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Recent studies have shown that adaptive networks driven by simple local rules can organize into "critical" global steady states, providing another framework for self-organized criticality (SOC). We focus on the important convergence to…
The background numerical noise $\varepsilon_{0} $ is determined by the maximum of truncation error and round-off error. For a chaotic system, the numerical error $\varepsilon(t)$ grows exponentially, say, $\varepsilon(t) = \varepsilon_{0}…
We study the problem of optimizing a function under a \emph{budgeted number of evaluations}. We only assume that the function is \emph{locally} smooth around one of its global optima. The difficulty of optimization is measured in terms of…
We devise a distributed asynchronous stochastic epsilon-gradient-based algorithm to enable a network of computing and communicating nodes to solve a constrained discrete-time time-varying stochastic convex optimization problem. Each node…
Variance reduction has been commonly used in stochastic optimization. It relies crucially on the assumption that the data set is finite. However, when the data are imputed with random noise as in data augmentation, the perturbed data set…
We present upper and lower bounds for the prediction error of the Lasso. For the case of random Gaussian design, we show that under mild conditions the prediction error of the Lasso is up to smaller order terms dominated by the prediction…
Long-term reservoir management often uses bounds on the reservoir level, between which the operator can work. However, these bounds are not always kept up-to-date with the latest knowledge about the reservoir drainage area, and thus become…
Most existing distance metric learning methods assume perfect side information that is usually given in pairwise or triplet constraints. Instead, in many real-world applications, the constraints are derived from side information, such as…
We analyze algorithms for solving stochastic variational inequalities (VI) without the bounded variance or bounded domain assumptions, where our main focus is min-max optimization with possibly unbounded constraint sets. We focus on two…
Diffusion models proved to be powerful models for generative speech enhancement. In recent SGMSE+ approaches, training involves a stochastic differential equation for the diffusion process, adding both Gaussian and environmental noise to…
This paper deals with the scenario approach to robust optimization. This relies on a random sampling of the possibly infinite number of constraints induced by uncertainties in the parameters of an optimization problem. Solving the resulting…
In this paper, we study consensus-based optimization (CBO), which is a multi-agent metaheuristic derivative-free optimization method that can globally minimize nonconvex nonsmooth functions and is amenable to theoretical analysis. Based on…
This paper considers the distributed convex-concave minimax optimization under the second-order similarity. We propose stochastic variance-reduced optimistic gradient sliding (SVOGS) method, which takes the advantage of the finite-sum…
In Stochastic Optimal Control (SOC) one minimizes the average cost-to-go, that consists of the cost-of-control (amount of efforts), cost-of-space (where one wants the system to be) and the target cost (where one wants the system to arrive),…
Stochastic compositional optimization (SCO) has attracted considerable attention because of its broad applicability to important real-world problems. However, existing works on SCO assume that the projection within a solution update is…
We investigate the problem of designing optimal classifiers in the strategic classification setting, where the classification is part of a game in which players can modify their features to attain a favorable classification outcome (while…
In this paper, we propose new sequential randomized algorithms for convex optimization problems in the presence of uncertainty. A rigorous analysis of the theoretical properties of the solutions obtained by these algorithms, for full…
Motivated by stochastic optimization, we introduce the problem of learning from samples of contextual value distributions. A contextual value distribution can be understood as a family of real-valued distributions, where each sample…
We design receding horizon control strategies for stochastic discrete-time linear systems with additive (possibly) unbounded disturbances, while obeying hard bounds on the control inputs. We pose the problem of selecting an appropriate…
This contribution examines optimization problems that involve stochastic dominance constraints. These problems have uncountably many constraints. We develop methods to solve the optimization problem by reducing the constraints to a finite…