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Multi-objective combinatorial optimization seeks Pareto-optimal solutions over exponentially large discrete spaces, yet existing methods sacrifice generality, scalability, or theoretical guarantees. We reformulate it as an online learning…
A generalization of modularity, called block modularity, is defined. This is a quality function which evaluates a label assignment against an arbitrary block pattern. Therefore, unlike standard modularity or its variants, arbitrary network…
Traditional network interdiction refers to the problem of an interdictor trying to reduce the throughput of network users by removing network edges. In this paper, we propose a new paradigm for network interdiction that models scenarios,…
We consider the problem of analyzing and designing gradient-based discrete-time optimization algorithms for a class of unconstrained optimization problems having strongly convex objective functions with Lipschitz continuous gradient. By…
We consider a class of combinatorial optimization problems that emerge in a variety of domains among which: condensed matter physics, theory of financial risks, error correcting codes in information transmissions, molecular and protein…
Machine learning models are widely used for real-world applications, such as document analysis and vision. Constrained machine learning problems are problems where learned models have to both be accurate and respect constraints. For…
The design of block codes for short information blocks (e.g., a thousand or less information bits) is an open research problem which is gaining relevance thanks to emerging applications in wireless communication networks. In this work, we…
We consider the problem of computing the capacity of a coded, multicast network over a small alphabet. We introduce a novel approach to this problem based on mixed integer programming. As an application of our approach, we recover, extend…
Traditional wireless network design relies on optimization algorithms derived from domain-specific mathematical models, which are often inefficient and unsuitable for dynamic, real-time applications due to high complexity. Deep learning has…
Robust Optimization is becoming increasingly important in machine learning applications. This paper studies the problem of robust submodular minimization subject to combinatorial constraints. Constrained Submodular Minimization arises in…
One major open problem in network coding is to characterize the capacity region of a general multi-source multi-demand network. There are some existing computational tools for bounding the capacity of general networks, but their…
We study the influence minimization problem: given a graph $G$ and a seed set $S$, blocking at most $b$ nodes or $b$ edges such that the influence spread of the seed set is minimized. This is a pivotal yet underexplored aspect of network…
In graph modification problems, one is given a graph G and the goal is to apply a minimum number of modification operations (such as edge deletions) to G such that the resulting graph fulfills a certain property. For example, the Cluster…
In this paper, we study a number of well-known combinatorial optimization problems that fit in the following paradigm: the input is a collection of (potentially inconsistent) local relationships between the elements of a ground set (e.g.,…
We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global…
This paper investigates a combinatorial optimization problem motived from a secure power network design application in [D\'{a}n and Sandberg 2010]. Two equivalent graph optimization formulations are derived. One of the formulations is a…
Decision-making problems are commonly formulated as optimization problems, which are then solved to make optimal decisions. In this work, we consider the inverse problem where we use prior decision data to uncover the underlying…
Branch-and-bound is a typical way to solve combinatorial optimization problems. This paper proposes a graph pointer network model for learning the variable selection policy in the branch-and-bound. We extract the graph features, global…
Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…
We present a novel approach for constructing discrete optimization benchmarks that enables fine-grained control over problem properties, and such benchmarks can facilitate analyzing discrete algorithm behaviors. We build benchmark problems…