Related papers: Variational Sufficiency and Solution Stability in …
Algorithmic stability is a central notion in learning theory that quantifies the sensitivity of an algorithm to small changes in the training data. If a learning algorithm satisfies certain stability properties, this leads to many important…
The stability analysis of model predictive control schemes without terminal constraints and/or costs has attracted considerable attention during the last years. We pursue a recently proposed approach which can be used to determine a…
The efficacy of robust optimization spans a variety of settings with uncertainties bounded in predetermined sets. In many applications, uncertainties are affected by decisions and cannot be modeled with current frameworks. This paper takes…
A new measure to characterize stability of complex dynamical systems against large perturbation is suggested, the stability threshold (ST). It quantifies the magnitude of the weakest perturbation capable to disrupt the system and switch it…
We examine the stability of loss-minimizing training processes that are used for deep neural networks (DNN) and other classifiers. While a classifier is optimized during training through a so-called loss function, the performance of…
In computing, as in many aspects of life, changes incur cost. Many optimization problems are formulated as a one-time instance starting from scratch. However, a common case that arises is when we already have a set of prior assignments, and…
A fractional generalization of variations is used to define a stability of non-integer order. Fractional variational derivatives are suggested to describe the properties of dynamical systems at fractional perturbations. We formulate…
We define and explore the concept of ideal stabilization. The program is ideally stabilizing if its every state is legitimate. Ideal stabilization allows the specification designer to prescribe with arbitrary degree of precision not only…
Stability of nonconvex quadratic programming problems under finitely many convex quadratic constraints in Hilbert spaces is investigated. We present several stability properties of the global solution map, and the continuity of the optimal…
Empirical diagnosis of stability has received considerable attention, mostly focused on variance metrics for early warning signals of abrupt system change. Despite this, the theoretical foundation and application has been limited to…
Stability is a central property in learning and statistics promising the output of an algorithm $A$ does not change substantially when applied to similar datasets $S$ and $S'$. It is an elementary fact that any sufficiently stable algorithm…
Optimizing decision problems under uncertainty can be done using a variety of solution methods. Soft computing and heuristic approaches tend to be powerful for solving such problems. In this overview article, we survey Evolutionary…
The notion of tail adversarial stability has been proven useful in obtaining limit theorems for tail dependent time series. Its implication and advantage over the classical strong mixing framework has been examined for max-linear processes,…
The use of available disturbance predictions within a nominal model predictive control formulation is studied. The main challenge that arises is the loss of recursive feasibility and stability guarantees when a persistent disturbance is…
In robust optimization, we would like to find a solution that is immunized against all scenarios that are modeled in an uncertainty set. Which scenarios to include in such a set is therefore of central importance for the tractability of the…
We derive a sufficient condition for stability in probability of an equilibrium of a randomly perturbed map in ${\mathbb R}^d$. This condition can be used to stabilize weakly unstable equilibria by random forcing. Analytical results on…
The subject of the present paper are stability properties of the solution set to set-valued inclusions. The latter are problems emerging in robust optimization and mathematical economics, which can not be cast in traditional generalized…
In this paper, we focus on the implementation of distributed programs in using a key-value store where the state of the nodes is stored in a replicated and partitioned data store to improve performance and reliability. Applications of such…
In optimal control problems, disturbances are typically dealt with using robust solutions, such as H-infinity or tube model predictive control, that plan control actions feasible for the worst-case disturbance. Yet, planning for every…
Self-stabilization is a strong property that guarantees that a network always resume correct behavior starting from an arbitrary initial state. Weaker guarantees have later been introduced to cope with impossibility results: probabilistic…