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Prescribed-time algorithms based on time-varying gains may have remarkable properties, such as regulation in a user-prescribed finite time that is the same for every nonzero initial condition and that holds even under matched disturbances.…

The problem of synthesizing stochastic explicit model predictive control policies is known to be quickly intractable even for systems of modest complexity when using classical control-theoretic methods. To address this challenge, we present…

In this work we provide a computationally tractable procedure for designing affine control policies, applied to constrained, discrete-time, partially observable, linear systems subject to set bounded disturbances, stochastic noise and…

In view of solving convex optimization problems with noisy gradient input, we analyze the asymptotic behavior of gradient-like flows under stochastic disturbances. Specifically, we focus on the widely studied class of mirror descent schemes…

Nonlinear systems are often subject to random influences. Sometimes the noise enters the system through physical boundaries and this leads to stochastic dynamic boundary conditions. A dynamic, as opposed to static, boundary condition…

Most biological systems are formed by component parts that to some degree are inter-related. Groups of parts that are more associated among themselves and are relatively autonomous from others are called modules. One of the consequences of…

We consider a 2-dimensional stochastic differential equation in polar coordinates depending on several parameters. We show that if these parameters belong to a specific regime then the deterministic system explodes in finite time, but the…

Increasing effort is put into the development of methods for learning mechanistic models from data. This task entails not only the accurate estimation of parameters but also a suitable model structure. Recent work on the discovery of…

Linear functions of many independent random variables lead to classical noises (white, Poisson, and their combinations) in the scaling limit. Some singular stochastic flows and some models of oriented percolation involve very nonlinear…

We present a full stochastic description of the pair approximation scheme to study binary-state dynamics on heterogeneous networks. Within this general approach, we obtain a set of equations for the dynamical correlations, fluctuations and…

This note is addressed to giving a short introduction to control theory of stochastic systems, governed by stochastic differential equations in both finite and infinite dimensions. We will mainly explain the new phenomenon and difficulties…

Policy gradient methods are widely used in reinforcement learning. Yet, the nonconvexity of policy optimization poses significant challenges in understanding the global convergence of policy gradient methods. For a class of finite-horizon…

In this work, we consider a multi-population system where the dynamics of each agent evolve according to a system of stochastic differential equations in a general functional setup, determined by the global state of the system. Each agent…

The policy gradient theorem describes the gradient of the expected discounted return with respect to an agent's policy parameters. However, most policy gradient methods drop the discount factor from the state distribution and therefore do…

This work is concerned with existence of weak solutions to discon- tinuous stochastic differential equations driven by multiplicative Gaus- sian noise and sliding mode control dynamics generated by stochastic differential equations with…

This paper examines learning the optimal filtering policy, known as the Kalman gain, for a linear system with unknown noise covariance matrices using noisy output data. The learning problem is formulated as a stochastic policy optimization…

To sample from an unconditionally trained Denoising Diffusion Probabilistic Model (DDPM), classifier guidance adds conditional information during sampling, but the gradients from classifiers, especially those not trained on noisy images,…

In this paper, we present a methodology to deploy the deterministic policy gradient method, using actor-critic techniques, when the optimal policy is approximated using a parametric optimization problem, where safety is enforced via hard…

We find that the performance of state-of-the-art models on Natural Language Inference (NLI) and Reading Comprehension (RC) analysis/stress sets can be highly unstable. This raises three questions: (1) How will the instability affect the…

Stochastic inverse problems considered in this article consist of estimating the probability distributions of intrinsically random inputs of computer models. These estimations are based on observable outputs affected by model noise, and…