Related papers: Coarse-Grained Smoothness for RL in Metric Spaces
We analyze nonlinearly preconditioned gradient methods for solving smooth minimization problems. We introduce a generalized smoothness property, based on the notion of abstract convexity, that is broader than Lipschitz smoothness and…
The starting assumptions to study the convergence and complexity of gradient-type methods may be the smoothness (also called Lipschitz continuity of gradient) and the strong convexity. In this note, we revisit these two basic properties…
The common idea behind complexity reduction in physical systems is separation of information into "physically meaningful" and "safely ignorable". Here we consider a generic notion of such separation -- implemented by coarse-graining the…
In the last several years, the intimate connection between convex optimization and learning problems, in both statistical and sequential frameworks, has shifted the focus of algorithmic machine learning to examine this interplay. In…
This paper proposes that Lipschitz continuity is a natural outcome of regularized least squares in kernel-based learning. Lipschitz continuity is an important proxy for robustness of input-output operators. It is also instrumental for…
We poorly understand the macroscopic properties of complex fluids and of amorphous bodies in general. This is mainly due to the interplay between phenomena at different levels and length-scales. In particular, it is not necessarily true…
The underlying theme of this article is a class of sequences in metric structures satisfying a much weaker kind of Cauchy condition, namely quasi-Cauchy sequences (introduced in \cite{bc}) that has been used to define several new concepts…
An expression for the stress tensor near an external boundary of a discrete mechanical system is derived explicitly in terms of the constituents' degrees of freedom and interaction forces. Starting point is the exact and general coarse…
The goal of this note is to prove that every real-valued Lipschitz function on a Banach space can be pointwise approximated on a given $\sigma$-compact set by smooth cylindrical functions whose asymptotic Lipschitz constants are controlled.…
Iteration complexities for optimizing smooth functions with first-order algorithms are typically stated in terms of a global Lipschitz constant of the gradient, and near-optimal results are then achieved using fixed step sizes. But many…
In the present paper, we use a generalised shift operator in order to define a generalised modulus of smoothness. By its means, we define generalised Lipschitz classes of functions, and we give their constructive characteristics.…
Estimating the state of an open quantum system monitored over time requires incorporating information from past measurements (filtering) and, for improved accuracy, also from future measurements (smoothing). While classical smoothing is…
For continuous state-action space scenarios, classical reinforcement learning (RL) theory predominantly focuses on low-rank Markov decision processes (MDPs), which provide sample-efficient guarantees at the expense of restrictive structural…
Bilevel programming has recently received a great deal of attention due to its abundant applications in many areas. The optimal value function approach provides a useful reformulation of the bilevel problem, but its utility is often limited…
Shuffling-type gradient methods are favored in practice for their simplicity and rapid empirical performance. Despite extensive development of convergence guarantees under various assumptions in recent years, most require the Lipschitz…
Estimating associations between spatial covariates and responses - rather than merely predicting responses - is central to environmental science, epidemiology, and economics. For instance, public health officials might be interested in…
In traditional models of supervised learning, the goal of a learner -- given examples from an arbitrary joint distribution on $\mathbb{R}^d \times \{\pm 1\}$ -- is to output a hypothesis that is competitive (to within $\epsilon$) of the…
The increasing availability of network data has driven the development of advanced statistical models specifically designed for metric graphs, where Gaussian processes play a pivotal role. While models such as Whittle-Mat\'ern fields have…
A function between two metric spaces is said to be totally bounded regular if it preserves totally bounded sets. These functions need not be continuous in general. Hence the purpose of this article is to study such functions vis-\'a-vis…
In these notes, we present a general result concerning the Lipschitz regularity of a certain type of set-valued maps often found in constrained optimization and control problems. The class of multifunctions examined in this paper is…