Related papers: A Unifying Modeling Abstraction for Infinite-Dimen…

Several machine learning models are defined for inputs of any size, such as graphs with different numbers of nodes and point clouds containing varying numbers of points. The universality properties of such any-dimensional models remain…

We develop a general compactification framework to facilitate analysis of nonlinear nonautonomous ODEs where nonautonomous terms decay asymptotically. The strategy is to compactify the problem: the phase space is augmented with a bounded…

Lying on the heart of intelligent decision-making systems, how policy is represented and optimized is a fundamental problem. The root challenge in this problem is the large scale and the high complexity of policy space, which exacerbates…

Optimal transport has been an essential tool for reconstructing dynamics from complex data. With the increasingly available multifaceted data, a system can often be characterized across multiple spaces. Therefore, it is crucial to maintain…

We develop a general framework for data-driven approximation of input-output maps between infinite-dimensional spaces. The proposed approach is motivated by the recent successes of neural networks and deep learning, in combination with…

Solving optimal control problems (OCPs) of autonomous agents operating under spatial and temporal constraints fast and accurately is essential in applications ranging from eco-driving of autonomous vehicles to quadrotor navigation. However,…

Diffusion models have had a profound impact on many application areas, including those where data are intrinsically infinite-dimensional, such as images or time series. The standard approach is first to discretize and then to apply…

In this paper, we propose an incremental abstraction method for dynamically over-approximating nonlinear systems in a bounded domain by solving a sequence of linear programs, resulting in a sequence of affine upper and lower hyperplanes…

We study a class of infinite-dimensional singular stochastic control problems with applications in economic theory and finance. The control process linearly affects an abstract evolution equation on a suitable partially-ordered…

Inverse problems are ubiquitous in science and engineering. Many of these are naturally formulated as a PDE-constrained optimization problem. These non-linear, large-scale, constrained optimization problems know many challenges, of which…

This survey is focused on certain sequential decision-making problems that involve optimizing over probability functions. We discuss the relevance of these problems for learning and control. The survey is organized around a framework that…

Partial differential equation (PDE)-constrained optimization arises in many scientific and engineering domains, such as energy systems, fluid dynamics and material design. In these problems, the decision variables (e.g., control inputs or…

We provide a generalization of first-order necessary conditions of optimality for infinite-dimensional optimization problems with a finite number of inequality constraints and with a finite number of inequality and equality constraints. Our…

Neural abstractions have been recently introduced as formal approximations of complex, nonlinear dynamical models. They comprise a neural ODE and a certified upper bound on the error between the abstract neural network and the concrete…

In many optimization problems arising from scientific, engineering and artificial intelligence applications, objective and constraint functions are available only as the output of a black-box or simulation oracle that does not provide…

The Distributed Constraint Optimization Problem (DCOP) formulation is a powerful tool to model multi-agent coordination problems that are distributed by nature. The formulation is suitable for problems where variables are discrete and…

Inverse optimal control (IOC) aims to estimate the underlying cost that governs the observed behavior of an expert system. However, in practical scenarios, the collected data is often corrupted by noise, which poses significant challenges…

In practice, optimization tasks have some structure that allows developing new algorithms for every problem with faster convergence rates. Using the structure of optimization tasks, we can propose algorithms with more optimistic convergence…

We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…

In optimization the duality gap between the primal and the dual problems is a measure of the suboptimality of any primal-dual point. In classical mechanics the equations of motion of a system can be derived from the Hamiltonian function,…