Related papers: Stochastic Differential Inclusions driven by Maxim…
We derive novel concentration inequalities for the operator norm of the sum of self-adjoint operators that do not explicitly depend on the underlying dimension of the operator, but rather an intrinsic notion of it. Our analysis leads to…
Second-order continuous-time dissipative dynamical systems with viscous and Hessian driven damping have inspired effective first-order algorithms for solving convex optimization problems. While preserving the fast convergence properties of…
Stochastic policies (also known as relaxed controls) are widely used in continuous-time reinforcement learning algorithms. However, executing a stochastic policy and evaluating its performance in a continuous-time environment remain open…
Monotone systems, also known as order-preserving or cooperative systems, are prevalent in models of engineering applications such as transportation and biological networks. In this paper, we investigate the problem of finding a control…
We consider monotone inclusions defined on a Hilbert space where the operator is given by the sum of a maximal monotone operator $T$ and a single-valued monotone, Lipschitz continuous, and expectation-valued operator $V$. We draw motivation…
In this paper, we prove the existence and uniqueness of solutions of the fractional p-Laplace equation with a polynomial drift of arbitrary order driven by superlinear transport noise. By the monotone argument, we first prove the existence…
Lipschitz continuity characterizes the worst-case sensitivity of neural networks to small input perturbations; yet its dynamics (i.e. temporal evolution) during training remains under-explored. We present a rigorous mathematical framework…
In this work, we shall consider the existence and uniqueness of stationary solutions to stochastic partial functional differential equations with additive noise in which a neutral type of delay is explicitly presented. We are especially…
We study extension theorems for Lipschitz-type operators acting on metric spaces and with values on spaces of integrable functions. Pointwise domination is not a natural feature of such spaces, and so almost everywhere inequalities and…
Robust stability and stochastic stability have separately seen intense study in control theory for many decades. In this work we establish relations between these properties for discrete-time systems and employ them for robust control…
Multi-time-scale stochastic approximation is an iterative algorithm for finding the fixed point of a set of $N$ coupled operators given their noisy samples. It has been observed that due to the coupling between the decision variables and…
This paper presents a comprehensive analysis of a broad range of variations of the stochastic proximal point method (SPPM). Proximal point methods have attracted considerable interest owing to their numerical stability and robustness…
We present a theory of backward stochastic differential equations in continuous time with an arbitrary filtered probability space. No assumptions are made regarding the left continuity of the filtration, of the predictable quadratic…
This paper is devoted to the investigation of inertial dynamical systems with implicit Hessian-driven damping for strongly quasiconvex optimization which is a specific class of nonconvex optimization problems. We first establish exponential…
Time-varying stochastic optimization problems frequently arise in machine learning practice (e.g. gradual domain shift, object tracking, strategic classification). Although most problems are solved in discrete time, the underlying process…
In this paper, under the monotonicity of pairs of operators, we propose some Generalized Proximal Point Algorithms to solve non-monotone inclusions using warped resolvents and transformed resolvents. The weak, strong, and linear convergence…
This paper aims to investigate the numerical approximation of a general second order parabolic stochastic partial differential equation(SPDE) driven by multiplicative and additive noise under more relaxed conditions. The SPDE is discretized…
The automated synthesis of control policies for stochastic dynamical systems presents significant challenges. A standard approach is to construct a finite-state abstraction of the continuous system, typically represented as a Markov…
We consider an abstract class of differential inclusions, which covers differential-algebraic and non-autonomous problems as well as problems with delay. Under weak assumptions on the operators involved, we prove the well-posedness of those…
In this article, we study the existence and uniqueness problem for linear Stochastic PDEs involving a bilaplacian operator. Our results on the existence and uniqueness are obtained through an application of a Monotonicity inequality, which…