Related papers: Risk-Averse Models in Bilevel Stochastic Linear Pr…
We present a multilevel stochastic gradient descent method for the optimal control of systems governed by partial differential equations under uncertain input data. The gradient descent method used to find the optimal control leverages a…
Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…
This paper concerns parameterized convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional Banach (resp. finite-dimensional) spaces and that are indexed by an arbitrary fixed set T…
In this work we study optimization problems subject to a failure constraint. This constraint is expressed in terms of a condition that causes failure, representing a physical or technical breakdown. We formulate the problem in terms of a…
We propose a risk-averse statistical learning framework wherein the performance of a learning algorithm is evaluated by the conditional value-at-risk (CVaR) of losses rather than the expected loss. We devise algorithms based on stochastic…
The multilevel reverse Stackelberg game is considered. In this game, the leader controls the outcome by announcing a strategy as a function of decision variables of the followers to his/her own decision space. Corresponding to the leader's…
We consider discrete bilevel optimization problems where the follower solves an integer program with a fixed number of variables. Using recent results in parametric integer programming, we present polynomial time algorithms for pure and…
We primarily consider bilevel programs where the lower level is a convex quadratic minimization problem under integer constraints. We show that it is $\Sigma_2^p$-hard to decide if the optimal objective for the leader is lesser than a given…
This paper develops a method to upper-bound extreme-values of time-windowed risks for stochastic processes. Examples of such risks include the maximum average or 90% quantile of the current along a transmission line in any 5-minute window.…
Motivated by emerging applications in wireless sensor networks and large-scale data processing, we consider distributed optimization over directed networks where the agents communicate their information locally to their neighbors to…
The (gradient-based) bilevel programming framework is widely used in hyperparameter optimization and has achieved excellent performance empirically. Previous theoretical work mainly focuses on its optimization properties, while leaving the…
Many large-scale constrained optimization problems can be formulated as bilevel distributed optimization tasks over undirected networks, where agents collaborate to minimize a global cost function while adhering to constraints, relying only…
The derivation of multi-step-ahead prediction models from sampled data of a linear system is considered. A dedicated prediction model is built for each future time step of interest. In addition to a nominal model, the set of all models…
We present a convex approach to probabilistic segmentation and modeling of time series data. Our approach builds upon recent advances in multivariate total variation regularization, and seeks to learn a separate set of parameters for the…
We consider a stochastic control problem where the set of controls is not necessarily convex and the system is governed by a nonlinear backward stochastic differential equation. We establish necessary as well as sufficient conditions of…
We consider a class of stochastic interdiction games between an upper-level decision-maker (the leader) and a lower-level decision-maker (the follower), where uncertainty lies in the follower's objective function coefficients. Specifically,…
Uncertainty is prevalent in engineering design, data-driven problems, and decision making broadly. Due to inherent risk-averseness and ambiguity about assumptions, it is common to address uncertainty by formulating and solving conservative…
In this paper, we consider a risk-averse decision problem for controlled-diffusion processes, with dynamic risk measures, in which multiple risk-averse agents choose their decisions in such a way to minimize their individual accumulated…
Variational regularization methods are commonly used to approximate solutions of inverse problems. In recent years, model-based variational regularization methods have often been replaced with data-driven ones such as the fields-of-expert…
This paper generalizes results concerning strong convexity of two-stage mean-risk models with linear recourse to distortion risk measures. Introducing the concept of (restricted) partial strong convexity, we conduct an in-depth analysis of…