no code implementations • 21 May 2024 • Georgiy A. Bondar, Robert Gifford, Linh Thi Xuan Phan, Abhishek Halder
We propose to learn the time-varying stochastic computational resource usage of software as a graph structured Schr\"odinger bridge problem.
no code implementations • 15 Jan 2024 • Alexis M. H. Teter, Iman Nodozi, Abhishek Halder
We show that the Lambert problem with endpoint joint probability density constraints is a generalized optimal mass transport (OMT) problem, thereby connecting this classical astrodynamics problem with a burgeoning area of research in modern stochastic control and stochastic machine learning.
no code implementations • 1 Oct 2023 • Georgiy A. Bondar, Robert Gifford, Linh Thi Xuan Phan, Abhishek Halder
The solution of the path structured multimarginal Schr\"{o}dinger bridge problem (MSBP) is the most-likely measure-valued trajectory consistent with a sequence of observed probability measures or distributional snapshots.
no code implementations • 12 Sep 2023 • Alexis M. H. Teter, Yongxin Chen, Abhishek Halder
In this work, we study a priori estimates for the contraction coefficients associated with the convergence of respective Schr\"{o}dinger systems.
no code implementations • 26 Jul 2023 • Iman Nodozi, Charlie Yan, Mira Khare, Abhishek Halder, Ali Mesbah
We show that the minimum effort control of colloidal self-assembly can be naturally formulated in the order-parameter space as a generalized Schr\"{o}dinger bridge problem -- a class of fixed-horizon stochastic optimal control problems that originated in the works of Erwin Schr\"{o}dinger in the early 1930s.
1 code implementation • 25 Oct 2022 • Alexis Teter, Iman Nodozi, Abhishek Halder
We propose a custom learning algorithm for shallow over-parameterized neural networks, i. e., networks with single hidden layer having infinite width.
no code implementations • 4 Oct 2022 • Shadi Haddad, Abhishek Halder
We consider estimating a compact set from finite data by approximating the support function of that set via sublinear regression.
no code implementations • 19 Aug 2022 • Iman Nodozi, Jared O'Leary, Ali Mesbah, Abhishek Halder
We propose formulating the finite-horizon stochastic optimal control problem for colloidal self-assembly in the space of probability density functions (PDFs) of the underlying state variables (namely, order parameters).
no code implementations • 17 Feb 2022 • Iman Nodozi, Abhishek Halder
We propose a distributed nonparametric algorithm for solving measure-valued optimization problems with additive objectives.
no code implementations • 25 Mar 2021 • Isin M. Balci, Abhishek Halder, Efstathios Bakolas
In particular, we show that when the terminal state covariance is upper bounded, with respect to the L\"{o}wner partial order, by the covariance matrix of the desired terminal normal distribution, then our problem admits a unique global minimizing state feedback gain.
no code implementations • 23 Feb 2021 • Shadi Haddad, Abhishek Halder
This is the first of a two part paper investigating the geometry of the integrator reach sets, and the applications thereof.
no code implementations • 14 Jul 2020 • Walid Krichene, Kenneth F. Caluya, Abhishek Halder
Recent results have shown that for two-layer fully connected neural networks, gradient flow converges to a global optimum in the infinite width limit, by making a connection between the mean field dynamics and the Wasserstein gradient flow.
no code implementations • 31 Mar 2020 • Kenneth F. Caluya, Abhishek Halder
How to steer a given joint state probability density function to another over finite horizon subject to a controlled stochastic dynamics with hard state (sample path) constraints?
no code implementations • 4 Aug 2019 • Abhishek Halder, Kenneth F. Caluya, Bertrand Travacca, Scott J. Moura
We provide gradient flow interpretations for the continuous-time continuous-state Hopfield neural network (HNN).
no code implementations • 1 Aug 2019 • Kenneth F. Caluya, Abhishek Halder
The need for computing the transient joint PDFs subject to prior dynamics arises in uncertainty propagation, nonlinear filtering and stochastic control.
no code implementations • 29 Dec 2018 • Abhishek Halder
We provide a variational interpretation of the DeGroot-Friedkin map in opinion dynamics.
1 code implementation • 28 Sep 2018 • Kenneth F. Caluya, Abhishek Halder
We develop a new method to solve the Fokker-Planck or Kolmogorov's forward equation that governs the time evolution of the joint probability density function of a continuous-time stochastic nonlinear system.
Optimization and Control