277 citations · 564 across the 48 of their papers we have counts for
26 papers · 1 filter
Functional role of synchronization: A mean-field control perspective
Prashant Mehta, Sean Meyn
The broad goal of the research surveyed in this article is to develop methods for understanding the aggregate behavior of interconnected dynamical systems, as found in mathematical…
Variance Decay Property for Filter Stability
Jin Won Kim, Prashant G. Mehta
This paper is concerned with the problem of nonlinear (stochastic) filter stability of a hidden Markov model (HMM) with white noise observations. A contribution is the variance dec…
Sufficient Exploration for Convex Q-learning
Fan Lu, Prashant Mehta, Sean Meyn +1
In recent years there has been a collective research effort to find new formulations of reinforcement learning that are simultaneously more efficient and more amenable to analysis.…
Duality for Nonlinear Filtering II: Optimal Control
Jin Won Kim, Prashant G. Mehta
This paper is concerned with the development and use of duality theory for a nonlinear filtering model with white noise observations. The main contribution of this paper is to intr…
Duality for Nonlinear Filtering I: Observability
Jin Won Kim, Prashant G. Mehta
This paper is concerned with the development and use of duality theory for a hidden Markov model (HMM) with white noise observations. The main contribution of this work is to intro…
How does a Rational Agent Act in an Epidemic?
S. Yagiz Olmez, Shubham Aggarwal, Jin Won Kim +4
Evolution of disease in a large population is a function of the top-down policy measures from a centralized planner, as well as the self-interested decisions (to be socially active…
Modeling Presymptomatic Spread in Epidemics via Mean-Field Games
S. Yagiz Olmez, Shubham Aggarwal, Jin Won Kim +4
This paper is concerned with developing mean-field game models for the evolution of epidemics. Specifically, an agent's decision -- to be socially active in the midst of an epidemi…
A Dynamic Programming Formulation for the Nonlinear Filter
Jin Won Kim, Prashant G. Mehta
This paper build on our recent work where we presented a dual stochastic optimal control formulation of the nonlinear filtering problem [1]. The constraint for the dual problem is…
Minimum variance constrained estimator
Prabhat K. Mishra, Girish Chowdhary, Prashant G. Mehta
This paper is concerned with the problem of state estimation for discrete-time linear systems in the presence of additional (equality or inequality) constraints on the state (or es…
Optimality vs Stability Trade-off in Ensemble Kalman Filters
Amirhossein Taghvaei, Prashant G. Mehta, Tryphon T. Georgiou
This paper is concerned with optimality and stability analysis of a family of ensemble Kalman filter (EnKF) algorithms. EnKF is commonly used as an alternative to the Kalman filter…
Feedback Particle Filter for Collective Inference
Jin Won Kim, Amirhossein Taghvaei, Yongxin Chen +1
The purpose of this paper is to describe the feedback particle filter algorithm for problems where there are a large number () of non-interacting agents (targets) with a large n…
Optimal Control of a Soft CyberOctopus Arm
Tixian Wang, Udit Halder, Heng-Sheng Chang +2
In this paper, we use the optimal control methodology to control a flexible, elastic Cosserat rod. An inspiration comes from stereotypical movement patterns in octopus arms, which…
Convex Q-Learning, Part 1: Deterministic Optimal Control
Prashant G. Mehta, Sean P. Meyn
It is well known that the extension of Watkins' algorithm to general function approximation settings is challenging: does the projected Bellman equation have a solution? If so, is…
An Optimal Control Derivation of Nonlinear Smoothing Equations
Jin W. Kim, Prashant G. Mehta
The purpose of this paper is to review and highlight some connections between the problem of nonlinear smoothing and optimal control of the Liouville equation. The latter has been…
Optimal Rate of Convergence for Quasi-Stochastic Approximation
Andrey Bernstein, Yue Chen, Marcello Colombino +3
The Robbins-Monro stochastic approximation algorithm is a foundation of many algorithmic frameworks for reinforcement learning (RL), and often an efficient approach to solving (or…
What is the Lagrangian for Nonlinear Filtering?
Jin W. Kim, Prashant G. Mehta, Sean P. Meyn
Duality between estimation and optimal control is a problem of rich historical significance. The first duality principle appears in the seminal paper of Kalman-Bucy, where the prob…
Diffusion map-based algorithm for Gain function approximation in the Feedback Particle Filter
Amirhossein Taghvaei, Prashant G. Mehta, Sean P. Meyn
Feedback particle filter (FPF) is a numerical algorithm to approximate the solution of the nonlinear filtering problem in continuous-time settings. In any numerical implementation…
Derivation and Extensions of the Linear Feedback Particle Filter based on Duality Formalisms
Jin W. Kim, Amirhossein Taghvaei, Prashant G. Mehta
This paper is concerned with a duality-based approach to derive the linear feedback particle filter (FPF). The FPF is a controlled interacting particle system where the control law…
How regularization affects the critical points in linear networks
Amirhossein Taghvaei, Jin W. Kim, Prashant G. Mehta
This paper is concerned with the problem of representing and learning a linear transformation using a linear neural network. In recent years, there has been a growing interest in t…
Kalman Filter and its Modern Extensions for the Continuous-time Nonlinear Filtering Problem
Amirhossein Taghvaei, Jana de Wiljes, Prashant G. Mehta +1
This paper is concerned with the filtering problem in continuous-time. Three algorithmic solution approaches for this problem are reviewed: (i) the classical Kalman-Bucy filter whi…
Feedback Particle Filter on Matrix Lie Groups
Chi Zhang, Amirhossein Taghvaei, Prashant G. Mehta
This paper is concerned with the problem of continuous-time nonlinear filtering for stochastic processes on a connected matrix Lie group. The main contribution of this paper is to…
A Controlled Particle Filter for Global Optimization
Chi Zhang, Amirhossein Taghvaei, Prashant G. Mehta
A particle filter is introduced to numerically approximate a solution of the global optimization problem. The theoretical significance of this work comes from its variational aspec…
Attitude Estimation with Feedback Particle Filter
Chi Zhang, Amirhossein Taghvaei, Prashant G. Mehta
This paper presents theory, application, and comparisons of the feedback particle filter (FPF) algorithm for the problem of attitude estimation. The paper builds upon our recent wo…
Feedback Particle Filter on Matrix Lie Groups
Chi Zhang, Amirhossein Taghvaei, Prashant G. Mehta
This paper is concerned with the problem of continuous-time nonlinear filtering for stochastic processes on a compact and connected matrix Lie group without boundary, e.g. SO(n) an…