arXiv subjects

Michele Lombardi

Publications and source records attributed to Michele Lombardi.

At least 19 recordsLinked to original sources

arXiv2026

The Paradox of Strategic Altruism

Can altruism serve as the behavioral foundation for efficient institutional design? We study full implementation in Berge equilibrium, the solution concept that formalizes strategic altruism: each agent's opponents collectively maximize her payoff. While Berge equilibrium resolves the Prisoner's Dilemma and can eliminate cooperation failures in social dilemmas, we show that this optimism does not survive the move from individual behavior to institutional design. First, we show that the weak Pareto optimal rule is not implementable in Berge equilibrium. Second, on the unrestricted domain of strict preferences, any social choice rule that is both weakly Pareto efficient and implementable in Berge equilibrium must be dictatorial. Finally, we show that Berge implementability is strictly more demanding than Nash implementability: every social goal achievable under strategic altruism is also achievable under self-interest, but not vice versa. The very feature that makes Berge equilibrium appealing at the behavioral level, that is, opponents protecting each agent's payoff, is precisely what forecloses efficient, non-dictatorial institutions at the design level.

econ.TH↗

arXiv2026

Hybrid Reinforcement Learning and Search for Flight Trajectory Planning

This paper explores the combination of Reinforcement Learning (RL) and search-based path planners to speed up the optimization of flight paths for airliners, where in case of emergency a fast route re-calculation can be crucial. The fundamental idea is to train an RL Agent to pre-compute near-optimal paths based on location and atmospheric data and use those at runtime to constrain the underlying path planning solver and find a solution within a certain distance from the initial guess. The approach effectively reduces the size of the solver's search space, significantly speeding up route optimization. Although global optimality is not guaranteed, empirical results conducted with Airbus aircraft's performance models show that fuel consumption remains nearly identical to that of an unconstrained solver, with deviations typically within 1%. At the same time, computation speed can be improved by up to 50% as compared to using a conventional solver alone. This paper discusses the theoretical framework, the different implementation strategies, the adopted testing procedures, the obtained results and finally further possible developments and future perspectives.can be improved by up to 50% as compared to using a conventional solver alone.

cs.AI↗

arXiv2026

Revealed Preference Analysis of Shapley-Scarf Housing Markets

We ask what the reallocation of indivisible objects reveals about the market that produced it. A central authority assigns the objects, after which recipients exchange them among themselves. Preferences are never observed, and individuals of the same type have identical preferences. A reallocation is rationalizable as Pareto efficient and individually rational exactly when a directed graph built from the data is acyclic, and as weak core-stable exactly when a mixed graph admits an orientation acyclic within types and free of alternating cycles. Deciding the latter is NP-complete, and on the single-crossing domain, although the test becomes more restrictive, it turns out to be more useful in practice. Both properties are less demanding than the strict core, so their rejection eliminates a broader set of possibilities. We apply the tests to administrative data on social housing lettings in England.

econ.TH↗

arXiv2026

SEER: Supervised Learning to Control Energetic Reasoning

One of the main strengths of Constraint Programming is the ability to reduce the search space via propagation. However, propagation is a double-edged sword, with more pruning power coming at the price of larger computation time. For each problem constraint, the best propagator depends on the specific instance and may change at search time. In the literature, Machine Learning (ML) techniques and activity-based heuristics have been applied respectively for choosing (statically) the propagators for a batch of problems and to adapt (dynamically) the propagation strength. We propose to merge those efforts by using an oracle function, obtained via ML, to decide whether to run complex propagators for a target constraint. A combination of design choices makes the approach flexible and easy to embed in state-of-the-art solvers. In this paper, we focus on investigating the feasibility of building an oracle for the Energetic Reasoning propagator. Our experiments show that high prediction accuracy can be obtained, provide suggestions for classification features, and highlight important issues to address when building such an oracle.

cs.AI↗

arXiv2026

Score Function Gradient Estimation to Widen the Applicability of Decision-Focused Learning

