Related papers: Recursive Maximum Likelihood Estimation for Intera…
The continuous dynamical system approach to deep learning is explored in order to devise alternative frameworks for training algorithms. Training is recast as a control problem and this allows us to formulate necessary optimality conditions…
In this paper, we analyse the rate of convergence of a system of $N$ interacting particles with mean-field rank based interaction in the drift coefficient and constant diffusion coefficient. We first adapt arguments by Kolli and Shkolnikhov…
Maximum likelihood iteration is one of the most commonly used reconstruction algorithms in quantum tomography. The main appeal of the method is that it is easy to implement and that it converges reliably to a physically meaningful density…
Stochastic kinetic models describe systems across biology, chemistry, and physics where discrete events and small populations render deterministic approximations inadequate. Parameter inference and inverse design in these systems require…
Policy gradient methods are a vital ingredient behind the success of modern reinforcement learning. Modern policy gradient methods, although successful, introduce a residual error in gradient estimation. In this work, we argue that this…
This paper considers the problem of randomized influence maximization over a Markovian graph process: given a fixed set of nodes whose connectivity graph is evolving as a Markov chain, estimate the probability distribution (over this fixed…
We study the problem of computing the maximum likelihood estimator (MLE) of multivariate log-concave densities. Our main result is the first computationally efficient algorithm for this problem. In more detail, we give an algorithm that, on…
This paper studies an infinite horizon optimal control problem for discrete-time linear system and quadratic criteria, both with random parameters which are independent and identically distributed with respect to time. In this general…
We consider the safety evaluation of discrete time, stochastic systems over a finite horizon. Therefore, we discuss and link probabilistic invariance with reachability as well as reach-avoid problems. We show how to efficiently compute…
In this paper, we present a novel iterative Monte Carlo method for approximating the stationary probability of a single state of a positive recurrent Markov chain. We utilize the characterization that the stationary probability of a state…
We consider the problem of estimating the asymptotic variance of a function defined on a Markov chain, an important step for statistical inference of the stationary mean. We design a novel recursive estimator that requires $O(1)$…
This paper presents a particle-based optimization method designed for addressing minimization problems with equality constraints, particularly in cases where the loss function exhibits non-differentiability or non-convexity. The proposed…
We study the problem of parameter estimation for large exchangeable interacting particle systems when a sample of discrete observations from a single particle is known. We propose a novel method based on martingale estimating functions…
In this article we study the convergence of a stochastic particle system that interacts through threshold hitting times towards a novel equation of McKean-Vlasov type. The particle system is motivated by an original model for the behavior…
This paper investigates the problem of tracking solutions of stochastic optimization problems with time-varying costs that depend on random variables with decision-dependent distributions. In this context, we propose the use of an online…
We give a general existence and convergence result for interacting particle systems on locally finite graphs with possibly unbounded degrees or jump rates. We allow the local state space to be Polish, and the jumps at a site to affect the…
For algorithms based on interacting particle systems that admit a mean-field description, convergence analysis is often more accessible at the mean-field level. In order to transfer convergence results obtained at the mean-field level to…
In this paper, we study secure distributed optimization against arbitrary gradient attack in multi-agent networks. In distributed optimization, there is no central server to coordinate local updates, and each agent can only communicate with…
An infinite system of point particles placed in $\mathds{R}^d$ is studied. Its constituents perform random jumps with mutual repulsion described by a translation-invariant jump kernel and interaction potential, respectively. The pure states…
We analyse the performance of a recursive Monte Carlo method for the Bayesian estimation of the static parameters of a discrete--time state--space Markov model. The algorithm employs two layers of particle filters to approximate the…