Related papers: An Online Convex Optimization Approach to Blackwel…
The online matching problem was introduced by Karp, Vazirani and Vazirani nearly three decades ago. In that seminal work, they studied this problem in bipartite graphs with vertices arriving only on one side, and presented optimal…
We examine the problem of smoothed online optimization, where a decision maker must sequentially choose points in a normed vector space to minimize the sum of per-round, non-convex hitting costs and the costs of switching decisions between…
This paper considers online optimization of a renewal-reward system. A controller performs a sequence of tasks back-to-back. Each task has a random vector of parameters, called the task type vector, that affects the task processing options…
This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…
In this paper, we consider an online optimization process, where the objective functions are not convex (nor concave) but instead belong to a broad class of continuous submodular functions. We first propose a variant of the Frank-Wolfe…
This thesis presents some geometric insights into three different types of two player prediction games -- namely general learning task, prediction with expert advice, and online convex optimization. These games differ in the nature of the…
Devising efficient algorithms that track the optimizers of continuously varying convex optimization problems is key in many applications. A possible strategy is to sample the time-varying problem at constant rate and solve the resulting…
We present a causality-based algorithm for solving two-player reachability games represented by logical constraints. These games are a useful formalism to model a wide array of problems arising, e.g., in program synthesis. Our technique for…
This paper considers a distributed stochastic strongly convex optimization, where agents connected over a network aim to cooperatively minimize the average of all agents' local cost functions. Due to the stochasticity of gradient estimation…
We consider the problem of convex function chasing with black-box advice, where an online decision-maker aims to minimize the total cost of making and switching between decisions in a normed vector space, aided by black-box advice such as…
A novel Follow-the-Perturbed-Leader type algorithm is proposed and analyzed for solving general long-term constrained optimization problems in an online manner, where the target and constraint functions are oblivious adversarially generated…
We consider online learning when the time horizon is unknown. We apply a minimax analysis, beginning with the fixed horizon case, and then moving on to two unknown-horizon settings, one that assumes the horizon is chosen randomly according…
We study the basic allocation problem of assigning resources to players so as to maximize fairness. This is one of the few natural problems that enjoys the intriguing status of having a better estimation algorithm than approximation…
Recently, several universal methods have been proposed for online convex optimization, and attain minimax rates for multiple types of convex functions simultaneously. However, they need to design and optimize one surrogate loss for each…
Computing reachability probabilities is a fundamental problem in the analysis of probabilistic programs. This paper aims at a comprehensive and comparative account on various martingale-based methods for over- and under-approximating…
Boosting is a popular way to derive powerful learners from simpler hypothesis classes. Following previous work (Mason et al., 1999; Friedman, 2000) on general boosting frameworks, we analyze gradient-based descent algorithms for boosting…
Projection methods are popular algorithms for iteratively solving feasibility problems in Euclidean or even Hilbert spaces. They employ (selections of) nearest point mappings to generate sequences that are designed to approximate a point in…
We give an algorithmic framework for minimizing general convex objectives (that are differentiable and monotone non-decreasing) over a set of covering constraints that arrive online. This substantially extends previous work on online…
Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we…
Recently, bandit optimization has received significant attention in real-world safety-critical systems that involve repeated interactions with humans. While there exist various algorithms with performance guarantees in the literature,…