Many real-world optimization problems contain parameters that are unknown before deployment time, either due to stochasticity or to lack of information (e.g., demand or travel times in delivery problems). A common strategy in such cases is to estimate said parameters via machine learning (ML) models trained to minimize the prediction error, which however is not necessarily aligned with the downstream task-level error. The decision-focused learning (DFL) paradigm overcomes this limitation by training to directly minimize a task loss, e.g. regret. Since the latter has non-informative gradients for combinatorial problems, state-of-the-art DFL methods introduce surrogates and approximations that enable training. But these methods exploit specific assumptions about the problem structures (e.g., convex or linear problems, unknown parameters only in the objective function). We propose an alternative method that makes no such assumptions, it combines stochastic smoothing with score function gradient estimation which works on any task loss. This opens up the use of DFL methods to nonlinear objectives, uncertain parameters in the problem constraints, and even two-stage stochastic optimization. Experiments show that it typically requires more epochs, but that it is on par with specialized methods and performs especially well for the difficult case of problems with uncertainty in the constraints, in terms of solution quality, scalability, or both.

cs.LG↗

arXiv2026

How to Evaluate and Refine your CAM

Class attribution maps (CAMs) provide local explanations for the decisions of convolutional neural networks. While widely used in practice, the evaluation of CAMs remains challenging due to the lack of ground-truth explanations, making it difficult to evaluate the soundness of existing metrics. Independently, most commonly used CAM methods produce low-resolution attribution maps, which limits their usefulness for detailed interpretability. To address the evaluation challenge, we introduce a synthetic dataset with ground-truth attributions that enables a rigorous comparison of CAM evaluation metrics. Using this dataset, we analyze existing metrics and propose ARCC, a new composite metric that more reliably identifies faithful explanations. To address the low resolution issue, we introduce RefineCAM, a method that produces high-resolution attribution maps by aggregating CAMs across multiple network layers. Our results show that RefineCAM consistently outperforms existing methods according to the proposed evaluation.

cs.CV↗

arXiv2025

Scalable Decision Focused Learning via Online Trainable Surrogates

Decision support systems often rely on solving complex optimization problems that may require to estimate uncertain parameters beforehand. Recent studies have shown how using traditionally trained estimators for this task can lead to suboptimal solutions. Using the actual decision cost as a loss function (called Decision Focused Learning) can address this issue, but with a severe loss of scalability at training time. To address this issue, we propose an acceleration method based on replacing costly loss function evaluations with an efficient surrogate. Unlike previously defined surrogates, our approach relies on unbiased estimators reducing the risk of spurious local optima and can provide information on its local confidence allowing one to switch to a fallback method when needed. Furthermore, the surrogate is designed for a black-box setting, which enables compensating for simplifications in the optimization model and accounting for recourse actions during cost computation. In our results, the method reduces costly inner solver calls, with a solution quality comparable to other state-of-the-art techniques.

cs.LG↗

arXiv2025

SMiLE: Provably Enforcing Global Relational Properties in Neural Networks

Artificial Intelligence systems are increasingly deployed in settings where ensuring robustness, fairness, or domain-specific properties is essential for regulation compliance and alignment with human values. However, especially on Neural Networks, property enforcement is very challenging, and existing methods are limited to specific constraints or local properties (defined around datapoints), or fail to provide full guarantees. We tackle these limitations by extending SMiLE, a recently proposed enforcement framework for NNs, to support global relational properties (defined over the entire input space). The proposed approach scales well with model complexity, accommodates general properties and backbones, and provides full satisfaction guarantees. We evaluate SMiLE on monotonicity, global robustness, and individual fairness, on synthetic and real data, for regression and classification tasks. Our approach is competitive with property-specific baselines in terms of accuracy and runtime, and strictly superior in terms of generality and level of guarantees. Overall, our results emphasize the potential of the SMiLE framework as a platform for future research and applications.

cs.LG↗

arXiv2025

Robust Non-Linear Correlations via Polynomial Regression

The Hirschfeld-Gebelein-Rényi (HGR) correlation coefficient is an extension of Pearson's correlation that is not limited to linear correlations, with potential applications in algorithmic fairness, scientific analysis, and causal discovery. Recently, novel algorithms to estimate HGR in a differentiable manner have been proposed to facilitate its use as a loss regularizer in constrained machine learning applications. However, the inherent uncomputability of HGR requires a bias-variance trade-off, which can possibly compromise the robustness of the proposed methods, hence raising technical concerns if applied in real-world scenarios. We introduce a novel computational approach for HGR that relies on user-configurable polynomial kernels, offering greater robustness compared to previous methods and featuring a faster yet almost equally effective restriction. Our approach provides significant advantages in terms of robustness and determinism, making it a more reliable option for real-world applications. Moreover, we present a brief experimental analysis to validate the applicability of our approach within a constrained machine learning framework, showing that its computation yields an insightful subgradient that can serve as a loss regularizer.

