Giuseppe C. Calafiore

Giuseppe C. Calafiore, Lorenzo Fagiano

This paper discusses a novel probabilistic approach for the design of robust model predictive control (MPC) laws for discrete-time linear systems affected by parametric uncertainty and additive disturbances. The proposed technique is based on the iterated solution, at each step, of a finite-horizon optimal control problem (FHOCP) that takes into account a suitable number of randomly extracted scenarios of uncertainty and disturbances, followed by a specific command selection rule implemented in a receding horizon fashion. The scenario FHOCP is always convex, also when the uncertain parameters and disturbance belong to non-convex sets, and irrespective of how the model uncertainty influences the system's matrices. Moreover, the computational complexity of the proposed approach does not depend on the uncertainty/disturbance dimensions, and scales quadratically with the control horizon. The main result in this paper is related to the analysis of the closed loop system under receding-horizon implementation of the scenario FHOCP, and essentially states that the devised control law guarantees constraint satisfaction at each step with some a-priori assigned probability p, while the system's state reaches the target set either asymptotically, or in finite time with probability at least p. The proposed method may be a valid alternative when other existing techniques, either deterministic or stochastic, are not directly usable due to excessive conservatism or to numerical intractability caused by lack of convexity of the robust or chance-constrained optimization problem.

Giuseppe C. Calafiore

Repetitive Scenario Design (RSD) is a randomized approach to robust design based on iterating two phases: a standard scenario design phase that uses $N$ scenarios (design samples), followed by randomized feasibility phase that uses $N_o$ test samples on the scenario solution. We give a full and exact probabilistic characterization of the number of iterations required by the RSD approach for returning a solution, as a function of $N$, $N_o$, and of the desired levels of probabilistic robustness in the solution. This novel approach broadens the applicability of the scenario technology, since the user is now presented with a clear tradeoff between the number $N$ of design samples and the ensuing expected number of repetitions required by the RSD algorithm. The plain (one-shot) scenario design becomes just one of the possibilities, sitting at one extreme of the tradeoff curve, in which one insists in finding a solution in a single repetition: this comes at the cost of possibly high $N$. Other possibilities along the tradeoff curve use lower $N$ values, but possibly require more than one repetition.

Giuseppe C. Calafiore, Luca Ambrosino, Khai Manh Nguyen et al.

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.

Giuseppe C. Calafiore

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.

Giuseppe C. Calafiore

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.

Giuseppe C. Calafiore

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.

Giulia Fracastoro, Sophie M. Fosson, Andrea Migliorati et al.

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.

Giuseppe C. Calafiore, Marisa H. Morales, Vittorio Tiozzo et al.

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.

Giuseppe C. Calafiore, Giulia Fracastoro

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.

Giuseppe C. Calafiore, Stephane Gaubert, Member et al.

We show that a neural network whose output is obtained as the difference of the outputs of two feedforward networks with exponential activation function in the hidden layer and logarithmic activation function in the output node (LSE networks) is a smooth universal approximator of continuous functions over convex, compact sets. By using a logarithmic transform, this class of networks maps to a family of subtraction-free ratios of generalized posynomials, which we also show to be universal approximators of positive functions over log-convex, compact subsets of the positive orthant. The main advantage of Difference-LSE networks with respect to classical feedforward neural networks is that, after a standard training phase, they provide surrogate models for design that possess a specific difference-of-convex-functions form, which makes them optimizable via relatively efficient numerical methods. In particular, by adapting an existing difference-of-convex algorithm to these models, we obtain an algorithm for performing effective optimization-based design. We illustrate the proposed approach by applying it to data-driven design of a diet for a patient with type-2 diabetes.

Giuseppe C. Calafiore, Stephane Gaubert, Corrado Possieri

We show in this paper that a one-layer feedforward neural network with exponential activation functions in the inner layer and logarithmic activation in the output neuron is an universal approximator of convex functions. Such a network represents a family of scaled log-sum exponential functions, here named LSET. Under a suitable exponential transformation, the class of LSET functions maps to a family of generalized posynomials GPOST, which we similarly show to be universal approximators for log-log-convex functions. A key feature of an LSET network is that, once it is trained on data, the resulting model is convex in the variables, which makes it readily amenable to efficient design based on convex optimization. Similarly, once a GPOST model is trained on data, it yields a posynomial model that can be efficiently optimized with respect to its variables by using geometric programming (GP). The proposed methodology is illustrated by two numerical examples, in which, first, models are constructed from simulation data of the two physical processes (namely, the level of vibration in a vehicle suspension system, and the peak power generated by the combustion of propane), and then optimization-based design is performed on these models.

Luca Carlone, Giuseppe C. Calafiore

Pose Graph Optimization involves the estimation of a set of poses from pairwise measurements and provides a formalization for many problems arising in mobile robotics and geometric computer vision. In this paper, we consider the case in which a subset of the measurements fed to pose graph optimization is spurious. Our first contribution is to develop robust estimators that can cope with heavy-tailed measurement noise, hence increasing robustness to the presence of outliers. Since the resulting estimators require solving nonconvex optimization problems, we further develop convex relaxations that approximately solve those problems via semidefinite programming. We then provide conditions under which the proposed relaxations are exact. Contrarily to existing approaches, our convex relaxations do not rely on the availability of an initial guess for the unknown poses, hence they are more suitable for setups in which such guess is not available (e.g., multi-robot localization, recovery after localization failure). We tested the proposed techniques in extensive simulations, and we show that some of the proposed relaxations are indeed tight (i.e., they solve the original nonconvex problem 10 exactly) and ensure accurate estimation in the face of a large number of outliers.

Giuseppe C. Calafiore, Carlo Novara, Michele Taragna

This paper deals with the problem of finding a low-complexity estimate of the impulse response of a linear time-invariant discrete-time dynamic system from noise-corrupted input-output data. To this purpose, we introduce an identification criterion formed by the average (over the input perturbations) of a standard prediction error cost, plus a weighted l1 regularization term which promotes sparse solutions. While it is well known that such criteria do provide solutions with many zeros, a critical issue in our identification context is where these zeros are located, since sensible low-order models should be zero in the tail of the impulse response. The flavor of the key results in this paper is that, under quite standard assumptions (such as i.i.d. input and noise sequences and system stability), the estimate of the impulse response resulting from the proposed criterion is indeed identically zero from a certain time index (named the leading order) onwards, with arbitrarily high probability, for a sufficiently large data cardinality. Numerical experiments are reported that support the theoretical results, and comparisons are made with some other state-of-the-art methodologies.