Related papers: Fixed Point Theory Analysis of a Lambda Policy Ite…
We introduce a weak asymptotic version of nonlinear contraction, termed \emph{asymptotic pointwise contraction}. For a mapping on a metric space, this notion requires the existence of a sequence of functions that dominate the distances…
In this article we consider a consistent convex feasibility problem in a real Hilbert space defined by a finite family of sets $C_i$. We are interested, in particular, in the case where for each $i$, $C_i=Fix (U_i)=\{z\in \mathcal H\mid…
Reinforcement learning methods often produce brittle policies -- policies that perform well during training, but generalize poorly beyond their direct training experience, thus becoming unstable under small disturbances. To address this…
This paper studies the robustness of reinforcement learning algorithms to errors in the learning process. Specifically, we revisit the benchmark problem of discrete-time linear quadratic regulation (LQR) and study the long-standing open…
Based on the idea of randomizing the traditional space theory of functional analysis, random functional analysis has been developed as functional analysis over random metric spaces, random normed modules and random locally convex modules.…
We introduce a new extragradient iterative process, motivated and inspired by [S. H. Khan, A Picard-Mann Hybrid Iterative Process, Fixed Point Theory and Applications, doi:10.1186/1687-1812-2013-69], for finding a common element of the set…
In this article we discuss a possibility to implement a well-known scheme of proof for contraction mapping theorems in a situation, when convergence, families of Cauchy sequences, and contractiveness of mappings are defined axiomatically.…
This paper revisits and extends the convergence and robustness properties of value and policy iteration algorithms for discrete-time linear quadratic regulator problems. In the model-based case, we extend current results concerning the…
Fixed point iterations are a fundamental tool in numerical analysis and scientific computing for the approximation of solutions to nonlinear problems. Their convergence is often established via the Banach fixed point theorem, provided that…
There has recently been an increased interest in reinforcement learning for nonlinear control problems. However standard reinforcement learning algorithms can often struggle even on seemingly simple set-point control problems. This paper…
Recently, there has been a surge in interest in safe and robust techniques within reinforcement learning (RL). Current notions of risk in RL fail to capture the potential for systemic failures such as abrupt stoppages from system failures…
We introduce "logically contractive mappings" nonexpansive self-maps that contract along a subsequence of iterates and prove a fixed-point theorem that extends Banach's principle. We obtain event-indexed convergence rates and, under bounded…
We study a posterior sampling approach to efficient exploration in constrained reinforcement learning. Alternatively to existing algorithms, we propose two simple algorithms that are more efficient statistically, simpler to implement and…
Quadratic programming is a workhorse of modern nonlinear optimization, control, and data science. Although regularized methods offer convergence guarantees under minimal assumptions on the problem data, they can exhibit the slow…
In many branches of engineering, Banach contraction mapping theorem is employed to establish the convergence of certain deterministic algorithms. Randomized versions of these algorithms have been developed that have proved useful in…
When applying imitation learning techniques to fit a policy from expert demonstrations, one can take advantage of prior stability/robustness assumptions on the expert's policy and incorporate such control-theoretic prior knowledge…
The goal of this work is to serve as a foundation for deep studies of the topology of state, action, and policy spaces in reinforcement learning. By studying these spaces from a mathematical perspective, we expect to gain more insight into…
The paper is devoted to the fixed point theory in four aspects: of contractions, nonexpansive mappings, generalized inward mappings, and of the tool theorems. The manuscript was written about ten years ago. At first Nadler's concept of…
We investigate the important problem of certifying stability of reinforcement learning policies when interconnected with nonlinear dynamical systems. We show that by regulating the input-output gradients of policies, strong guarantees of…
This paper presents a novel approach to reinforcement learning (RL) for control systems that provides probabilistic stability guarantees using finite data. Leveraging Lyapunov's method, we propose a probabilistic stability theorem that…