Related papers: Featurized Occupation Measures for Structured Glob…
Proximal operations are among the most common primitives appearing in both practical and theoretical (or high-level) optimization methods. This basic operation typically consists in solving an intermediary (hopefully simpler) optimization…
In model-based reinforcement learning for safety-critical control systems, it is important to formally certify system properties (e.g., safety, stability) under the learned controller. However, as existing methods typically apply formal…
Semi-discrete optimal transport (SOT), which maps a continuous probability measure to a discrete one, is a fundamental problem with wide-ranging applications. Entropic regularization is often employed to solve the SOT problem, leading to a…
In this paper, a combined formation acquisition and cooperative extremum seeking control scheme is proposed for a team of three robots moving on a plane. The extremum seeking task is to find the maximizer of an unknown two-dimensional…
Aligning Large Language Models (LLMs) with human values often involves balancing multiple, conflicting objectives such as helpfulness and harmlessness. Training these models is computationally intensive, and centralizing the process raises…
Hamilton-Jacobi (HJ) reachability analysis provides a formal method for guaranteeing safety in constrained control problems. It synthesizes a value function to represent a long-term safe set called feasible region. Early synthesis methods…
This work addresses the occupation measure relaxation of calculus of variations problems, which is an infinite-dimensional linear programming relaxation amenable to numerical approximation by a hierarchy of semidefinite optimization…
Mechanical systems are usually modeled by second-order Ordinary Differential Equations (ODE) which take the form $\ddot{q} = f(t, q, \dot{q})$. While simulation methods tailored to these equations have been studied, using them in direct…
We develop a dynamic version of the primal-dual method for optimization problems, and apply it to obtain the following results. (1) For the dynamic set-cover problem, we maintain an $O(f^2)$-approximately optimal solution in $O(f \cdot \log…
In this paper, we present and analyse a class of "filtered" numerical schemes for second order Hamilton-Jacobi-Bellman equations. Our approach follows the ideas introduced in B.D. Froese and A.M. Oberman, Convergent filtered schemes for the…
Hamilton-Jacobi (HJ) reachability-based filtering provides a powerful framework to co-optimize performance and safety (or liveness) for autonomous systems. Under this filtering scheme, a nominal controller is minimally modified to ensure…
Time-optimal control for high-order chain-of-integrators systems with full state constraints and arbitrarily given terminal states remains a challenging problem in the optimal control theory domain, yet to be resolved. To enhance further…
Numerical homogenization for mechanical multiscale modeling by means of the finite element method (FEM) is an elegant way of obtaining structure-property relations, if the behavior of the constituents of the lower scale is well understood.…
The time-fractional optimal transport (OT) and mean-field planning (MFP) models are developed to describe the anomalous transport of the agents in a heterogeneous environment such that their densities are transported from the initial…
Generalized measurements, also called positive operator-valued measures (POVMs), can offer advantages over projective measurements in various quantum information tasks. Here, we realize a generalized measurement of one and two…
We present a partial-differential-equation-based optimal path-planning framework for curvature constrained motion, with application to vehicles in 2- and 3-spatial-dimensions. This formulation relies on optimal control theory, dynamic…
This work addresses a Multi-Objective Shortest Path Problem (MO-SPP) on a graph where the goal is to find a set of Pareto-optimal solutions from a start node to a destination in the graph. A family of approaches based on MOA* have been…
Many real-world classification tasks require predicting multiple labels per instance, necessitating the optimization of complex evaluation metrics such as the $F$-measure and Jaccard index. While the Empirical Utility Maximization (EUM)…
Neural network algorithms have been recently applied to construct Parton Distribution Function (PDF) parametrizations which provide an alternative to standard global fitting procedures. We propose a technique based on an interactive neural…
We study a scenario where an aircraft has multiple heterogeneous sensors collecting measurements to track a target vehicle of unknown location. The measurements are sampled along the flight path and our goals to optimize sensor placement to…