arXiv subjects

Giuseppe C. Calafiore

Publications and source records attributed to Giuseppe C. Calafiore.

At least 19 recordsLinked to original sources

arXiv2026

Exact Risk-Complexity Laws for Projective Boundaries in Scenario Optimization and Distribution-Free Certification

Scenario optimization, conformal prediction, and related distribution-free certification methods use finite samples to construct decisions or prediction sets with violation-risk guarantees for fresh observations. In several classical settings, the conditional violation risk follows an exact beta law, whose tail has a beta-binomial representation and whose parameter is a support, calibration, or compression dimension. This paper identifies the deterministic boundary mechanism behind these formulas and derives the corresponding law when the observed boundary size is random. A decision rule is represented by an acceptance set for future observations, together with a boundary map selecting the sample points responsible for that set. The resulting pair is called a {\em proper projective boundary scheme} when held-out samples are accepted precisely if the full-sample boundary is retained, and accepted non-boundary samples can be deleted without changing that boundary. For every such scheme, the conditional law of the violation risk given the observed boundary size is determined by the boundary's cross-sample complexity profile. A stable profile yields the usual beta law, whereas a varying profile produces an exact profile correction. The framework covers scalar order-statistic calibration, support-reconstructive scenario programs, cascaded support-removal certificates, coordinatewise envelopes, and Pareto-frontier calibration with vector scores. It also yields conditional probabilistic certificates and a no-go result explaining why observed complexity alone is insufficient.

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arXiv2026

Implicit Neural Networks as Static Controllers: Certificates and Performance Separation

Implicit neural controllers (INCs) are static feedback laws that are evaluated through an algebraic fixed point {equation}; they include as special cases neural network controllers. We propose a so-called implicit representation of neural networks as a key enabling device that exposes the controller as a trainable linear interconnection closed through a known static activation map, thereby making well-posedness and Lyapunov/IQC analysis mathematically easy to handle. For finite-dimensional LTI plants, we first develop a rigorous analysis theory for a given INC, including Perron--Frobenius and norm conditions for well posedness, LMI/IQC certificates for exponential stability, and LMIs for discounted infinite-horizon quadratic performance. We then formulate synthesis as a certification-compatible heuristic search: training is carried out under explicit well-posedness constraints, implicit-differentiation formulas provide gradients, and the resulting controller is accepted only after independent post-training LMIs or regional admissibility checks are feasible. Finally, we establish constrained-control separation results: for a specific scalar unstable plant with hard actuator bounds, an INC achieves a strictly smaller discounted infinite-horizon cost than any admissible finite-order dynamic linear controller. Additional results cover quadratic state-input costs, comparison with linear static output feedback, and computable upper/lower-bound certificates. Numerical examples illustrate the mechanism and the resulting certified performance.

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arXiv2026

Class-Based Smart Charging Control for Electric Vehicles

This paper proposes a stochastic control framework for the operation of electric-vehicle (EV) charging stations equipped with on-site photovoltaic (PV) generation and battery storage. To preserve scalability for large fleets, vehicles are aggregated into a finite number of classes according to their residual charging demand, yielding a compact state description and avoiding vehicle-level optimization. The charging-station dynamics are modeled in discrete time and capture stochastic arrivals, charging-induced class transitions, stochastic departures, PV generation, battery operation, and power exchange with the grid. Based on the corresponding expectation model, we formulate a finite-horizon smart-charging problem that jointly optimizes class-wise charging actions and energy-management variables to balance electricity-purchase cost and transitions toward lower residual-demand classes. The resulting stage problem is a linear program, solved in shrinking-horizon form and implemented online after integer discretization of the first charging action. We also derive a robust counterpart that preserves feasibility under interval uncertainty on the first moments of arrivals, departures, and PV generation. To validate scalability and robustness, we conduct an extensive simulation campaign across nine configurations, combining three real-world electricity price patterns with three EV-arrival profiles. Numerical results show that, at comparable but slightly lower service levels, the proposed controller reduces the cost per kWh by up to 17.5% relative to a service-greedy First-In-First-Out baseline; the total daily cost decreases even more substantially because the controller avoids economically unattractive charging. Overall, the results demonstrate a tunable Pareto trade-off between economic efficiency and charging-service quality for large-scale charging hubs.

