Mixed-Integer Optimization with Constraint Learning

We establish a broad methodological foundation for mixed-integer optimization with learned constraints. We propose an end-to-end pipeline for data-driven decision making in which constraints and objectives are directly learned from data using machine learning, and the trained models are embedded in an optimization formulation. We exploit the mixed-integer optimization-representability of many machine learning methods, including … Read more

Inexact bilevel stochastic gradient methods for constrained and unconstrained lower-level problems

Two-level stochastic optimization formulations have become instrumental in a number ofmachine learning contexts such as continual learning, neural architecture search, adversariallearning, and hyperparameter tuning. Practical stochastic bilevel optimization problemsbecome challenging in optimization or learning scenarios where the number of variables ishigh or there are constraints. In this paper, we introduce a bilevel stochastic gradient method … Read more

Sparse Plus Low Rank Matrix Decomposition: A Discrete Optimization Approach

We study the Sparse Plus Low Rank decomposition problem (SLR), which is the problem of decomposing a corrupted data matrix D into a sparse matrix Y containing the perturbations plus a low rank matrix X. SLR is a fundamental problem in Operations Research and Machine Learning arising in many applications such as data compression, latent … Read more

Solving Cut-Generating Linear Programs via Machine Learning

Cut-generating linear programs (CGLPs) play a key role as a separation oracle to produce valid inequalities for the feasible region of optimization problems. When incorporated inside of branch-and-bound, the cutting planes obtained from CGLPs help to tighten relaxations and improve dual bounds. Running CGLPs at nodes of the branch-and-bound tree, however, is computationally cumbersome due … Read more

A stochastic alternating balance k-means algorithm for fair clustering

In the application of data clustering to human-centric decision-making systems, such as loan applications and advertisement recommendations, the clustering outcome might discriminate against people across different demographic groups, leading to unfairness. A natural conflict occurs between the cost of clustering (in terms of distance to cluster centers) and the balance representation of all demographic groups … Read more

Beyond Symmetry: Best Submatrix Selection for the Sparse Truncated SVD

Truncated singular value decomposition (SVD), also known as the best low-rank matrix approximation, has been successfully applied to many domains such as biology, healthcare, and others, where high-dimensional datasets are prevalent. To enhance the interpretability of the truncated SVD, sparse SVD (SSVD) is introduced to select a few rows and columns of the original matrix … Read more

Unbiased Subdata Selection for Fair Classification: A Unified Framework and Scalable Algorithms

As an important problem in modern data analytics, classification has witnessed varieties of applications from different domains. Different from conventional classification approaches, fair classification concerns the issues of unintentional biases against the sensitive features (e.g., gender, race). Due to high nonconvexity of fairness measures, existing methods are often unable to model exact fairness, which can … Read more

A dynamic programming approach to segmented isotonic regression

This paper proposes a polynomial-time algorithm to construct the monotone stepwise curve that minimizes the sum of squared errors with respect to a given cloud of data points. The fitted curve is also constrained on the maximum number of steps it can be composed of and on the minimum step length. Our algorithm relies on … Read more

Accuracy and fairness trade-offs in machine learning: A stochastic multi-objective approach

In the application of machine learning to real life decision-making systems, e.g., credit scoring and criminal justice, the prediction outcomes might discriminate against people with sensitive attributes, leading to unfairness. The commonly used strategy in fair machine learning is to include fairness as a constraint or a penalization term in the minimization of the prediction … Read more

The block mutual coherence property condition for signal recovery

Compressed sensing shows that a sparse signal can stably be recovered from incomplete linear measurements. But, in practical applications, some signals have additional structure, where the nonzero elements arise in some blocks. We call such signals as block-sparse signals. In this paper, the $\ell_2/\ell_1-\alpha\ell_2$ minimization method for the stable recovery of block-sparse signals is investigated. … Read more