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Generative modeling within constrained sets is essential for scientific and engineering applications involving physical, geometric, or safety requirements (e.g., molecular generation, robotics). We present a unified framework for…
In this paper, we consider a class of optimal control problems for a one-dimensional time-discrete constrained quasilinear diffusion state-systems of singular Allen--Cahn types and its regularized approximating problems. We note that the…
We consider the problem of estimating the possibly non-convex cost of an agent by observing its interactions with a nonlinear, non-stationary and stochastic environment. For this inverse problem, we give a result that allows to estimate the…
Recent advancements in diffusion models and diffusion bridges primarily focus on finite-dimensional spaces, yet many real-world problems necessitate operations in infinite-dimensional function spaces for more natural and interpretable…
We obtain a probabilistic solution to linear-quadratic optimal control problems with state constraints. Given a closed set $\mathcal{D}\subseteq [0,T]\times\mathbb{R}^d$, a diffusion $X$ in $\mathbb{R}^d$ must be linearly controlled in…
Diffusion models have demonstrated empirical successes in various applications and can be adapted to task-specific needs via guidance. This paper studies a form of gradient guidance for adapting a pre-trained diffusion model towards…
Generative (diffusion) priors demonstrate remarkable performance in addressing inverse problems in imaging. Yet, for scientific and medical imaging, it is crucial that reconstruction techniques remain stable and reliable under imperfect…
Many discrete-time optimal stopping problems are known to have more tractable limit forms based on a planar Poisson process. Using this tool we find a solution to the optimal stopping problem for i.i.d. sequence of $n$ discrete uniform…
We study the optimal dividend problem for a firm's manager who has partial information on the profitability of the firm. The problem is formulated as one of singular stochastic control with partial information on the drift of the underlying…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
Control of continuous time dynamics with multiplicative noise is a classic topic in stochastic optimal control. This work addresses the problem of designing infinite horizon optimal controls with stability guarantees for \textit{a single…
This paper discusses a general and useful stability principle which, roughly speaking, says that given a uniformly continuous function defined on an arbitrary metric space, if the function is bounded on the constraint set and we slightly…
A new class of control problems is discussed - homeostasis control. Homeostasis control problems can be considered as control problems with a given target set, in particular, as a problem of stabilizing the values of some target function,…
We present a formulation of an optimal control problem for a two-dimensional diffusion process governed by a Fokker-Planck equation to achieve a nonequilibrium steady state with a desired circulation while accelerating convergence toward…
In this paper we study optimal stopping problems with respect to distorted expectations of the form \begin{eqnarray*} \mathcal{E}(X)=\int_{-\infty}^{\infty} x\,dG(F_X(x)), \end{eqnarray*} where $F_X$ is the distribution function of $X$ and…
Various bias-correction methods such as EXTRA, gradient tracking methods, and exact diffusion have been proposed recently to solve distributed {\em deterministic} optimization problems. These methods employ constant step-sizes and converge…
Resetting or restart, when applied to a stochastic process, usually brings its dynamics to a time-independent stationary state. In turn, the optimal resetting rate makes the mean time to reach a target to be the shortest one. These and…
We survey continuous-time generative modeling methods based on transporting a simple reference distribution to a data distribution via stochastic or deterministic dynamics. We present a unified framework in which diffusion models,…
This paper introduces a statistical treatment of inverse problems constrained by models with stochastic terms. The solution of the forward problem is given by a distribution represented numerically by an ensemble of simulations. The goal is…
Inverse optimization (Inverse optimal control) is the task of imputing a cost function such that given test points (trajectories) are (nearly) optimal with respect to the discovered cost. Prior methods in inverse optimization assume that…