Related papers: Multidimensional Balanced Allocation for Multiple …
We study the binary choice problem in a data-rich environment with asymmetric loss functions. The econometrics literature covers nonparametric binary choice problems but does not offer computationally attractive solutions in data-rich…
We consider systems of "pinned balls," i.e., balls that have fixed positions and pseudo-velocities. Pseudo-velocities change according to the same rules as those for velocities of totally elastic collisions between moving balls. The times…
We consider a sequential assortment selection problem where the user choice is given by a multinomial logit (MNL) choice model whose parameters are unknown. In each period, the learning agent observes a $d$-dimensional contextual…
Imagine that there are two bins to which balls are added sequentially, and each incoming ball joins a bin with probability proportional to the p-th power of the number of balls already there. A general result says that if p>1/2, there…
A new method for binning a set of $n$ data values into a set of m bins for the case where the bins are of different sizes is proposed. The method skips binning using a binary search across the bins all the time. It is proven the method…
There has recently been much progress on exact algorithms for the (un)weighted graph (bi)partitioning problem using branch-and-bound and related methods. In this note we present and improve an easily computable, purely combinatorial lower…
Bin covering is a dual version of classic bin packing. Thus, the goal is to cover as many bins as possible, where covering a bin means packing items of total size at least one in the bin. For online bin covering, competitive analysis fails…
We consider two-player games played on weighted directed graphs with mean-payoff and total-payoff objectives, two classical quantitative objectives. While for single-dimensional games the complexity and memory bounds for both objectives…
In many applications such as rationing medical care and supplies, university admissions, and the assignment of public housing, the decision of who receives an allocation can be justified by various normative criteria. Such settings have…
We consider long-range Bernoulli bond percolation on the $d$-dimensional hierarchical lattice in which each pair of points $x$ and $y$ are connected by an edge with probability $1-\exp(-\beta\|x-y\|^{-d-\alpha})$, where $0<\alpha<d$ is…
A Multinomial Logit (MNL) model is composed of a finite universe of items $[n]=\{1,..., n\}$, each assigned a positive weight. A query specifies an admissible subset -- called a slate -- and the model chooses one item from that slate with…
We study a resource allocation setting where $m$ discrete items are to be divided among $n$ agents with additive utilities, and the agents' utilities for individual items are drawn at random from a probability distribution. Since common…
In the online sorting problem, a sequence of $n$ numbers in $[0, 1]$ (including $\{0,1\}$) have to be inserted in an array of size $m \ge n$ so as to minimize the sum of absolute differences between pairs of numbers occupying consecutive…
Basket designs are prospective clinical trials that are devised with the hypothesis that the presence of selected molecular features determine a patient's subsequent response to a particular "targeted" treatment strategy. Basket trials are…
The beta polytope $P_{n,d}^\beta$ is the convex hull of $n$ i.i.d. random points distributed in the unit ball of $\mathbb{R}^d$ according to a density proportional to $(1-\lVert{x}\rVert^2)^{\beta}$ if $\beta>-1$ (in particular, $\beta=0$…
We consider $N$ Bernoulli random variables, which are independent conditional on a common random factor determining their probability distribution. We show that certain expected functionals of the proportion $L_N$ of variables in a given…
Multi-armed bandit problems are considered as a paradigm of the trade-off between exploring the environment to find profitable actions and exploiting what is already known. In the stationary case, the distributions of the rewards do not…
Closed-loop decision-making systems (e.g., lending, screening, or recidivism risk assessment) often operate under fairness and service constraints while inducing feedback effects: decisions change who appears in the future, yielding…
The input to the stochastic orienteering problem consists of a budget $B$ and metric $(V,d)$ where each vertex $v$ has a job with deterministic reward and random processing time (drawn from a known distribution). The processing times are…
In this paper we consider multi-objective optimization problems over a box. The problem is very relevant and several computational approaches have been proposed in the literature. They broadly fall into two main classes: evolutionary…