Alessandro Scagliotti
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View article: Towards optimal control of ensembles of discrete-time systems
Towards optimal control of ensembles of discrete-time systems Open
The control of ensembles of dynamical systems is an intriguing and challenging problem, arising for example in quantum control. We initiate the investigation of optimal control of ensembles of discrete-time systems, focusing on minimising …
View article: Normalizing flows as approximations of optimal transport maps via linear-control neural ODEs
Normalizing flows as approximations of optimal transport maps via linear-control neural ODEs Open
View article: Approximation of Diffeomorphisms for Quantum State Transfers
Approximation of Diffeomorphisms for Quantum State Transfers Open
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View article: Trade-off Invariance Principle for minimizers of regularized functionals
Trade-off Invariance Principle for minimizers of regularized functionals Open
In this paper, we consider functionals of the form $H_α(u)=F(u)+αG(u)$ with $α\in[0,+\infty)$, where $u$ varies in a set $U\neq\emptyset$ (without further structure). We first revisit a result stating that, excluding at most countably many…
View article: Shortest-path recovery from signature with an optimal control approach
Shortest-path recovery from signature with an optimal control approach Open
In this paper, we consider the signature-to-path reconstruction problem from the control-theoretic perspective. Namely, we design an optimal control problem whose solution leads to the minimal-length path that generates a given signature. …
View article: Minimax problems for ensembles of control-affine systems
Minimax problems for ensembles of control-affine systems Open
In this paper, we consider ensembles of control-affine systems in $\mathbb{R}^d$, and we study simultaneous optimal control problems related to the worst-case minimization. After proving that such problems admit solutions, denoting with $(…
View article: From NeurODEs to AutoencODEs: A mean-field control framework for width-varying neural networks
From NeurODEs to AutoencODEs: A mean-field control framework for width-varying neural networks Open
The connection between Residual Neural Networks (ResNets) and continuous-time control systems (known as NeurODEs) has led to a mathematical analysis of neural networks, which has provided interesting results of both theoretical and practic…
View article: Normalizing flows as approximations of optimal transport maps via linear-control neural ODEs
Normalizing flows as approximations of optimal transport maps via linear-control neural ODEs Open
In this paper, we consider the problem of recovering the $W_2$-optimal transport map T between absolutely continuous measures $μ,ν\in\mathcal{P}(\mathbb{R}^n)$ as the flow of a linear-control neural ODE, where the control depends only on t…
View article: A minimax optimal control approach for robust neural ODEs
A minimax optimal control approach for robust neural ODEs Open
In this paper, we address the adversarial training of neural ODEs from a robust control perspective. This is an alternative to the classical training via empirical risk minimization, and it is widely used to enforce reliable outcomes for i…
View article: Shortest-path recovery from signature with an optimal control approach
Shortest-path recovery from signature with an optimal control approach Open
In this paper, we consider the signature-to-path reconstruction problem from the control theoretic perspective. Namely, we design an optimal control problem whose solution leads to the minimal-length path that generates a given signature. …
View article: A subgradient method with constant step-size for $$\ell _1$$-composite optimization
A subgradient method with constant step-size for $$\ell _1$$-composite optimization Open
Subgradient methods are the natural extension to the non-smooth case of the classical gradient descent for regular convex optimization problems. However, in general, they are characterized by slow convergence rates, and they require decrea…
View article: From NeurODEs to AutoencODEs: a mean-field control framework for width-varying Neural Networks
From NeurODEs to AutoencODEs: a mean-field control framework for width-varying Neural Networks Open
The connection between Residual Neural Networks (ResNets) and continuous-time control systems (known as NeurODEs) has led to a mathematical analysis of neural networks which has provided interesting results of both theoretical and practica…
View article: A subgradient method with constant step-size for $\ell_1$-composite optimization
A subgradient method with constant step-size for $\ell_1$-composite optimization Open
Subgradient methods are the natural extension to the non-smooth case of the classical gradient descent for regular convex optimization problems. However, in general, they are characterized by slow convergence rates, and they require decrea…
View article: Optimal control of ensembles of dynamical systems
Optimal control of ensembles of dynamical systems Open
In this paper we consider the problem of the optimal control of an ensemble of affine-control systems. After proving the well-posedness of the minimization problem under examination, we establish a Γ-convergence result that allows us to su…
View article: Losing momentum in continuous-time stochastic optimisation
Losing momentum in continuous-time stochastic optimisation Open
The training of modern machine learning models often consists in solving high-dimensional non-convex optimisation problems that are subject to large-scale data. In this context, momentum-based stochastic optimisation algorithms have become…
View article: Deep Learning approximation of diffeomorphisms via linear-control systems
Deep Learning approximation of diffeomorphisms via linear-control systems Open
In this paper we propose a Deep Learning architecture to approximate\ndiffeomorphisms diffeotopic to the identity. We consider a control system of\nthe form $\\dot x = \\sum_{i=1}^lF_i(x)u_i$, with linear dependence in the\ncontrols, and w…
View article: A Gradient Flow Equation for Optimal Control Problems With End-point Cost
A Gradient Flow Equation for Optimal Control Problems With End-point Cost Open
In this paper, we consider a control system of the form $\dot x = F(x)u$ , linear in the control variable u . Given a fixed starting point, we study a finite-horizon optimal control problem, where we want to minimize a weighted …
View article: Optimal Control of ensembles of dynamical systems
Optimal Control of ensembles of dynamical systems Open
In this paper we consider the problem of the optimal control of an ensemble of affine-control systems. After proving the well-posedness of the minimization problem under examination, we establish a $Γ$-convergence result that allows us to …
View article: A piecewise conservative method for unconstrained convex optimization
A piecewise conservative method for unconstrained convex optimization Open
View article: Deep Learning Approximation of Diffeomorphisms via Linear-Control Systems
Deep Learning Approximation of Diffeomorphisms via Linear-Control Systems Open
In this paper we propose a Deep Learning architecture to approximate diffeomorphisms diffeotopic to the identity. We consider a control system of the form $\dot x = \sum_{i=1}^lF_i(x)u_i$, with linear dependence in the controls, and we use…
View article: A gradient flow equation for optimal control problems with end-point cost
A gradient flow equation for optimal control problems with end-point cost Open
In this paper we consider a control system of the form $\dot x = F(x)u$, linear in the control variable $u$. Given a fixed starting point, we study a finite-horizon optimal control problem, where we want to minimize a weighted sum of an en…