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arXiv2026

A Multi-Criterion Approach to Smart EV Charging with CO2 Emissions and Cost Minimization

We study carbon-aware smart charging in a fossil-dominated grid by coupling a simplified hydro-thermal-renewable dispatch model with a tractable linear charging scheduler. The case study is informed by Vietnam's regional data. Thermal units remain dominant, renewables are time-varying, and hydropower is modeled through a single reservoir budget. From the day-ahead dispatch we derive hourly carbon intensity and a corresponding carbon-cost signal; these are combined with a local time-of-use tariff in the EV charging problem. The resulting weighted-sum linear program is multi-objective: by sweeping the trade-off coefficient, we recover the supported Pareto frontier between electricity cost and charging-associated emissions. In a 300-EV public-charging scenario with a 0.8 MW feeder cap, the proposed carbon-aware scheduler preserves the 19.8% bill reduction of a cost-only optimizer while lowering charging-associated emissions by 7.3%; a more carbon-focused tuning still remains 12.6% cheaper and 9.3% cleaner than a FIFO baseline. A hydro-sensitivity study shows that changing the reservoir budget by +/- 20% moves the mean grid carbon intensity from 360 to 466 g/kWh, yet the carbon-aware scheduler remains consistently cheaper and cleaner than FIFO. The dispatch and charging LPs solve in few milliseconds on a standard desktop computer, showing that the framework is lightweight enough for repeated day-ahead studies.

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arXiv2026

Budgeted Robust Intervention Design for Financial Networks with Common Asset Exposures

In the context of containment of default contagion in financial networks, we here study a regulator that allocates pre-shock capital or liquidity buffers across banks connected by interbank liabilities and common external asset exposures. The regulator chooses a nonnegative buffer vector under a linear budget before asset-price shocks realize. Shocks are modeled as belonging to either an $\ell_{\infty}$ or an $\ell_{1}$ uncertainty set, and the design objective is either to enlarge the certified no-default/no-insolvency region or to minimize worst-case clearing losses at a prescribed stress radius. Four exact synthesis results are derived. The buffer that maximizes the default resilience margin is obtained from a linear program and admits a closed-form minimal-budget certificate for any target margin. The buffer that maximizes the insolvency resilience margin is computed by a single linear program. At a fixed radius, minimizing the worst-case systemic loss is again a linear program under $\ell_{\infty}$ uncertainty and a linear program with one scenario block per asset under $\ell_{1}$ uncertainty. Crucially, under $\ell_{1}$ uncertainty, exact robustness adds only one LP block per asset, ensuring that the computational complexity grows linearly with the number of assets. A corollary identifies the exact budget at which the optimized worst-case loss becomes zero. Numerical experiments on the 8-bank benchmark of \cite{Calafiore2025}, on a synthetic core-periphery network, and on a data-backed 107-bank calibration built from the 2025 EBA transparency exercise show large gains over uniform and exposure-proportional allocations. The empirical results also indicate that resilience-maximizing and loss-minimizing interventions nearly coincide under diffuse $\ell_\infty$ shocks, but diverge under concentrated $\ell_1$ shocks.

