Related papers: Binary Search with Distance-Dependent Costs
We study the design of a decentralized two-sided matching market in which agents' search is guided by the platform. There are finitely many agent types, each with (potentially random) preferences drawn from known type-specific…
In this paper a search algorithm is proposed to find a sub optimal path for a non-holonomic system. For this purpose the algorithm starts sampling the front part of the vehicle and moves towards the destination with a cost function. The…
The contraction cost of a tensor network depends on the contraction order. However, the optimal contraction ordering problem is known to be NP-hard. We show that the linear contraction ordering problem for tree tensor networks admits a…
This paper presents the formulation of a combinatorial optimization problem with the following characteristics: i.the search space is the power set of a finite set structured as a Boolean lattice; ii.the cost function forms a U-shaped curve…
We introduce a natural online allocation problem that connects several of the most fundamental problems in online optimization. Let $M$ be an $n$-point metric space. Consider a resource that can be allocated in arbitrary fractions to the…
We consider the problem of minimizing the worst-case search time for a hidden point target in the plane using multiple mobile agents of differing speeds, all starting from a common origin. The search time is normalized by the target's…
Beam search is a go-to strategy for decoding neural sequence models. The algorithm can naturally be viewed as a subset optimization problem, albeit one where the corresponding set function does not reflect interactions between candidates.…
To tackle the exponentiality associated with NP-hard problems, two paradigms have been proposed. First, Branch & Bound, like Dynamic Programming, achieve efficient exact inference but requires extensive information and analysis about the…
In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in terms of the number of points of the metric space. We…
Training autoregressive models to better predict under the test metric, instead of maximizing the likelihood, has been reported to be beneficial in several use cases but brings additional complications, which prevent wider adoption. In this…
In this paper we present and evaluate a search strategy called Decomposition Based Search (DBS) which is based on two steps: subproblem generation and subproblem solution. The generation of subproblems is done through value ranking and…
We consider two active binary-classification problems with atypical objectives. In the first, active search, our goal is to actively uncover as many members of a given class as possible. In the second, active surveying, our goal is to…
We provide simple and fast polynomial time approximation schemes (PTASs) for several variants of the max-sum diversification problem which, in its most basic form, is as follows: Given n points p_1,...,p_n in R^d and an integer k, select k…
A fundamental challenge in deep learning is that the optimal step sizes for update steps of stochastic gradient descent are unknown. In traditional optimization, line searches are used to determine good step sizes, however, in deep…
We introduce the lazy search tree data structure. The lazy search tree is a comparison-based data structure on the pointer machine that supports order-based operations such as rank, select, membership, predecessor, successor, minimum, and…
In sequential hypothesis testing, Generalized Binary Search (GBS) greedily chooses the test with the highest information gain at each step. It is known that GBS obtains the gold standard query cost of $O(\log n)$ for problems satisfying the…
We consider a framework for structured prediction based on search in the space of complete structured outputs. Given a structured input, an output is produced by running a time-bounded search procedure guided by a learned cost function, and…
We introduce and study the problem of dueling optimization with a monotone adversary, which is a generalization of (noiseless) dueling convex optimization. The goal is to design an online algorithm to find a minimizer $\mathbf{x}^{*}$ for a…
In this paper, we initiate the study of the multiplicative bidding language adopted by major Internet search companies. In multiplicative bidding, the effective bid on a particular search auction is the product of a base bid and bid…
Inspired by the great success of machine learning in the past decade, people have been thinking about the possibility of improving the theoretical results by exploring data distribution. In this paper, we revisit a fundamental problem…