solve reasonably sized instances efficiently. To the best of our knowledge, we are the first to propose an exact algorithm for solving these problems.

Same-day deliveries (SDD) have become a new standard to satisfy the "instant gratification" of online customers. Despite the existing powerful technologies deployed in last-mile delivery, SDD services face new decision-making challenges related to the trade-off between delivery cost and time. In addition, new challenges related to environmental issues, customer satisfaction, or fairness arise. Researchers have explored various approaches to face these challenges in the context of SDD, where stochastic and dynamic data uncertainty plays a fundamental role. In this paper, we carefully review the emerging routing problems and solutions proposed in the existing literature for SDD services. We survey papers related to how to deal with dynamic arrival times of orders, how to allocate time slots to deliveries, how to select the right delivery options, how to design pickup and delivery routes, or how to partition the delivery areas and decide the composition of the fleet. We also formulate and compare models for representative problems elaborating on the pros and cons that might guide practitioners in choosing the most appropriate objectives and constraints. Finally, we sketch challenges and identify future research directions.

Neural cellular automata represent an evolution of the traditional cellular automata model, enhanced by the integration of a deep learning-based transition function. This shift from a manual to a data-driven approach significantly increases the adaptability of these models, enabling their application in diverse domains, including content generation and artificial life. However, their widespread application has been hampered by significant computational requirements. In this work, we introduce the Latent Neural Cellular Automata (LNCA) model, a novel architecture designed to address the resource limitations of neural cellular automata. Our approach shifts the computation from the conventional input space to a specially designed latent space, relying on a pre-trained autoencoder. We apply our model in the context of image restoration, which aims to reconstruct high-quality images from their degraded versions. This modification not only reduces the model's resource consumption but also maintains a flexible framework suitable for various applications. Our model achieves a significant reduction in computational requirements while maintaining high reconstruction fidelity. This increase in efficiency allows for inputs up to 16 times larger than current state-of-the-art neural cellular automata models, using the same resources.

The AI-SPRINT project, launched in 2021 and funded by the European Commission, focuses on the development and implementation of AI applications across the computing continuum. This continuum ensures the coherent integration of computational resources and services from centralized data centers to edge devices, facilitating efficient and adaptive computation and application delivery. AI-SPRINT has achieved significant scientific advances, including streamlined processes, improved efficiency, and the ability to operate in real time, as evidenced by three practical use cases. This paper provides an in-depth examination of these applications -- Personalized Healthcare, Maintenance and Inspection, and Farming 4.0 -- highlighting their practical implementation and the objectives achieved with the integration of AI-SPRINT technologies. We analyze how the proposed toolchain effectively addresses a range of challenges and refines processes, discussing its relevance and impact in multiple domains. After a comprehensive overview of the main AI-SPRINT tools used in these scenarios, the paper summarizes of the findings and key lessons learned.

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.

Survival analysis is a fundamental tool in medicine, modeling the time until an event of interest occurs in a population. However, in real-world applications, survival data are often incomplete, censored, distributed, and confidential, especially in healthcare settings where privacy is critical. The scarcity of data can severely limit the scalability of survival models to distributed applications that rely on large data pools. Federated learning is a promising technique that enables machine learning models to be trained on multiple datasets without compromising user privacy, making it particularly well-suited for addressing the challenges of survival data and large-scale survival applications. Despite significant developments in federated learning for classification and regression, many directions remain unexplored in the context of survival analysis. In this work, we propose an extension of the Federated Survival Forest algorithm, called FedSurF++. This federated ensemble method constructs random survival forests in heterogeneous federations. Specifically, we investigate several new tree sampling methods from client forests and compare the results with state-of-the-art survival models based on neural networks. The key advantage of FedSurF++ is its ability to achieve comparable performance to existing methods while requiring only a single communication round to complete. The extensive empirical investigation results in a significant improvement from the algorithmic and privacy preservation perspectives, making the original FedSurF algorithm more efficient, robust, and private. We also present results on two real-world datasets demonstrating the success of FedSurF++ in real-world healthcare studies. Our results underscore the potential of FedSurF++ to improve the scalability and effectiveness of survival analysis in distributed settings while preserving user privacy.