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arXiv2026

Bridging Conformal Prediction and Scenario Optimization: Discarded Constraints and Modular Risk Allocation

Scenario optimization and conformal prediction share a common goal, that is, turning finite samples into safety margins. Yet, different terminology often obscures the connection between their respective guarantees. This paper revisits that connection directly from a systems-and-control viewpoint. Building on the recent conformal/scenario bridge of \citet{OSullivanRomaoMargellos2026}, we extend the forward direction to feasible sample-and-discard scenario algorithms. Specifically, if the final decision is determined by a stable subset of the retained sampled constraints, the classical mean violation law admits a direct exchangeability-based derivation. In this view, discarded samples naturally appear as admissible exceptions. We also introduce a simple modular composition rule that combines several blockwise calibration certificates into a single joint guarantee. This rule proves particularly useful in multi-output prediction and finite-horizon control, where engineers must distribute risk across coordinates, constraints, or prediction steps. Finally, we provide numerical illustrations using a calibrated multi-step tube around an identified predictor. These examples compare alternative stage-wise risk allocations and highlight the resulting performance and safety trade-offs in a standard constraint-tightening problem.

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arXiv2026

Geometry-Aware Set-Membership Multilateration: Directional Bounds and Anchor Selection

In this paper, we study anchor selection for range-based localization under unknown-but-bounded measurement errors. We start from the convex localization set $\X=\Xd\cap\Hset$ recently introduced in \cite{CalafioreSIAM}, where $\Xd$ is a polyhedron obtained from pairwise differences of squared-range equations between the unknown location $x$ and the anchors, and $\Hset$ is the intersection of upper-range hyperspheres. Our first goal is \emph{offline} design: we derive geometry-only E- and D-type scores from the centered scatter matrix $S(A)=AQ_mA\tran$, where $A$ collects the anchor coordinates and $Q_m=I_m-\frac{1}{m}\one\one\tran$ is the centering projector, showing that $λ_{\min}(S(A))$ controls worst-direction and diameter surrogates for the polyhedral certificate $\Xd$, while $\det S(A)$ controls principal-axis volume surrogates. Our second goal is \emph{online} uncertainty assessment for a selected subset of anchors: exploiting the special structure $\X=\Xd\cap\Hset$, we derive a simplex-aggregated enclosing ball for $\Hset$ and an exact support-function formula for $\Hset$, which lead to finite hybrid bounds for the actual localization set $\X$, even when the polyhedral certificate deteriorates. Numerical experiments are performed in two dimensions, showing that geometry-based subset selection is close to an oracle combinatorial search, that the D-score slightly dominates the E-score for the area-oriented metric considered here, and that the new $\Hset$-aware certificates track the realized size of the selected localization set closely.

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arXiv2026

Set-Membership Localization via Range Measurements

In this paper we discuss a classical geometrical problem of estimating an unknown point's location in $\Real{n}$ from several noisy measurements of the Euclidean distances from this point to a set of known reference points (anchors). We approach the problem via a set-mem\-ber\-ship methodology, in which we assume the distance measurements to be affected by unknown-but-bounded errors, and we characterize the set of all points that are consistent with the measurements and their assumed error model. This set is nonconvex, but we show in the paper that it is contained in a region given by the intersection of certain closed balls and a polytope, which we call the {\em localization set}. Then, we develop efficient methods, based on convex programming, for computing a tight outer-bounding set of simple structure (a box, or an ellipsoid) for the localization set, which then acts as a guaranteed set-valued location estimate. % The center of the bounding set also serves as a point location estimate. Related problems of inner approximation of the localization set via balls and ellipsoids are also posed as convex programming problems. Different from existing methods based on semidefinite programming relaxations of a nonconvex cost minimization problem, our approach is direct, geometric and based on a polyhedral set of points that satisfy pairwise differences of the measurement equations.

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arXiv2025

A kernel-based approach to physics-informed nonlinear system identification

This paper presents a kernel-based framework for physics-informed nonlinear system identification. The key contribution is a structured methodology that extends kernel-based techniques to seamlessly embed partially known physics-based models, improving parameter estimation and overall model accuracy. The proposed method enhances traditional modeling approaches by embedding a parametric model, which provides physical interpretability, with a kernel-based function, which accounts for unmodeled dynamics. The two models' components are identified from the data simultaneously, thereby minimizing a suitable cost that balances the relative importance of the physical and the black-box parts of the model. Additionally, nonlinear state smoothing is employed to address scenarios involving state-space models with not fully measurable states. Numerical simulations on an experimental benchmark system demonstrate the effectiveness of the proposed approach, achieving up to 51% reduction in simulation root mean square error compared to physics-only models and 31% performance improvement over state-of-the-art identification techniques.

