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We compute the integral of a function or the expectation of a random variable with minimal cost and use, for our new algorithm and for upper bounds of the complexity, i.i.d. samples. Under certain assumptions it is possible to select a…
Optimal values and solutions of empirical approximations of stochastic optimization problems can be viewed as statistical estimators of their true values. From this perspective, it is important to understand the asymptotic behavior of these…
This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization parameters by marginal maximum likelihood estimation. We prove…
Maximum consensus estimation plays a critically important role in robust fitting problems in computer vision. Currently, the most prevalent algorithms for consensus maximization draw from the class of randomized hypothesize-and-verify…
This paper tackles the challenge of parameter calibration in stochastic models, particularly in scenarios where the likelihood function is unavailable in an analytical form. We introduce a gradient-based simulated parameter estimation…
In performative stochastic optimization, decisions can influence the distribution of random parameters, rendering the data-generating process itself decision-dependent. In practice, decision-makers rarely have access to the true…
When an expert operates a perilous dynamic system, ideal constraint information is tacitly contained in their demonstrated trajectories and controls. The likelihood of these demonstrations can be computed, given the system dynamics and task…
We consider the problem of model multiplicity in downstream decision-making, a setting where two predictive models of equivalent accuracy cannot agree on the best-response action for a downstream loss function. We show that even when the…
Several problems in modeling and control of stochastically-driven dynamical systems can be cast as regularized semi-definite programs. We examine two such representative problems and show that they can be formulated in a similar manner. The…
Majorization-minimization algorithms consist of iteratively minimizing a majorizing surrogate of an objective function. Because of its simplicity and its wide applicability, this principle has been very popular in statistics and in signal…
Discrete-time stochastic systems are an essential modelling tool for many engineering systems. We consider stochastic control systems that are evolving over continuous spaces. For this class of models, methods for the formal verification…
This paper addresses the task of estimating a covariance matrix under a patternless sparsity assumption. In contrast to existing approaches based on thresholding or shrinkage penalties, we propose a likelihood-based method that regularizes…
Maximum likelihood estimators are often of limited practical use due to the intensive computation they require. We propose a family of alternative estimators that maximize a stochastic variation of the composite likelihood function. Each of…
The determination of acceptability prices of contingent claims requires the choice of a stochastic model for the underlying asset price dynamics. Given this model, optimal bid and ask prices can be found by stochastic optimization. However,…
We study multistage distributionally robust linear optimization, where the uncertainty set is defined as a ball of distribution centered at a scenario tree using the nested distance. The resulting minimax problem is notoriously difficult to…
We study two-stage stochastic optimization problems with random recourse, where the adaptive decisions are multiplied with the uncertain parameters in both the objective function and the constraints. To mitigate the computational…
In this paper we consider a network of processors aiming at cooperatively solving linear programming problems subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a…
We study the sample complexity of stochastic convex optimization when problem parameters, e.g., the distance to optimality, are unknown. We pursue two strategies. First, we develop a reliable model selection method that avoids overfitting…
We describe stochastic Newton and stochastic quasi-Newton approaches to efficiently solve large linear least-squares problems where the very large data sets present a significant computational burden (e.g., the size may exceed computer…
Applying standard statistical methods after model selection may yield inefficient estimators and hypothesis tests that fail to achieve nominal type-I error rates. The main issue is the fact that the post-selection distribution of the data…