This study explores the potential of using public transportation systems for freight delivery, where we intend to utilize the spare capacities of public vehicles like buses, trams, metros, and trains, particularly during off-peak hours, to transport packages within the city instead of using dedicated delivery vehicles. The study contributes {to the growing} literature on innovative strategies for performing sustainable last mile deliveries. We study an operational level problem called the Three-Tier Delivery Problem on Public Transportation, where packages are first transported from the Consolidation and Distribution Center (CDC) to nearby public vehicle stations by delivery trucks. From there, public vehicles transport them into the city area. The last leg of the delivery is performed to deliver the packages to their respective customers using green vehicles or eco-friendly systems. We propose mixed-integer linear programming formulations to study the transport of packages from the CDC to the customers, use decomposition approaches to solve them, and provide numerical experiments to demonstrate the efficiency and effectiveness of the system. Our results show that this system has the potential to drastically reduce the length of trips performed by dedicated delivery vehicles, thereby reducing the negative social and environmental impacts of existing last mile delivery systems.

The remarkable proliferation of deep learning across various industries has underscored the importance of data privacy and security in AI pipelines. As the evolution of sophisticated Membership Inference Attacks (MIAs) threatens the secrecy of individual-specific information used for training deep learning models, Differential Privacy (DP) raises as one of the most utilized techniques to protect models against malicious attacks. However, despite its proven theoretical properties, DP can significantly hamper model performance and increase training time, turning its use impractical in real-world scenarios. Tackling this issue, we present Discriminative Adversarial Privacy (DAP), a novel learning technique designed to address the limitations of DP by achieving a balance between model performance, speed, and privacy. DAP relies on adversarial training based on a novel loss function able to minimise the prediction error while maximising the MIA's error. In addition, we introduce a novel metric named Accuracy Over Privacy (AOP) to capture the performance-privacy trade-off. Finally, to validate our claims, we compare DAP with diverse DP scenarios, providing an analysis of the results from performance, time, and privacy preservation perspectives.

In last-mile delivery logistics, peer-to-peer logistic platforms play an important role in connecting senders, customers, and independent carriers to fulfill delivery requests. Since the carriers are not under the platform's control, the platform has to anticipate their reactions, while deciding how to allocate the delivery operations. Indeed, carriers' decisions largely affect the platform's revenue. In this paper, we model this problem using bilevel programming. At the upper level, the platform decides how to assign the orders to the carriers; at the lower level, each carrier solves a profitable tour problem to determine which offered requests to accept, based on her own profit maximization. Possibly, the platform can influence carriers' decisions by determining also the compensation paid for each accepted request. The two considered settings result in two different formulations: the bilevel profitable tour problem with fixed compensation margins and with margin decisions, respectively. For each of them, we propose single-level reformulations and alternative formulations where the lower-level routing variables are projected out. A branch-and-cut algorithm is proposed to solve the bilevel models, with a tailored warm-start heuristic used to speed up the solution process. Extensive computational tests are performed to compare the proposed formulations and analyze solution characteristics.

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes.

Survival analysis is a subfield of statistics concerned with modeling the occurrence time of a particular event of interest for a population. Survival analysis found widespread applications in healthcare, engineering, and social sciences. However, real-world applications involve survival datasets that are distributed, incomplete, censored, and confidential. In this context, federated learning can tremendously improve the performance of survival analysis applications. Federated learning provides a set of privacy-preserving techniques to jointly train machine learning models on multiple datasets without compromising user privacy, leading to a better generalization performance. However, despite the widespread development of federated learning in recent AI research, few studies focus on federated survival analysis. In this work, we present a novel federated algorithm for survival analysis based on one of the most successful survival models, the random survival forest. We call the proposed method Federated Survival Forest (FedSurF). With a single communication round, FedSurF obtains a discriminative power comparable to deep-learning-based federated models trained over hundreds of federated iterations. Moreover, FedSurF retains all the advantages of random forests, namely low computational cost and natural handling of missing values and incomplete datasets. These advantages are especially desirable in real-world federated environments with multiple small datasets stored on devices with low computational capabilities. Numerical experiments compare FedSurF with state-of-the-art survival models in federated networks, showing how FedSurF outperforms deep-learning-based federated algorithms in realistic environments with non-identically distributed data.