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arXiv2025

Playing the Lottery With Concave Regularizers for Sparse Trainable Neural Networks

The design of sparse neural networks, i.e., of networks with a reduced number of parameters, has been attracting increasing research attention in the last few years. The use of sparse models may significantly reduce the computational and storage footprint in the inference phase. In this context, the lottery ticket hypothesis (LTH) constitutes a breakthrough result, that addresses not only the performance of the inference phase, but also of the training phase. It states that it is possible to extract effective sparse subnetworks, called winning tickets, that can be trained in isolation. The development of effective methods to play the lottery, i.e., to find winning tickets, is still an open problem. In this article, we propose a novel class of methods to play the lottery. The key point is the use of concave regularization to promote the sparsity of a relaxed binary mask, which represents the network topology. We theoretically analyze the effectiveness of the proposed method in the convex framework. Then, we propose extended numerical tests on various datasets and architectures, that show that the proposed method can improve the performance of state-of-the-art algorithms.

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arXiv2024

Power minimization and resource allocation in HetNets with uncertain channel-gains

We propose an optimization problem to minimize the base stations transmission powers in OFDMA heterogeneous networks, while respecting users' individual throughput demands. The decision variables are the users' working bandwidths, their association, and the base stations transmission powers. To deal with wireless channel uncertainty, the channel gains are treated as random variables respecting a log-normal distribution, leading to a non-convex chance constrained mixed-integer optimization problem, which is then formulated as a mixed-integer Robust Geometric Program. The efficacy of the proposed method is shown in a real-world scenario of a large European city.

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arXiv2024

A Joint Optimization Approach for Power-Efficient Heterogeneous OFDMA Radio Access Networks

Heterogeneous networks have emerged as a popular solution for accommodating the growing number of connected devices and increasing traffic demands in cellular networks. While offering broader coverage, higher capacity, and lower latency, the escalating energy consumption poses sustainability challenges. In this paper a novel optimization approach for OFDMA heterogeneous networks is proposed to minimize transmission power while respecting individual users throughput constraints. The problem is formulated as a mixed integer geometric program, and optimizes at once multiple system variables such as user association, working bandwidth, and base stations transmission powers. Crucially, the proposed approach becomes a convex optimization problem when user-base station associations are provided. Evaluations in multiple realistic scenarios from the production mobile network of a major European operator and based on precise channel gains and throughput requirements from measured data validate the effectiveness of the proposed approach. Overall, our original solution paves the road for greener connectivity by reducing the energy footprint of heterogeneous mobile networks, hence fostering more sustainable communication systems.

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arXiv2022

Clearing Payments in Dynamic Financial Networks

This paper proposes a novel dynamical model for determining clearing payments in financial networks. We extend the classical Eisenberg-Noe model of financial contagion to multiple time periods, allowing financial operations to continue after possible initial pseudo defaults, thus permitting nodes to recover and eventually fulfil their liabilities. Optimal clearing payments in our model are computed by solving a suitable linear program, both in the full matrix payments case and in the pro-rata constrained case. We prove that the proposed model obeys the \emph{priority of debt claims} requirement, that is, each node at every step either pays its liabilities in full, or it pays out all its balance. In the pro-rata case, the optimal dynamic clearing payments are unique, and can be determined via a time-decoupled sequential optimization approach.

