Related papers: Low-regret shape optimization in the presence of m…

We consider the setting of iterative learning control, or model-based policy learning in the presence of uncertain, time-varying dynamics. In this setting, we propose a new performance metric, planning regret, which replaces the standard…

Modern control designs in robotics, aerospace, and cyber-physical systems rely heavily on real-world data obtained through system outputs. However, these outputs can be compromised by system faults and malicious attacks, distorting critical…

We develop parameter-free algorithms for unconstrained online learning with regret guarantees that scale with the gradient variation $V_T(u) = \sum_{t=2}^T \|\nabla f_t(u)-\nabla f_{t-1}(u)\|^2$. For $L$-smooth convex loss, we provide…

In shape optimisation it is desirable to obtain deformations of a given mesh without negative impact on the mesh quality. We propose a new algorithm using least square formulations of the Cauchy-Riemann equations. Our method allows to…

We study a time-varying Bayesian optimization problem with bandit feedback, where the reward function belongs to a Reproducing Kernel Hilbert Space (RKHS). We approach the problem via an upper-confidence bound Gaussian Process algorithm,…

We characterize approximate global optimal solutions (${\varepsilon}$-optima) to reverse optimization problems, namely, problems whose non-convex constraint is of the form $h(x) \geq 0$. This issue has not been addressed previously in the…

Model complexity plays an essential role in its selection, namely, by choosing a model that fits the data and is also succinct. Two-part codes and the minimum description length have been successful in delivering procedures to single out…

We study the problem of determining an effective exploration strategy in static and non-linear optimization problems, which depend on an unknown scalar parameter to be learned from online collected noisy data. An optimal trade-off between…

We propose a new fictitious domain finite element method, well suited for elliptic problems posed in a domain given by a level-set function without requiring a mesh fitting the boundary. To impose the Dirichlet boundary conditions, we…

In this correspondence, we introduce a minimax regret criteria to the least squares problems with bounded data uncertainties and solve it using semi-definite programming. We investigate a robust minimax least squares approach that minimizes…

In this paper, we consider the finite element approximation to a parabolic Dirichlet boundary control problem and establish new a priori error estimates. In the temporal semi-discretization we apply the DG(0) method for the state and the…

In this paper, the problem of distributed optimization is studied via a network of agents. Each agent only has access to a stochastic gradient of its own objective function in the previous time, and can communicate with its neighbors via a…

An important step in shape optimization with partial differential equation constraints is to adapt the geometry during each optimization iteration. Common strategies are to employ mesh-deformation or re-meshing, where one or the other…

This paper explores the reconstruction of a space-dependent parameter in inverse diffusion problems, proposing a shape-optimization-based approach. We consider a Robin boundary condition, physically motivated in diffuse optical tomography…

We study the problem of adaptively controlling a known discrete-time nonlinear system subject to unmodeled disturbances. We prove the first finite-time regret bounds for adaptive nonlinear control with matched uncertainty in the stochastic…

Bilevel optimization problems arise in many applications where decisions must account for the optimal response of another system, such as in game-theoretic settings. However, these problems are notoriously challenging, as even linear…

We address the problem of the achievable regret rates with online logistic regression. We derive lower bounds with logarithmic regret under $L_1$, $L_2$, and $L_\infty$ constraints on the parameter values. The bounds are dominated by $d/2…

Regret minimization is a powerful tool for solving large-scale problems; it was recently used in breakthrough results for large-scale extensive-form game solving. This was achieved by composing simplex regret minimizers into an overall…

In performative prediction, the deployment of a predictive model triggers a shift in the data distribution. As these shifts are typically unknown ahead of time, the learner needs to deploy a model to get feedback about the distribution it…

In this article we consider shape optimization problems as optimal control problems via the method of mappings. Instead of optimizing over a set of admissible shapes a reference domain is introduced and it is optimized over a set of…