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Given subsets of uncertain values, we study the problem of identifying the subset of minimum total value (sum of the uncertain values) by querying as few values as possible. This set selection problem falls into the field of explorable…
The assortment planning problem is a central piece in the revenue management strategy of any company in the retail industry. In this paper, we study a robust assortment optimization problem for substitutable products under a sequential…
Motivated by fairness concerns, we study the `portfolio problem': given an optimization problem with set $D$ of feasible solutions, a class $\mathbf{C}$ of fairness objective functions on $D$, and an approximation factor $\alpha \ge 1$, a…
A sorted set (or map) is one of the most used data types in computer science. In addition to standard set operations, like Insert, Remove, and Contains, it can provide set-set operations such as Union,Intersection, and Difference. Each of…
Query complexity is a model of computation in which we have to compute a function $f(x_1, \ldots, x_N)$ of variables $x_i$ which can be accessed via queries. The complexity of an algorithm is measured by the number of queries that it makes.…
Training models to map natural language instructions to programs given target world supervision only requires searching for good programs at training time. Search is commonly done using beam search in the space of partial programs or…
Sorting is one of the most basic primitives in many algorithms and data analysis tasks. Comparison-based sorting algorithms, like quick-sort and merge-sort, are known to be optimal when the outcome of each comparison is error-free. However,…
We investigate the complexity of sorting in the model of sequential quantum circuits. While it is known that in general a quantum algorithm based on comparisons alone cannot outperform classical sorting algorithms by more than a constant…
We initiate a study of a query-driven approach to designing partition trees for range-searching problems. Our model assumes that a data structure is to be built for an unknown query distribution that we can access through a sampling oracle,…
Quality diversity~(QD) is a branch of evolutionary computation that gained increasing interest in recent years. The Map-Elites QD approach defines a feature space, i.e., a partition of the search space, and stores the best solution for each…
Learning to hash pictures a list-wise sorting problem. Its testing metrics, e.g., mean-average precision, count on a sorted candidate list ordered by pair-wise code similarity. However, scarcely does one train a deep hashing model with the…
A common problem in machine learning is to rank a set of n items based on pairwise comparisons. Here ranking refers to partitioning the items into sets of pre-specified sizes according to their scores, which includes identification of the…
Many important multiple-objective decision problems can be cast within the framework of ranking under constraints and solved via a weighted bipartite matching linear program. Some of these optimization problems, such as personalized content…
Anytime heuristic search algorithms try to find a (potentially suboptimal) solution as quickly as possible and then work to find better and better solutions until an optimal solution is obtained or time is exhausted. The most widely-known…
A very simple first-order algorithm is proposed for solving nonlinear optimization problems with deterministic nonlinear equality constraints. This algorithm adaptively selects steps in the plane tangent to the constraints or steps that…
This paper is about searching the combinatorial space of contingency tables during the inner loop of a nonlinear statistical optimization. Examples of this operation in various data analytic communities include searching for nonlinear…
Constrained sequential pattern mining aims at identifying frequent patterns on a sequential database of items while observing constraints defined over the item attributes. We introduce novel techniques for constraint-based sequential…
In this work, we study the generalized sorting problem, where we are given a set of $n$ elements to be sorted, but only a subset of all possible pairwise element comparisons is allowed. We look at the problem from the perspective of the…
Let $\RR$ be a real closed field (e.g. the field of real numbers) and $\mathscr{S} \subset \RR^n$ be a semi-algebraic set defined as the set of points in $\RR^n$ satisfying a system of $s$ equalities and inequalities of multivariate…
Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second-…