Tight Probability Bounds with Pairwise Independence

\(\) While useful probability bounds for \(n\) pairwise independent Bernoulli random variables adding up to at least an integer \(k\) have been proposed in the literature, none of these bounds are tight in general. In this paper, we provide several results in this direction. Firstly, when \(k = 1\), the tightest upper bound on the … Read more

Decision Diagrams for Discrete Optimization: A Survey of Recent Advances

In the last decade, decision diagrams (DDs) have been the basis for a large array of novel approaches for modeling and solving optimization problems. Many techniques now use DDs as a key tool to achieve state-of-the-art performance within other optimization paradigms, such as integer programming and constraint programming. This paper provides a survey of the … Read more

The follower optimality cuts for mixed-integer linear bilevel programming problems

We address mixed-integer linear bilevel programming. A discussion ofthe relationships between the optimistic and the pessimistic setting ispresented, providing necessary and sufficient conditions for them to beequivalent. A new class of inequalities, the follower optimality cuts, isintroduced and a related single-level non-compact reformulation of theproblem is derived. The same is done for a revision of … Read more

Γ-counterparts for robust nonlinear combinatorial and discrete optimization

Γ-uncertainty sets have been introduced for adjusting the degree of conservatism of robust counterparts of (discrete) linear programs. The contribution of this paper is a generalization of this approach to (mixed–integer) nonlinear optimization programs. We focus on the cases in which the uncertainty is linear or concave but also derive formulations for the general case. … Read more

Optimal switching sequence for switched linear systems

We study the following optimization problem over a dynamical system that consists of several linear subsystems: Given a finite set of n-by-n matrices and an n-dimensional vector, find a sequence of K matrices, each chosen from the given set of matrices, to maximize a convex function over the product of the K matrices and the … Read more

Distributionally Robust Linear and Discrete Optimization with Marginals

In this paper, we study the class of linear and discrete optimization problems in which the objective coefficients are chosen randomly from a distribution, and the goal is to evaluate robust bounds on the expected optimal value as well as the marginal distribution of the optimal solution. The set of joint distributions is assumed to … Read more

Network-based Approximate Linear Programming for Discrete Optimization

We develop a new class of approximate linear programs (ALPs) that project the high-dimensional value function of dynamic programs onto a class of basis functions, each defined as a network that represents aggregrations over the state space. The resulting ALP is a minimum-cost flow problem over an extended variable space that synchronizes flows across multiple … Read more

Alternating Criteria Search: A Parallel Large Neighborhood Search Algorithm for Mixed Integer Programs

We present a parallel large neighborhood search framework for finding high quality primal solutions for generic Mixed Integer Programs (MIPs). The approach simultaneously solves a large number of sub-MIPs with the dual objective of reducing infeasibility and optimizing with respect to the original objective. Both goals are achieved by solving restricted versions of two auxiliary … Read more

Robust Nonparametric Testing for Causal Inference in Observational Studies

We consider the decision problem of making causal conclusions from observational data. Typically, using standard matched pairs techniques, there is a source of uncertainty that is not usually quanti fied, namely the uncertainty due to the choice of the experimenter: two di fferent reasonable experimenters can easily have opposite results. In this work we present an alternative … Read more

Robust Testing for Causal Inference in Observational Studies

A vast number of causal inference studies use matching techniques, where treatment cases are matched with similar control cases. For observational data in particular, we claim there is a major source of uncertainty that is essentially ignored in these tests, which is the way the assignments of matched pairs are constructed. It is entirely possible, … Read more