Related papers: Geometry of Online Packing Linear Programs
Offline model-based optimization (MBO) aims to identify a design that maximizes a black-box function using only a fixed, pre-collected dataset of designs and their corresponding scores. A common approach in offline MBO is to train a…
We give an approximation algorithm for packing and covering linear programs (linear programs with non-negative coefficients). Given a constraint matrix with n non-zeros, r rows, and c columns, the algorithm computes feasible primal and dual…
Traditional online algorithms encapsulate decision making under uncertainty, and give ways to hedge against all possible future events, while guaranteeing a nearly optimal solution as compared to an offline optimum. On the other hand,…
Previous works suggested the use of Branch and Bound techniques for finding the optimal allocation in (multi-unit) combinatorial auctions. They remarked that Linear Programming could provide a good upper-bound to the optimal allocation, but…
In this paper, we consider the problem of column subset selection. We present a novel analysis of the spectral norm reconstruction for a simple randomized algorithm and establish a new bound that depends explicitly on the sampling…
We revisit the classic online bin packing problem. In this problem, items of positive sizes no larger than 1 are presented one by one to be packed into subsets called "bins" of total sizes no larger than 1, such that every item is assigned…
In the problem of learning with label proportions, which we call LLP learning, the training data is unlabeled, and only the proportions of examples receiving each label are given. The goal is to learn a hypothesis that predicts the…
We consider a variant of the online caching problem where the items exhibit dependencies among each other: an item can reside in the cache only if all its dependent items are also in the cache. The dependency relations can form any directed…
Randomized mechanisms, which map a set of bids to a probability distribution over outcomes rather than a single outcome, are an important but ill-understood area of computational mechanism design. We investigate the role of randomized…
In many online learning problems we are interested in predicting local information about some universe of items. For example, we may want to know whether two items are in the same cluster rather than computing an assignment of items to…
Active regression considers a linear regression problem where the learner receives a large number of data points but can only observe a small number of labels. Since online algorithms can deal with incremental training data and take…
We introduce the Online Unbounded Knapsack Problem with Removal, a variation of the well-known Online Knapsack Problem. Items, each with a weight and value, arrive online and an algorithm must decide on whether or not to pack them into a…
We propose a general framework for studying adaptive regret bounds in the online learning framework, including model selection bounds and data-dependent bounds. Given a data- or model-dependent bound we ask, "Does there exist some algorithm…
Adversarial online linear optimization (OLO) is essentially about making performance tradeoffs with respect to the unknown difficulty of the adversary. In the setting of one-dimensional fixed-time OLO on a bounded domain, it has been…
We develop a framework for approximation limits of polynomial-size linear programs from lower bounds on the nonnegative ranks of suitably defined matrices. This framework yields unconditional impossibility results that are applicable to any…
Online linear programming plays an important role in both revenue management and resource allocation, and recent research has focused on developing efficient first-order online learning algorithms. Despite the empirical success of…
Column generation (CG) is one of the most successful approaches for solving large-scale linear programming (LP) problems. Given an LP with a prohibitively large number of variables (i.e., columns), the idea of CG is to explicitly consider…
The LETOR website contains three information retrieval datasets used as a benchmark for testing machine learning ideas for ranking. Algorithms participating in the challenge are required to assign score values to search results for a…
In the Online List Labeling problem, a set of $n \leq N$ elements from a totally ordered universe must be stored in sorted order in an array with $m=N+\lceil\varepsilon N \rceil$ slots, where $\varepsilon \in (0,1]$ is constant, while an…
Aligning large language models (LLMs) depends on high-quality datasets of human preference labels, which are costly to collect. Although active learning has been studied to improve sample efficiency relative to passive collection, many…