最优化与控制
We classify a family of matrices of shift operators that can be factorised in a computationally tractable manner with the Cholesky algorithm. Such matrices arise in the linear quadratic regulator problem, and related areas. We use the…
We study data-driven stabilization of continuous-time systems in autoregressive form when only noisy input-output data are available. First, we provide an operator-based characterization of the set of systems consistent with the data. Next,…
High-fidelity digital twins rely on the accurate assimilation of sensor data into physics-based computational models. In structural applications, such twins aim to identify spatially distributed quantities--such as elementwise weakening…
This paper proposes a novel and efficient optimization-based method for generating near time-optimal trajectories for holonomic vehicles navigating through complex but structured environments. The approach aims to solve the problem of…
In this paper, we present a generalization of the certainty equivalence principle of stochastic control. One interpretation of the classical certainty equivalence principle for linear systems with output feedback and quadratic costs is as…
The rapid growth of data centers increasingly requires data center operators to "bring own generation" to complement the available utility power plants to supply all or part of data center load. This practice sharply increases the number of…
Bilevel optimization has garnered significant attention in the machine learning community recently, particularly regarding the development of efficient numerical methods. While substantial progress has been made in developing efficient…
The LogSumExp function, dual to the Kullback-Leibler (KL) divergence, plays a central role in many important optimization problems, including entropy-regularized optimal transport (OT) and distributionally robust optimization (DRO). In…
This paper analyzes and explicitly solves a class of long-term average impulse control problems with a specific mean-field interaction. The underlying process is a general one-dimensional diffusion with appropriate boundary behavior. The…
We revisit the problem of ensuring strong test set performance via cross-validation, and propose a nested k-fold cross-validation scheme that selects hyperparameters by minimizing a weighted sum of the usual cross-validation metric and an…
In this paper, we introduce a new class of structured polynomials, called separable plus lower degree (SPLD) polynomials. The formal definition of an SPLD polynomial, which extends the concept of SPQ polynomials (Ahmadi et al. in Math Oper…
We consider optimal control problems involving nonlinear ordinary differential equations with uncertain inputs. Using the sample average approximation, we obtain optimal control problems with ensembles of deterministic dynamical systems.…
We often rely on probabilistic measures -- e.g. event probability or expected time -- to characterize systems' safety. However, determining these quantities for extremely low-probability events is generally challenging, as standard safety…
In this article, we study a simplified version of a density-dependent first-order mean field game, in which the players face a penalization equal to the population density at their final position. We consider the problem of finding an…
A major barrier to wide adoption of Electric Vehicles (EVs) is the absence of reliable and equitable charging infrastructure. Poorly located charging stations create coverage gaps and slow down EV adoption, especially in underserved…
Classical game theory is a powerful framework to analyze the strategic interactions among rational players. However, in many real-life scenarios, players choose actions based on their inherent natural tendencies rather than deliberate…
Kullback-Leibler divergence (KL) regularization is widely used in reinforcement learning, but it becomes infinite under support mismatch and can degenerate in low-noise limits. Utilizing a unified information-geometric framework, we…
Proximal operators are now ubiquitous in non-smooth optimization. Since their introduction in the seminal work of Moreau, many papers have shown their effectiveness on a wide variety of problems, culminating in their use to construct…
In this paper we address the problem of optimal liquidation of a large portfolio composed by securities exposed to default risk. The default time is described in terms of a Brownian motion representing the evolution of the value of the…
Zeroth-order (ZO) optimization is popular in real-world applications that accessing the gradient information is expensive or unavailable. Recently, adaptive ZO methods that normalize gradient estimators by the empirical standard deviation…