18 papers
Second-Order Mean-Field Schrödinger Bridges with Partial State Information
Asmaa Eldesoukey, Md Zulfiqur Haider, Italo Napolitano +2
Motivated by scenarios in control systems where decision making is informed by only partial information about the states, we introduce a novel formulation of the Schrödinger bridge…
On the Equivalence of Stochastic Control and Path Space Formulations for Schrödinger Bridges over Compact Connected Lie Groups
Hamza Mahmood, Georgiy A. Bondar, Abhishek Halder +1
We establish the equivalence between the stochastic optimal control and path space formulations of the Schrödinger bridge problem (SBP) for the kinematic equation on a compact conn…
Schrödinger Bridges over Kinetic Swarming Models
Asmaa Eldesoukey, Md Zulfiqur Haider, Italo Napolitano +2
Paradigmatic interaction models explain how collective behaviors can emerge in complex systems from interactions among the constituent agents. In bio-inspired swarms, however, inte…
Control Laguerre Tessellation: Semi-discrete Optimal Transport Over Control Systems
Ripon C. Sarker, Abhishek Halder
We study the optimal transport of optimally controlled agents from a compactly supported absolutely continuous source to a discrete target measure. The ground cost for the transpor…
Nonlinear Non-Gaussian Density Steering with Input and Noise Channel Mismatch: Sinkhorn with Memory for Solving the Control-affine Schrödinger Bridge Problem
Georgiy A. Bondar, Asmaa Eldesoukey, Yongxin Chen +1
Solutions to the Schrödinger bridge problem and its generalizations yield feedback control policies for optimal density steering over a controlled diffusion. To numerically compute…
A Generalized Sinkhorn Algorithm for Mean-Field Schrödinger Bridge
Asmaa Eldesoukey, Yongxin Chen, Abhishek Halder
The mean-field Schrödinger bridge (MFSB) problem concerns designing a minimum-effort controller that guides a diffusion process with nonlocal interaction to reach a given distribut…
Schrödinger Bridge Over A Compact Connected Lie Group
Hamza Mahmood, Abhishek Halder, Adeel Akhtar
This work studies the Schrödinger bridge problem for the kinematic equation on a compact connected Lie group. The objective is to steer a controlled diffusion between given initial…
Learning Concave Bid Shading Strategies in Online Auctions via Measure-valued Proximal Optimization
Iman Nodozi, Djordje Gligorijevic, Abhishek Halder
This work proposes a bid shading strategy for first-price auctions as a measure-valued optimization problem. We consider a standard parametric form for bid shading and formulate th…
Control-affine Schrödinger Bridge and Generalized Bohm Potential
Alexis M. H. Teter, Abhishek Halder, Michael D. Schneider +4
The control-affine Schrödinger bridge concerns with a stochastic optimal control problem. Its solution is a controlled evolution of joint state probability density subject to a con…
Set Invariance with Probability One for Controlled Diffusion: Score-based Approach
Wenqing Wang, Alexis M. H. Teter, Murat Arcak +1
Given a controlled diffusion and a connected, bounded, Lipschitz set, when is it possible to guarantee controlled set invariance with probability one? In this work, we answer this…
Markov Kernels, Distances and Optimal Control: A Parable of Linear Quadratic Non-Gaussian Distribution Steering
Alexis M. H. Teter, Wenqing Wang, Sachin Shivakumar +1
For a controllable linear time-varying (LTV) pair and positive semidefinite, we derive the Markov kernel for the Itô diff…
The Ground Cost for Optimal Transport of Angular Velocity
Karthik Elamvazhuthi, Abhishek Halder
We revisit the optimal transport problem over angular velocity dynamics given by the controlled Euler equation. The solution of this problem enables stochastic guidance of spin sta…
On the Hopf-Cole Transform for Control-affine Schrödinger Bridge
Alexis Teter, Abhishek Halder
The purpose of this note is to clarify the importance of the relation in solving control-affine Schrödinger bridge problems v…
Weyl Calculus and Exactly Solvable Schrödinger Bridges with Quadratic State Cost
Alexis M. H. Teter, Wenqing Wang, Abhishek Halder
Schrödinger bridge--a stochastic dynamical generalization of optimal mass transport--exhibits a learning-control duality. Viewed as a stochastic control problem, the Schrödinger br…
Schrödinger Bridge with Quadratic State Cost is Exactly Solvable
Alexis M. H. Teter, Wenqing Wang, Abhishek Halder
Schrödinger bridge is a diffusion process that steers a given distribution to another in a prescribed time while minimizing the effort to do so. It can be seen as the stochastic dy…
Solution of the Probabilistic Lambert's Problem: Optimal Transport Approach
Alexis M. H. Teter, Iman Nodozi, Abhishek Halder
The deterministic variant of the Lambert's problem was posed by Lambert in the 18th century and its solution for conic trajectory has been derived by many, including Euler, Lambert…
Solution of the Probabilistic Lambert Problem: Connections with Optimal Mass Transport, Schrödinger Bridge and Reaction-Diffusion PDEs
Alexis M. H. Teter, Iman Nodozi, Abhishek Halder
The Lambert problem originated in orbital mechanics. It concerns with determining the initial velocity for a boundary value problem involving the dynamical constraint due to gravit…
Wasserstein Consensus ADMM
Iman Nodozi, Abhishek Halder
We introduce Wasserstein consensus alternating direction method of multipliers (ADMM) and its entropic-regularized version: Sinkhorn consensus ADMM, to solve measure-valued optimiz…