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Uncertainty in optimization is often represented as stochastic parameters in the optimization model. In Predict-Then-Optimize approaches, predictions of a machine learning model are used as values for such parameters, effectively…
In this work we introduce a novel approach, based on sampling, for finding assignments that are likely to be solutions to stochastic constraint satisfaction problems and constraint optimisation problems. Our approach reduces the size of the…
In some estimation problems, especially in applications dealing with information theory, signal processing and biology, theory provides us with additional information allowing us to restrict the parameter space to a finite number of points.…
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…
A significant hurdle for analyzing large sample data is the lack of effective statistical computing and inference methods. An emerging powerful approach for analyzing large sample data is subsampling, by which one takes a random subsample…
Optimization under uncertainty deals with the problem of optimizing stochastic cost functions given some partial information on their inputs. These problems are extremely difficult to solve and yet pervade all areas of technological and…
The era of huge data necessitates highly efficient machine learning algorithms. Many common machine learning algorithms, however, rely on computationally intensive subroutines that are prohibitively expensive on large datasets. Oftentimes,…
Sample average approximation--based stochastic dynamic programming (SDP) and model predictive control (MPC) are two different methods for approaching multistage stochastic optimization. In this paper we investigate the conditions under…
Efficiency of self-optimizing systems is heavily dependent on their optimization strategies, e.g., choosing exact or approximate solver. A choice of such a strategy, in turn, is influenced by numerous factors, such as re-optimization time,…
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…
Implicit variables of an optimization problem are used to model variationally challenging feasibility conditions in a tractable way while not entering the objective function. Hence, it is a standard approach to treat implicit variables as…
Tuning parameters are parameters involved in an estimating procedure for the purpose of reducing the risk of some other estimator. Examples include the degree of penalization in penalized regression and likelihood problems, as well as the…
Recent works have proposed optimal subsampling algorithms to improve computational efficiency in large datasets and to design validation studies in the presence of measurement error. Existing approaches generally fall into two categories:…
This paper addresses the problem of sequential submodular maximization: selecting and ranking items in a sequence to optimize some composite submodular function. In contrast to most of the previous works, which assume access to the utility…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
Optimization problems with the objective function in the form of weighted sum and linear equality constraints are considered. Given that the number of local cost functions can be large as well as the number of constraints, a stochastic…
Running machine learning algorithms on large and rapidly growing volumes of data is often computationally expensive, one common trick to reduce the size of a data set, and thus reduce the computational cost of machine learning algorithms,…
Solving optimization problems with unknown parameters often requires learning a predictive model to predict the values of the unknown parameters and then solving the problem using these values. Recent work has shown that including the…
Importance sampling is a popular variance reduction method for Monte Carlo estimation, where a notorious question is how to design good proposal distributions. While in most cases optimal (zero-variance) estimators are theoretically…
Subsampling is one of the popular methods to balance statistical efficiency and computational efficiency in the big data era. Most approaches aim at selecting informative or representative sample points to achieve good overall information…