Related papers: On Data-Driven Prescriptive Analytics with Side In…
We analyze convergence rates of stochastic optimization procedures for non-smooth convex optimization problems. By combining randomized smoothing techniques with accelerated gradient methods, we obtain convergence rates of stochastic…
A framework for risk-averse optimization problems is introduced that is resilient to ambiguities in the true form of the underlying probability distribution. The focus is on problems with partial differential equations (PDEs) as…
Modern neural networks have proven to be powerful function approximators, providing state-of-the-art performance in a multitude of applications. They however fall short in their ability to quantify confidence in their predictions - this is…
As data-driven predictive models are increasingly used to inform decisions, it has been argued that decision makers should provide explanations that help individuals understand what would have to change for these decisions to be beneficial…
We consider the problem of regularized regression in a network of communication-constrained devices. Each node has local data and objectives, and the goal is for the nodes to optimize a global objective. We develop a distributed…
This paper focuses on inverse problems to identify parameters by incorporating information from measurements. These generally ill-posed problems are formulated here in a probabilistic setting based on Bayes's theorem because it leads to a…
Regularization methods allow one to handle a variety of inferential problems where there are more covariates than cases. This allows one to consider a potentially enormous number of covariates for a problem. We exploit the power of these…
Wasserstein distributionally robust optimization offers a framework for model fitting in machine learning under potential shifts in the data distribution. We study a regularized variant of this problem in which entropic smoothing produces a…
In optimization problems, the quality of a candidate solution can be characterized by the optimality gap. For most stochastic optimization problems, this gap must be statistically estimated. We show that for risk-averse problems, standard…
Optimal prediction (OP) methods compensate for a lack of resolution in the numerical solution of complex problems through the use of an invariant measure as a prior measure in the Bayesian sense. In first-order OP, unresolved information is…
Learning guarantees often rely on assumptions of i.i.d. data, which will likely be violated in practice once predictors are deployed to perform real-world tasks. Domain adaptation approaches thus appeared as a useful framework yielding…
We propose a novel distribution-free scheme to solve optimization problems where the goal is to minimize the expected value of a cost function subject to probabilistic constraints. Unlike standard sampling-based methods, our idea consists…
While nowadays most gradient-based optimization methods focus on exploring the high-dimensional geometric features, the random error accumulated in a stochastic version of any algorithm implementation has not been stressed yet. In this…
Real-world decision-making problems often involve decision-dependent uncertainty, where the probability distribution of the random vector depends on the model decisions. Few studies focus on two-stage stochastic programs with this type of…
We analyze a stochastic approximation algorithm for decision-dependent problems, wherein the data distribution used by the algorithm evolves along the iterate sequence. The primary examples of such problems appear in performative prediction…
We study infinite-horizon stochastic optimal control problems with observable side information: a Markov chain that modulates an unknown context-conditional randomness distribution. Since this distribution is unknown, we propose a Bayesian…
Distributed stochastic optimization has drawn great attention recently due to its effectiveness in solving large-scale machine learning problems. Though numerous algorithms have been proposed and successfully applied to general practical…
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…
We consider a distributionally robust second-order stochastic dominance constrained optimization problem. We require the dominance constraints hold with respect to all probability distributions in a Wasserstein ball centered at the…
We revisit the sample average approximation (SAA) approach for non-convex stochastic programming. We show that applying the SAA approach to problems with expected value equality constraints does not necessarily result in asymptotic…