cs.LG↗

arXiv2025

Constrained Machine Learning Through Hyperspherical Representation

The problem of ensuring constraints satisfaction on the output of machine learning models is critical for many applications, especially in safety-critical domains. Modern approaches rely on penalty-based methods at training time, which do not guarantee to avoid constraints violations; or constraint-specific model architectures (e.g., for monotonocity); or on output projection, which requires to solve an optimization problem that might be computationally demanding. We present the Hypersherical Constrained Representation, a novel method to enforce constraints in the output space for convex and bounded feasibility regions (generalizable to star domains). Our method operates on a different representation system, where Euclidean coordinates are converted into hyperspherical coordinates relative to the constrained region, which can only inherently represent feasible points. Experiments on a synthetic and a real-world dataset show that our method has predictive performance comparable to the other approaches, can guarantee 100% constraint satisfaction, and has a minimal computational cost at inference time.

cs.LG↗

arXiv2025

Language Models Are Implicitly Continuous

Language is typically modelled with discrete sequences. However, the most successful approaches to language modelling, namely neural networks, are continuous and smooth function approximators. In this work, we show that Transformer-based language models implicitly learn to represent sentences as continuous-time functions defined over a continuous input space. This phenomenon occurs in most state-of-the-art Large Language Models (LLMs), including Llama2, Llama3, Phi3, Gemma, Gemma2, and Mistral, and suggests that LLMs reason about language in ways that fundamentally differ from humans. Our work formally extends Transformers to capture the nuances of time and space continuity in both input and output space. Our results challenge the traditional interpretation of how LLMs understand language, with several linguistic and engineering implications.

cs.CL↗

arXiv2024

SMLE: Safe Machine Learning via Embedded Overapproximation

Despite the extent of recent advances in Machine Learning (ML) and Neural Networks, providing formal guarantees on the behavior of these systems is still an open problem, and a crucial requirement for their adoption in regulated or safety-critical scenarios. We consider the task of training differentiable ML models guaranteed to satisfy designer-chosen properties, stated as input-output implications. This is very challenging, due to the computational complexity of rigorously verifying and enforcing compliance in modern neural models. We provide an innovative approach based on three components: 1) a general, simple architecture enabling efficient verification with a conservative semantic; 2) a rigorous training algorithm based on the Projected Gradient Method; 3) a formulation of the problem of searching for strong counterexamples. The proposed framework, being only marginally affected by model complexity, scales well to practical applications, and produces models that provide full property satisfaction guarantees. We evaluate our approach on properties defined by linear inequalities in regression, and on mutually exclusive classes in multilabel classification. Our approach is competitive with a baseline that includes property enforcement during preprocessing, i.e. on the training data, as well as during postprocessing, i.e. on the model predictions. Finally, our contributions establish a framework that opens up multiple research directions and potential improvements.

cs.LG↗

arXiv2024

QAL-BP: An Augmented Lagrangian Quantum Approach for Bin Packing

The bin packing is a well-known NP-Hard problem in the domain of artificial intelligence, posing significant challenges in finding efficient solutions. Conversely, recent advancements in quantum technologies have shown promising potential for achieving substantial computational speedup, particularly in certain problem classes, such as combinatorial optimization. In this study, we introduce QAL-BP, a novel Quadratic Unconstrained Binary Optimization (QUBO) formulation designed specifically for bin packing and suitable for quantum computation. QAL-BP utilizes the Augmented Lagrangian method to incorporate the bin packing constraints into the objective function while also facilitating an analytical estimation of heuristic, but empirically robust, penalty multipliers. This approach leads to a more versatile and generalizable model that eliminates the need for empirically calculating instance-dependent Lagrangian coefficients, a requirement commonly encountered in alternative QUBO formulations for similar problems. To assess the effectiveness of our proposed approach, we conduct experiments on a set of bin packing instances using a real Quantum Annealing device. Additionally, we compare the results with those obtained from two different classical solvers, namely simulated annealing and Gurobi. The experimental findings not only confirm the correctness of the proposed formulation but also demonstrate the potential of quantum computation in effectively solving the bin packing problem, particularly as more reliable quantum technology becomes available.

