The Bayesian paradigm offers principled tools for sequential decision-making under uncertainty, but its reliance on a probabilistic model for all parameters can hinder the incorporation of complex structural constraints. We introduce a minimalist Bayesian framework that places a prior only on the component of interest, such as the location of the optimum. Nuisance parameters are … Read more
Wasserstein distributionally robust optimization (DRO), a leading paradigm in data-driven decision-making, requires evaluating worst-case risk over a high-dimensional Wasserstein ball. We study when this worst-case evaluation admits an exact reduction to a one-dimensional formulation, in the sense that it can be carried out over a one-dimensional Wasserstein ball centered at the projected reference distribution. We … Read more
This paper proposes a distributed asynchronous adaptive gradient tracking method, DASYAGT, to solve the distributed stochastic optimization problems with decision-dependent distributions over directed graphs. DASYAGT employs the local adaptive gradient to estimate the gradient of the objective function and introduces the auxiliary running-sum variable to handle asynchrony. We show that the iterates generated by DASYAGT … Read more
This paper aims to seek the performative stable solution and the optimal solution of the distributed stochastic optimization problem with decision-dependent distributions, which is a finite-sum stochastic optimization problem over a network and the distribution depends on the decision variables. For the performative stable solution, we provide an algorithm, DSGTD-GD, which combines the distributed stochastic … Read more
Contextual optimization enhances decision quality by leveraging side information to improve predictions of uncertain parameters. However, existing approaches face significant challenges when dealing with multimodal or mixtures of distributions. The inherent complexity of such structures often precludes an explicit functional relationship between the contextual information and the uncertain parameters, limiting the direct applicability of parametric … Read more
This paper presents a restart version of the Adaptive Moment Estimation (Adam) method for bound constrained nonlinear optimization problems. It aims to avoid getting trapped in a local minima and enable exploration the global optimum. The proposed method combines an adapted restart strategy coupling with barrier methodology to handle the bound constraints. Computational comparison with … Read more
We propose a novel algorithm for solving non-convex, nonlinear equality-constrained finite-sum optimization problems. The proposed algorithm incorporates an additional sampling strategy for sample size update into the well-known framework of quadratic penalty methods. Thus, depending on the problem at hand, the resulting method may exhibit a sample size strategy ranging from a mini-batch on one … Read more
In this work we consider unconstrained optimization problems. The objective function is known through a zeroth order stochastic oracle that gives an estimate of the true objective function. To solve these problems, we propose a derivativefree algorithm based on extrapolation techniques. Under reasonable assumptions we are able to prove convergence properties for the proposed algorithms. … Read more
We study a two-player zero-sum inspection game with incomplete information, where an inspector deploys resources to maximize the expected damage value of detected illegal items hidden by an adversary across capacitated locations. Inspection and illegal resources differ in their detection capabilities and damage values. Both players face uncertainty regarding each other’s available resources, modeled via … Read more
We study optimization over Riemannian embedded submanifolds, where the objective function is relatively smooth in the ambient Euclidean space. Such problems have broad applications but are still largely unexplored. We introduce two Riemannian first-order methods, namely the retraction-based and projection-based Riemannian Bregman gradient methods, by incorporating the Bregman distance into the update steps. The retraction-based … Read more