Survival analysis studies time-modeling techniques for an event of interest occurring for a population. Survival analysis found widespread applications in healthcare, engineering, and social sciences. However, the data needed to train survival models are often distributed, incomplete, censored, and confidential. In this context, federated learning can be exploited to tremendously improve the quality of the models trained on distributed data while preserving user privacy. However, federated survival analysis is still in its early development, and there is no common benchmarking dataset to test federated survival models. This work provides a novel technique for constructing realistic heterogeneous datasets by starting from existing non-federated datasets in a reproducible way. Specifically, we propose two dataset-splitting algorithms based on the Dirichlet distribution to assign each data sample to a carefully chosen client: quantity-skewed splitting and label-skewed splitting. Furthermore, these algorithms allow for obtaining different levels of heterogeneity by changing a single hyperparameter. Finally, numerical experiments provide a quantitative evaluation of the heterogeneity level using log-rank tests and a qualitative analysis of the generated splits. The implementation of the proposed methods is publicly available in favor of reproducibility and to encourage common practices to simulate federated environments for survival analysis.

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.

In social network analysis, the size of the k-core, i.e., the maximal induced subgraph of the network with minimum degree at least k, is frequently adopted as a typical metric to evaluate the cohesiveness of a community. We address the Collapsed k-Core Problem, which seeks to find a subset of $b$ users, namely the most critical users of the network, the removal of which results in the smallest possible k-core. For the first time, both the problem of finding the k-core of a network and the Collapsed k-Core Problem are formulated using mathematical programming. On the one hand, we model the Collapsed k-Core Problem as a natural deletion-round-indexed Integer Linear formulation. On the other hand, we provide two bilevel programs for the problem, which differ in the way in which the k-core identification problem is formulated at the lower level. The first bilevel formulation is reformulated as a single-level sparse model, exploiting a Benders-like decomposition approach. To derive the second bilevel model, we provide a linear formulation for finding the k-core and use it to state the lower-level problem. We then dualize the lower level and obtain a compact Mixed-Integer Nonlinear single-level problem reformulation. We additionally derive a combinatorial lower bound on the value of the optimal solution and describe some pre-processing procedures and valid inequalities for the three formulations. The performance of the proposed formulations is compared on a set of benchmarking instances with the existing state-of-the-art solver for mixed-integer bilevel problems proposed in (Fischetti et al., A New General-Purpose Algorithm for Mixed-Integer Bilevel Linear Programs, Operations Research 65(6), 2017)., Comment: Accepted for publication in European Journal of Operational Research; doi: 10.1016/j.ejor.2023.04.038

Consolidation of loose packages into transport units is a fundamental activity offered by logistics service-providers. Moving the transport units instead of loose packages is faster (with one movement only, multiple packages are loaded instead of having one load operation for each package), safer (chances of damage and loss is reduced) and cheaper. One of the typical objective of consolidation problems is the minimization of the number of transport units used, e.g. containers. In air transportation, however, transport units have multiple aspects which concur in the calculation of the cost and thus optimization in the number and characteristics of the transport units is required. In this paper, we present the air transport unit consolidation problem where the aim is to determine how to consolidate loose packages in transport units with the goal of minimizing the corresponding cost. The problem is a variant of the three-dimensional bin packing problem where the objective function is formulated according to the way costs are calculated in the air transport business. In addition, side constraints are included to take into account specific requirements. We propose a heuristic algorithm which construct an initial feasible solution and then improves it through a local search algorithm. Computational tests on randomly generated instances show that the algorithm provides high quality solutions in a reasonable computing time. In addition, tests on real data show that it improves solutions found in practice by the company providing the data.

