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We address combinatorial problems that can be formulated as minimization of a partially separable function of discrete variables (energy minimization in graphical models, weighted constraint satisfaction, pseudo-Boolean optimization, 0-1…
As attribution-based explanation methods are increasingly used to establish model trustworthiness in high-stakes situations, it is critical to ensure that these explanations are stable, e.g., robust to infinitesimal perturbations to an…
In many matching markets--such as athlete recruitment or academic admissions--participants on one side are evaluated by attribute vectors known to the other side, which in turn applies individual \emph{salience vectors} to assign relative…
We introduce a class of first-order methods for smooth constrained optimization that are based on an analogy to non-smooth dynamical systems. Two distinctive features of our approach are that (i) projections or optimizations over the entire…
Two-sided matching markets describe a large class of problems wherein participants from one side of the market must be matched to those from the other side according to their preferences. In many real-world applications (e.g. content…
Usually, to apply game-theoretic methods, we must specify utilities precisely, and we run the risk that the solutions we compute are not robust to errors in this specification. Ordinal games provide an attractive alternative: they require…
We consider a multi-organizational system in which each organization contributes processors to the global pool but also jobs to be processed on the common resources. The fairness of the scheduling algorithm is essential for the stability…
The stable allocation problem is a many-to-many generalization of the well-known stable marriage problem, where we seek a bipartite assignment between, say, jobs (of varying sizes) and machines (of varying capacities) that is "stable" based…
Formal explainability guarantees the rigor of computed explanations, and so it is paramount in domains where rigor is critical, including those deemed high-risk. Unfortunately, since its inception formal explainability has been hampered by…
A combination of implicit and explicit timestepping is analyzed for a system of ODEs motivated by ones arising from spatial discretizations of evolutionary partial differential equations. Loosely speaking, the method we consider is implicit…
Many-to-many matching with contracts is studied in the framework of revealed preferences. All preferences are described by choice functions that satisfy natural conditions. Under a no-externality assumption individual preferences can be…
Measuring how quickly iterative methods converge is essential in computational mathematics, but current approaches have significant limitations. Q-order analysis requires strict smoothness conditions, while R-order analysis lacks precision…
We study a variant of Newton's algorithm applied to under-determined systems of non-smooth equations. The notion of regularity employed in our work is based on Newton differentiability, which generalizes semi-smoothness. The classic notion…
Let $G = (A \cup B, E)$ be an instance of the stable marriage problem with strict preference lists. A matching $M$ is popular in $G$ if $M$ does not lose a head-to-head election against any matching where vertices are voters. Every stable…
A longer and more correct title is `a short and direct path to the theory of stable contract systems in a bipartite market'. There is no new meaningful results in the article. It is dedicated to the presentation of a short method for…
We consider the one-shot Prisoner's Dilemma between algorithms with read-access to one anothers' source codes, and we use the modal logic of provability to build agents that can achieve mutual cooperation in a manner that is robust, in that…
Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…
We address the following question in this paper: "What are the most robust statistical methods for social choice?'' By leveraging the theory of uniformly least favorable distributions in the Neyman-Pearson framework to finite models and…
The past few years have seen a surge of work on fairness in allocation problems where items must be fairly divided among agents having individual preferences. In comparison, fairness in settings with preferences on both sides, that is,…
We consider the stability of matchings when individuals strategically submit preference information to a publicly known algorithm. Most pure Nash equilibria of the ensuing game yield a matching that is unstable with respect to the…