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We study a discrete portfolio pricing problem that selects one price per product from a finite menu under margin and fairness constraints. To account for demand uncertainty, we incorporate a budgeted robust formulation that controls…
Hierarchical Clustering is a popular unsupervised machine learning method with decades of history and numerous applications. We initiate the study of differentially private approximation algorithms for hierarchical clustering under the…
We study the warehouse problem, arising in the area of inventory management and production planning. Here, a merchant wants to decide an optimal trading policy that computes quantities of a single commodity to purchase, store and sell…
Hidden Markov Models (HMMs) are one of the most fundamental and widely used statistical tools for modeling discrete time series. In general, learning HMMs from data is computationally hard (under cryptographic assumptions), and…
We show that certain ways of solving some combinatorial optimization problems can be understood as using query planes to divide the space of problem instances into polyhedra that could fit into those that characterize the problem's various…
We study the problem of exchange when 1) agents are endowed with heterogeneous indivisible objects, and 2) there is no money. In general, no rule satisfies the three central properties Pareto-efficiency, individual rationality, and…
We consider the problem of estimating sparse discrete distributions under local differential privacy (LDP) and communication constraints. We characterize the sample complexity for sparse estimation under LDP constraints up to a constant…
Recoverable robust optimization is a multi-stage approach, where it is possible to adjust a first-stage solution after the uncertain cost scenario is revealed. We analyze this approach for a class of selection problems. The aim is to choose…
In the maximum constraint satisfaction problem (Max CSP), one is given a finite collection of (possibly weighted) constraints on overlapping sets of variables, and the goal is to assign values from a given domain to the variables so as to…
Equilibrium in Economics has been seldom addressed in a situation where some variables are discrete. This work introduces a problem related to lot-sizing with several players, and analyses some strategies which are likely to be found in…
We study a class of semi-discrete variational problems that arise in economic matching and game theory, where agents with continuous attributes are matched to a finite set of outcomes with a one dimensional structure. Such problems appear…
The discretized Bethe-Salpeter eigenvalue problem arises in the Green's function evaluation in many body physics and quantum chemistry. Discretization leads to a matrix eigenvalue problem for $H \in \mathbb{C}^{2n\times 2n}$ with a…
The usual theory of asset pricing in finance assumes that the financial strategies, i.e. the quantity of risky assets to invest, are real-valued so that they are not integer-valued in general, see the Black and Scholes model for instance.…
We show that for continuous time dynamical systems described by polynomial differential equations of modest degree (typically equal to three), the following decision problems which arise in numerous areas of systems and control theory…
We show that the Revenue-Optimal Deterministic Mechanism Design problem for a single additive buyer is #P-hard, even when the distributions have support size 2 for each item and, more importantly, even when the optimal solution is…
Iterative hard thresholding (IHT) is a projected gradient descent algorithm, known to achieve state of the art performance for a wide range of structured estimation problems, such as sparse inference. In this work, we consider IHT as a…
We study the problem of differentially private query release assisted by access to public data. In this problem, the goal is to answer a large class $\mathcal{H}$ of statistical queries with error no more than $\alpha$ using a combination…
Heuristic algorithms have shown a good ability to solve a variety of optimization problems. Stockpile blending problem as an important component of the mine scheduling problem is an optimization problem with continuous search space…
The Stable Roommates problem involves matching a set of agents into pairs based on the agents' strict ordinal preference lists. The matching must be stable, meaning that no two agents strictly prefer each other to their assigned partners. A…
In this paper, we consider a Markov chain choice model with single transition. In this model, customers arrive at each product with a certain probability. If the arrived product is unavailable, then the seller can recommend a subset of…