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Online Set Cover and Load Balancing are central problems in online optimization, and there is a long line of work on developing algorithms for these problems with convex objectives. Although we know optimal online algorithms with…
A standard way to obtain convergence guarantees in stochastic convex optimization is to run an online learning algorithm and then output the average of its iterates: the actual iterates of the online learning algorithm do not come with…
Using an optimization algorithm to solve a machine learning problem is one of mainstreams in the field of science. In this work, we demonstrate a comprehensive comparison of some state-of-the-art first-order optimization algorithms for…
This paper addresses an online convex optimization problem where the cost function at each step depends on a history of past decisions (i.e., memory), and the decision maker has access to limited predictions of future cost values within a…
The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a…
Making use of predictions is a crucial, but under-explored, area of online algorithms. This paper studies a class of online optimization problems where we have external noisy predictions available. We propose a stochastic prediction error…
Inspired by online ad allocation, we study online stochastic packing linear programs from theoretical and practical standpoints. We first present a near-optimal online algorithm for a general class of packing linear programs which model…
The $b$-matching problem is an allocation problem where the vertices on the left-hand side of a bipartite graph, referred to as servers, may be matched multiple times. In the setting with stochastic rewards, an assignment between an…
Optimization problems under affine constraints appear in various areas of machine learning. We consider the task of minimizing a smooth strongly convex function F(x) under the affine constraint Kx=b, with an oracle providing evaluations of…
The minimization of convex functions which are only available through partial and noisy information is a key methodological problem in many disciplines. In this paper we consider convex optimization with noisy zero-th order information,…
In this paper, we analyze the problem of online convex optimization in different settings, including different feedback types (full-information/semi-bandit/bandit/etc) in either stochastic or non-stochastic setting and different notions of…
Existing approaches to online convex optimization (OCO) make sequential one-slot-ahead decisions, which lead to (possibly adversarial) losses that drive subsequent decision iterates. Their performance is evaluated by the so-called regret…
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…
In this paper we propose a framework for solving constrained online convex optimization problem. Our motivation stems from the observation that most algorithms proposed for online convex optimization require a projection onto the convex set…
We consider the unconstrained optimization problem whose objective function is composed of a smooth and a non-smooth conponents where the smooth component is the expectation a random function. This type of problem arises in some interesting…
We study three classical online problems -- $k$-server, $k$-taxi, and chasing size $k$ sets -- through a lens of smoothed analysis. Our setting allows request locations to be adversarial up to small perturbations, interpolating between…
We study the online load balancing problem on unrelated machines, with the objective of minimizing the square of the $\ell_2$ norm of the loads on the machines. The greedy algorithm of Awerbuch et al. (STOC'95) is optimal for deterministic…
We consider the online resource minimization problem in which jobs with hard deadlines arrive online over time at their release dates. The task is to determine a feasible schedule on a minimum number of machines. We rigorously study this…
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…
Frequently, when dealing with many machine learning models, optimization problems appear to be challenging due to a limited understanding of the constructions and characterizations of the objective functions in these problems. Therefore,…