quant-ph↗

arXiv2023

Computational Asymmetries in Robust Classification

In the context of adversarial robustness, we make three strongly related contributions. First, we prove that while attacking ReLU classifiers is $\mathit{NP}$-hard, ensuring their robustness at training time is $Σ^2_P$-hard (even on a single example). This asymmetry provides a rationale for the fact that robust classifications approaches are frequently fooled in the literature. Second, we show that inference-time robustness certificates are not affected by this asymmetry, by introducing a proof-of-concept approach named Counter-Attack (CA). Indeed, CA displays a reversed asymmetry: running the defense is $\mathit{NP}$-hard, while attacking it is $Σ_2^P$-hard. Finally, motivated by our previous result, we argue that adversarial attacks can be used in the context of robustness certification, and provide an empirical evaluation of their effectiveness. As a byproduct of this process, we also release UG100, a benchmark dataset for adversarial attacks.

cs.LG↗

arXiv2023

An analysis of Universal Differential Equations for data-driven discovery of Ordinary Differential Equations

In the last decade, the scientific community has devolved its attention to the deployment of data-driven approaches in scientific research to provide accurate and reliable analysis of a plethora of phenomena. Most notably, Physics-informed Neural Networks and, more recently, Universal Differential Equations (UDEs) proved to be effective both in system integration and identification. However, there is a lack of an in-depth analysis of the proposed techniques. In this work, we make a contribution by testing the UDE framework in the context of Ordinary Differential Equations (ODEs) discovery. In our analysis, performed on two case studies, we highlight some of the issues arising when combining data-driven approaches and numerical solvers, and we investigate the importance of the data collection process. We believe that our analysis represents a significant contribution in investigating the capabilities and limitations of Physics-informed Machine Learning frameworks.

cs.LG↗

arXiv2023

Generalized Disparate Impact for Configurable Fairness Solutions in ML

We make two contributions in the field of AI fairness over continuous protected attributes. First, we show that the Hirschfeld-Gebelein-Renyi (HGR) indicator (the only one currently available for such a case) is valuable but subject to a few crucial limitations regarding semantics, interpretability, and robustness. Second, we introduce a family of indicators that are: 1) complementary to HGR in terms of semantics; 2) fully interpretable and transparent; 3) robust over finite samples; 4) configurable to suit specific applications. Our approach also allows us to define fine-grained constraints to permit certain types of dependence and forbid others selectively. By expanding the available options for continuous protected attributes, our approach represents a significant contribution to the area of fair artificial intelligence.

cs.LG↗

arXiv2022

UNIFY: a Unified Policy Designing Framework for Solving Constrained Optimization Problems with Machine Learning

The interplay between Machine Learning (ML) and Constrained Optimization (CO) has recently been the subject of increasing interest, leading to a new and prolific research area covering (e.g.) Decision Focused Learning and Constrained Reinforcement Learning. Such approaches strive to tackle complex decision problems under uncertainty over multiple stages, involving both explicit (cost function, constraints) and implicit knowledge (from data), and possibly subject to execution time restrictions. While a good degree of success has been achieved, the existing methods still have limitations in terms of both applicability and effectiveness. For problems in this class, we propose UNIFY, a unified framework to design a solution policy for complex decision-making problems. Our approach relies on a clever decomposition of the policy in two stages, namely an unconstrained ML model and a CO problem, to take advantage of the strength of each approach while compensating for its weaknesses. With a little design effort, UNIFY can generalize several existing approaches, thus extending their applicability. We demonstrate the method effectiveness on two practical problems, namely an Energy Management System and the Set Multi-cover with stochastic coverage requirements. Finally, we highlight some current challenges of our method and future research directions that can benefit from the cross-fertilization of the two fields.

cs.LG↗

arXiv2022

Machine Learning for Combinatorial Optimisation of Partially-Specified Problems: Regret Minimisation as a Unifying Lens

It is increasingly common to solve combinatorial optimisation problems that are partially-specified. We survey the case where the objective function or the relations between variables are not known or are only partially specified. The challenge is to learn them from available data, while taking into account a set of hard constraints that a solution must satisfy, and that solving the optimisation problem (esp. during learning) is computationally very demanding. This paper overviews four seemingly unrelated approaches, that can each be viewed as learning the objective function of a hard combinatorial optimisation problem: 1) surrogate-based optimisation, 2) empirical model learning, 3) decision-focused learning (`predict + optimise'), and 4) structured-output prediction. We formalise each learning paradigm, at first in the ways commonly found in the literature, and then bring the formalisations together in a compatible way using regret. We discuss the differences and interactions between these frameworks, highlight the opportunities for cross-fertilization and survey open directions.

cs.LG↗