arXiv subjects

Davide Pucci

Publications and source records attributed to Davide Pucci.

7 recordsLinked to original sources

arXiv2026

Sample-wise Constrained Learning via a Sequential Penalty Approach with Applications in Image Processing

In many learning tasks, certain requirements on the processing of individual data samples should arguably be formalized as strict constraints in the underlying optimization problem, rather than by means of arbitrary penalties. We show that, in these scenarios, learning can be carried out exploiting a sequential penalty method that allows to properly deal with constraints. The proposed algorithm is shown to possess convergence guarantees under assumptions that are reasonable in deep learning scenarios. Moreover, the results of experiments on image processing tasks show that the method is indeed viable to be used in practice.

cs.LG↗

arXiv2025

Penalty decomposition derivative free method for the minimization of partially separable functions over a convex feasible set

In this paper, we consider the problem of minimizing a smooth function, given as finite sum of black-box functions, over a convex set. In order to advantageously exploit the structure of the problem, for instance when the terms of the objective functions are partially separable, noisy, costly or with first-order information partially accessible, we propose a framework where the penalty decomposition approach is combined with a derivative-free line-search-based method. Under standard assumptions, we state theoretical results showing that the proposed algorithm is well-defined and globally convergent to stationary points. The results of preliminary numerical experiments, performed on test problems with number of variables up to thousands, show the validity of the proposed method w.r.t. state of the art methods.

math.OC↗

arXiv2025

On the Computation of the Efficient Frontier in Advanced Sparse Portfolio Optimization

In this work, we deal with the problem of computing a comprehensive front of efficient solutions in multi-objective portfolio optimization problems in presence of sparsity constraints. We start the discussion pointing out some weaknesses of the classical linear scalarization approach when applied to the considered class of problems. We are then motivated to propose a suitable algorithmic framework that is designed to overcome these limitations: the novel algorithm combines a gradient-based exploration-refinement strategy with a tailored initialization scheme based on memetic or multi-start descent procedures. Thorough computational experiments highlight how the proposed method is far superior to both linear scalarization and popular genetic algorithms.

math.OC↗

arXiv2024

Effectively Leveraging Momentum Terms in Stochastic Line Search Frameworks for Fast Optimization of Finite-Sum Problems

In this work, we address unconstrained finite-sum optimization problems, with particular focus on instances originating in large scale deep learning scenarios. Our main interest lies in the exploration of the relationship between recent line search approaches for stochastic optimization in the overparametrized regime and momentum directions. First, we point out that combining these two elements with computational benefits is not straightforward. To this aim, we propose a solution based on mini-batch persistency. We then introduce an algorithmic framework that exploits a mix of data persistency, conjugate-gradient type rules for the definition of the momentum parameter and stochastic line searches. The resulting algorithm provably possesses convergence properties under suitable assumptions and is empirically shown to outperform other popular methods from the literature, obtaining state-of-the-art results in both convex and nonconvex large scale training problems.

math.OC↗

arXiv2024

Convergence Conditions for Stochastic Line Search Based Optimization of Over-parametrized Models

In this paper, we deal with algorithms to solve the finite-sum problems related to fitting over-parametrized models, that typically satisfy the interpolation condition. In particular, we focus on approaches based on stochastic line searches and employing general search directions. We define conditions on the sequence of search directions that guarantee finite termination and bounds for the backtracking procedure. Moreover, we shed light on the additional property of directions needed to prove fast (linear) convergence of the general class of algorithms when applied to PL functions in the interpolation regime. From the point of view of algorithms design, the proposed analysis identifies safeguarding conditions that could be employed in relevant algorithmic frameworks. In particular, it could be of interest to integrate stochastic line searches within momentum, conjugate gradient or adaptive preconditioning methods.

math.OC↗

arXiv2024

Effective Front-Descent Algorithms with Convergence Guarantees

In this manuscript, we address continuous unconstrained multi-objective optimization problems and we discuss descent type methods for the reconstruction of the Pareto set. Specifically, we analyze the class of Front Descent methods, which generalizes the Front Steepest Descent algorithm allowing the employment of suitable, effective search directions (e.g., Newton, Quasi-Newton, Barzilai-Borwein). We provide a deep characterization of the behavior and the mechanisms of the algorithmic framework, and we prove that, under reasonable assumptions, standard convergence results and some complexity bounds hold for the generalized approach. Moreover, we prove that popular search directions can indeed be soundly used within the framework. Then, we provide a completely novel type of convergence results, concerning the sequence of sets produced by the procedure. In particular, iterate sets are shown to asymptotically approach stationarity for all of their points; the convergence result is accompanied by a worst-case iteration complexity bound; additionally, in finite precision settings, the sets are shown to only be enriched through exploration steps in later iterations, and suitable stopping conditions can be devised. Finally, the results from a large experimental benchmark show that the proposed class of approaches far outperforms state-of-the-art methodologies.

math.OC↗

arXiv2024

A Globally Convergent Gradient Method with Momentum

In this work, we consider smooth unconstrained optimization problems and we deal with the class of gradient methods with momentum, i.e., descent algorithms where the search direction is defined as a linear combination of the current gradient and the preceding search direction. This family of algorithms includes nonlinear conjugate gradient methods and Polyak's heavy-ball approach, and is thus of high practical and theoretical interest in large-scale nonlinear optimization. We propose a general framework where the scalars of the linear combination defining the search direction are computed simultaneously by minimizing the approximate quadratic model in the 2 dimensional subspace. This strategy allows us to define a class of gradient methods with momentum enjoying global convergence guarantees and an optimal worst-case complexity bound in the nonconvex setting. Differently than all related works in the literature, the convergence conditions are stated in terms of the Hessian matrix of the bi-dimensional quadratic model. To the best of our knowledge, these results are novel to the literature. Moreover, extensive computational experiments show that the gradient method with momentum here presented is a solid choice to tackle some classes of nonconvex unconstrained problems.

math.OC↗