Related papers: Online Lower Bounds via Duality
Given a convex optimization problem and its dual, there are many possible first-order algorithms. In this paper, we show the equivalence between mirror descent algorithms and algorithms generalizing the conditional gradient method. This is…
The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…
Online optimization problems arise in many resource allocation tasks, where the future demands for each resource and the associated utility functions change over time and are not known apriori, yet resources need to be allocated at every…
We show that sparsity constrained optimization problems over low dimensional spaces tend to have a small duality gap. We use the Shapley-Folkman theorem to derive both data-driven bounds on the duality gap, and an efficient primalization…
This paper introduces a dual-based algorithm framework for solving the regularized online resource allocation problems, which have potentially non-concave cumulative rewards, hard resource constraints, and a non-separable regularizer. Under…
We study the problem of online resource allocation, where multiple customers arrive sequentially and the seller must irrevocably allocate resources to each incoming customer while also facing a procurement cost for the total allocation.…
We consider an online version of the well-studied network utility maximization problem, where users arrive one by one and an operator makes irrevocable decisions for each user without knowing the details of future arrivals. We propose a…
We study the on-line minimum weighted bipartite matching problem in arbitrary metric spaces. Here, $n$ not necessary disjoint points of a metric space $M$ are given, and are to be matched on-line with $n$ points of $M$ revealed one by one.…
We address the challenge of finding algorithms for online allocation (i.e. bipartite matching) using a machine learning approach. In this paper, we focus on the AdWords problem, which is a classical online budgeted matching problem of both…
The main task in analyzing a switching network design (including circuit-, multirate-, and photonic-switching) is to determine the minimum number of some switching components so that the design is non-blocking in some sense (e.g., strict-…
We study the problem of online binary classification where strategic agents can manipulate their observable features in predefined ways, modeled by a manipulation graph, in order to receive a positive classification. We show this setting…
The online bisection problem is a natural dynamic variant of the classic optimization problem, where one has to dynamically maintain a partition of $n$ elements into two clusters of cardinality $n/2$. During runtime, an online algorithm is…
Online algorithms process their inputs piece by piece, taking irrevocable decisions for each data item. This model is too restrictive for most partitioning problems, since data that is yet to arrive may render it impossible to extend…
Makespan minimization on identical machines is a fundamental problem in online scheduling. The goal is to assign a sequence of jobs to $m$ identical parallel machines so as to minimize the maximum completion time of any job. Already in the…
Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…
In Constraint Programming, solving discrete minimization problems with hard and soft constraints can be done either using (i) soft global constraints, (ii) a reformulation into a linear program, or (iii) a reformulation into local cost…
Pivoting methods are of vital importance for linear programming, the simplex method being the by far most well-known. In this paper, a primal-dual pair of linear programs in canonical form is considered. We show that there exists a sequence…
In the classical Online Metric Matching problem, we are given a metric space with $k$ servers. A collection of clients arrive in an online fashion, and upon arrival, a client should irrevocably be matched to an as-yet-unmatched server. The…
The online knapsack problem is a classic problem in the field of online algorithms. Its canonical version asks how to pack items of different values and weights arriving online into a capacity-limited knapsack so as to maximize the total…
We study the online budgeted allocation (also called ADWORDS) problem, where a set of impressions arriving online are allocated to a set of budget-constrained advertisers to maximize revenue. Motivated by connections to Internet…