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., Comment: 31 pages, 12 figures

In this paper, we study a sequential decision-making problem faced by e-commerce carriers related to when to send out a vehicle from the central depot to serve customer requests, and in which order to provide the service, under the assumption that the time at which parcels arrive at the depot is stochastic and dynamic. The objective is to maximize the expected number of parcels that can be delivered during service hours. We propose two reinforcement learning (RL) approaches for solving this problem. These approaches rely on a look-ahead strategy in which future release dates are sampled in a Monte-Carlo fashion and a batch approach is used to approximate future routes. Both RL approaches are based on value function approximation - one combines it with a consensus function (VFA-CF) and the other one with a two-stage stochastic integer linear programming model (VFA-2S). VFA-CF and VFA-2S do not need extensive training as they are based on very few hyper-parameters and make good use of integer linear programming (ILP) and branch-and-cut-based exact methods to improve the quality of decisions. We also establish sufficient conditions for partial characterization of optimal policy and integrate them into VFA-CF/VFA-2S. In an empirical study, we conduct a competitive analysis using upper bounds with perfect information. We also show that VFA-CF and VFA-2S greatly outperform alternative approaches that: 1) do not rely on future information, or 2) are based on point estimation of future information, or 3) employ heuristics rather than exact methods, or 4) use exact evaluations of future rewards., Comment: The final version will appear in Transportation Science

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.

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., Comment: 49 pages, 39 figures. arXiv admin note: substantial text overlap with arXiv:2102.07647

Privacy regulation laws, such as GDPR, impose transparency and security as design pillars for data processing algorithms. In this context, federated learning is one of the most influential frameworks for privacy-preserving distributed machine learning, achieving astounding results in many natural language processing and computer vision tasks. Several federated learning frameworks employ differential privacy to prevent private data leakage to unauthorized parties and malicious attackers. Many studies, however, highlight the vulnerabilities of standard federated learning to poisoning and inference, thus raising concerns about potential risks for sensitive data. To address this issue, we present SGDE, a generative data exchange protocol that improves user security and machine learning performance in a cross-silo federation. The core of SGDE is to share data generators with strong differential privacy guarantees trained on private data instead of communicating explicit gradient information. These generators synthesize an arbitrarily large amount of data that retain the distinctive features of private samples but differ substantially. In this work, SGDE is tested in a cross-silo federated network on images and tabular datasets, exploiting beta-variational autoencoders as data generators. From the results, the inclusion of SGDE turns out to improve task accuracy and fairness, as well as resilience to the most influential attacks on federated learning.

Thanks to the compact design and multi-functional light-manipulation capabilities, reconfigurable metalenses, which consist of arrays of sub-wavelength meta-atoms, offer unique opportunities for advanced optical systems, from microscopy to augmented reality platforms. Although poorly explored in the context of reconfigurable metalens, thermo-optical effects in resonant silicon nanoresonators have recently emerged as a viable strategy to realize tunable meta-atoms. In this work, we report the proof-of-concept design of an ultrathin (300 nm thick) and thermo-optically reconfigurable silicon metalens operating at a fixed, visible wavelength (632 nm). Importantly, we demonstrate continuous, linear modulation of the focal-length up to 21% (from 165 $\mu$m at 20$\deg$C to 135 $\mu$m at 260$\deg$C). Operating under right-circularly polarized light, our metalens exhibits an average conversion efficiency of 26%, close to mechanically modulated devices, and has a diffraction-limited performance. Overall, we envision that, combined with machine-learning algorithms for further optimization of the meta-atoms, thermally-reconfigurable metalenses with improved performance will be possible. Also, the generality of this approach could offer inspiration for the realization of active metasurfaces with other emerging material within field of thermo-nanophotonics.