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Pre-trained large models attract widespread attention in recent years, but they face challenges in applications that require high interpretability or have limited resources, such as physical sensing, medical imaging, and bioinformatics.…
Linear Programming (LP) relaxations have become powerful tools for finding the most probable (MAP) configuration in graphical models. These relaxations can be solved efficiently using message-passing algorithms such as belief propagation…
Statistical inference problems arising within signal processing, data mining, and machine learning naturally give rise to hard combinatorial optimization problems. These problems become intractable when the dimensionality of the data is…
In this paper, we consider the problem of partitioning a small data sample of size $n$ drawn from a mixture of 2 sub-gaussian distributions in $\R^p$. We consider semidefinite programming relaxations of an integer quadratic program that is…
Resolving a conjecture of Abbe, Bandeira and Hall, the authors have recently shown that the semidefinite programming (SDP) relaxation of the maximum likelihood estimator achieves the sharp threshold for exactly recovering the community…
In this paper we solve mixed-integer linear programs (MILPs) via distributed asynchronous saddle point computation. This work is motivated by the MILPs being able to model problems in multi-agent autonomy, such as task assignment problems…
Markov decision processes (MDPs) are a fundamental model in sequential decision making. Robust MDPs (RMDPs) extend this framework by allowing uncertainty in transition probabilities and optimizing against the worst-case realization of that…
The problem of minimizing a polynomial over a set of polynomial inequalities is an NP-hard non-convex problem. Thanks to powerful results from real algebraic geometry, one can convert this problem into a nested sequence of…
We introduce a dynamic sparse training algorithm based on linearized Bregman iterations / mirror descent that exploits the naturally incurred sparsity by alternating between periods of static and dynamic sparsity pattern updates. The key…
The linear programming (LP) approach has a long history in the theory of approximate dynamic programming. When it comes to computation, however, the LP approach often suffers from poor scalability. In this work, we introduce a relaxed…
In subset selection we search for the best linear predictor that involves a small subset of variables. From a computational complexity viewpoint, subset selection is NP-hard and few classes are known to be solvable in polynomial time. Using…
The winner determination problems of many attractive multi-winner voting rules are NP-complete. However, they often admit polynomial-time algorithms when restricting inputs to be single-peaked. Commonly, such algorithms employ dynamic…
In this work, we develop an adaptive, multivariate partitioning algorithm for solving mixed-integer nonlinear programs (MINLP) with multi-linear terms to global optimality. This iterative algorithm primarily exploits the advantages of…
It is well-known that by adding integrality constraints to the semidefinite programming (SDP) relaxation of the max-cut problem, the resulting integer semidefinite program is an exact formulation of the problem. In this paper we show…
Lagrangian Relaxation (LR) is a powerful technique for solving large-scale Mixed Integer Linear Programming (MILP), particularly those with decomposable structures, such as vehicle routing or unit commitment problems. By relaxing the…
We introduce fast randomized algorithms for solving semidefinite programming (SDP) relaxations of the partial permutation synchronization (PPS) problem, a core task in multi-image matching with significant relevance to 3D reconstruction.…
We study approximation algorithms for scheduling problems with the objective of minimizing total weighted completion time, under identical and related machine models with job precedence constraints. We give algorithms that improve upon many…
Coalition formation is often modeled as a static equilibrium problem, neglecting the dynamic processes governing how agents self-organize. This paper proposes a dynamic split-and-merge framework that balances two conflicting economic…
Quantum AI is an emerging field that uses quantum computing to solve typical complex problems in AI. In this work, we propose BILP-Q, the first-ever general quantum approach for solving the Coalition Structure Generation problem (CSGP),…
We prove a general result demonstrating the power of Lagrangian relaxation in solving constrained maximization problems with arbitrary objective functions. This yields a unified approach for solving a wide class of {\em subset selection}…