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arXiv2022

A barrier function approach to constrained Pontryagin-based Nonlinear Model Predictive Control

A Pontryagin-based approach to solve a class of constrained Nonlinear Model Predictive Control problems is proposed which employs the method of barrier functions for dealing with the state constraints. Unlike the existing works in literature the proposed method is able to cope with nonlinear input and state constraints without any significant modification of the optimization algorithm. A stability analysis of the closed-loop system is carried out by using the L-2 norm of the predicted state tracking error as a Lyapunov function. Theoretical results are tested and confirmed by numerical simulations on the Lotka-Volterra prey/predator system.

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arXiv2020

A Modified SIR Model for the COVID-19 Contagion in Italy

The purpose of this work is to give a contribution to the understanding of the COVID-19 contagion in Italy. To this end, we developed a modified Susceptible-Infected-Recovered (SIR) model for the contagion, and we used official data of the pandemic up to March 30th, 2020 for identifying the parameters of this model. The non standard part of our approach resides in the fact that we considered as model parameters also the initial number of susceptible individuals, as well as the proportionality factor relating the detected number of positives with the actual (and unknown) number of infected individuals. Identifying the contagion, recovery and death rates as well as the mentioned parameters amounts to a non-convex identification problem that we solved by means of a two-dimensional grid search in the outer loop, with a standard weighted least-squares optimization problem as the inner step.

physics.soc-ph↗

arXiv2019

Sparse $\ell_1$ and $\ell_2$ Center Classifiers

The nearest-centroid classifier is a simple linear-time classifier based on computing the centroids of the data classes in the training phase, and then assigning a new datum to the class corresponding to its nearest centroid. Thanks to its very low computational cost, the nearest-centroid classifier is still widely used in machine learning, despite the development of many other more sophisticated classification methods. In this paper, we propose two sparse variants of the nearest-centroid classifier, based respectively on $\ell_1$ and $\ell_2$ distance criteria. The proposed sparse classifiers perform simultaneous classification and feature selection, by detecting the features that are most relevant for the classification purpose. We show that training of the proposed sparse models, with both distance criteria, can be performed exactly (i.e., the globally optimal set of features is selected) and at a quasi-linear computational cost. The experimental results show that the proposed methods are competitive in accuracy with state-of-the-art feature selection techniques, while having a significantly lower computational cost.

cs.LG↗

arXiv2019

Survival and Neural Models for Private Equity Exit Prediction

Within the Private Equity (PE) market, the event of a private company undertaking an Initial Public Offering (IPO) is usually a very high-return one for the investors in the company. For this reason, an effective predictive model for the IPO event is considered as a valuable tool in the PE market, an endeavor in which publicly available quantitative information is generally scarce. In this paper, we describe a data-analytic procedure for predicting the probability with which a company will go public in a given forward period of time. The proposed method is based on the interplay of a neural network (NN) model for estimating the overall event probability, and Survival Analysis (SA) for further modeling the probability of the IPO event in any given interval of time. The proposed neuro-survival model is tuned and tested across nine industrial sectors using real data from the Thomson Reuters Eikon PE database.

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arXiv2019

Nonlinear system identification in Sobolev spaces

We consider the problem of deriving from experimental data an approximation of an unknown function, whose derivatives also approximate the unknown function derivatives. Solving this problem is useful, for instance, in the context of nonlinear system identification for obtaining models that are more accurate and reliable than the traditional ones, based on plain function approximation. Indeed, models identified by accounting for the derivatives can provide a better performance in several tasks, such as multi-step prediction, simulation, Nonlinear Model Predictive Control, and control design in general. In this paper, we propose a novel approach based on convex optimization, allowing us to solve the aforementioned identification problem. We develop an optimality analysis, showing that models derived using this approach enjoy suitable optimality properties in Sobolev spaces. The optimality analysis also leads to the derivation of tight uncertainty bounds on the unknown function and its derivatives. We demonstrate the effectiveness of the approach with two numerical examples. The first one is concerned with approximation of an univariate function, the second one with multi-step prediction of the Chua chaotic circuit.

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