Related papers: Online MinCut: Competitive and Regret Analysis
We consider online algorithms under both the competitive ratio criteria and the regret minimization one. Our main goal is to build a unified methodology that would be able to guarantee both criteria simultaneously. For a general class of…
We address online linear optimization problems when the possible actions of the decision maker are represented by binary vectors. The regret of the decision maker is the difference between her realized loss and the best loss she would have…
We consider algorithms for "smoothed online convex optimization" problems, a variant of the class of online convex optimization problems that is strongly related to metrical task systems. Prior literature on these problems has focused on…
We study an online mixed discrete and continuous optimization problem where a decision maker interacts with an unknown environment for a number of $T$ rounds. At each round, the decision maker needs to first jointly choose a discrete and a…
We study the problem of online learning with a notion of regret defined with respect to a set of strategies. We develop tools for analyzing the minimax rates and for deriving regret-minimization algorithms in this scenario. While the…
We study various discrete nonlinear combinatorial optimization problems in an online learning framework. In the first part, we address the question of whether there are negative results showing that getting a vanishing (or even vanishing…
We consider the problem of online learning in Linear Quadratic Control systems whose state transition and state-action transition matrices $A$ and $B$ may be initially unknown. We devise an online learning algorithm and provide guarantees…
We analyze and evaluate an online gradient descent algorithm with adaptive per-coordinate adjustment of learning rates. Our algorithm can be thought of as an online version of batch gradient descent with a diagonal preconditioner. This…
A new algorithm for regret minimization in online convex optimization is described. The regret of the algorithm after $T$ time periods is $O(\sqrt{T \log T})$ - which is the minimum possible up to a logarithmic term. In addition, the new…
In this paper, we broaden the horizon of online convex optimization (OCO), and consider multi-objective OCO, where there are $K$ distinct loss function sequences, and an algorithm has to choose its action at time $t$, before the $K$ loss…
Online learning aims to perform nearly as well as the best hypothesis in hindsight. For some hypothesis classes, though, even finding the best hypothesis offline is challenging. In such offline cases, local search techniques are often…
Most microeconomic models of interest involve optimizing a piecewise linear function. These include contract design in hidden-action principal-agent problems, selling an item in posted-price auctions, and bidding in first-price auctions.…
In many sequential decision making applications, the change of decision would bring an additional cost, such as the wear-and-tear cost associated with changing server status. To control the switching cost, we introduce the problem of online…
This paper investigates online composite optimization in dynamic environments, where each objective or loss function contains a time-varying nondifferentiable regularizer. To resolve it, an online proximal gradient algorithm is studied for…
We introduce a new algorithm for online linear-quadratic control in a known system subject to adversarial disturbances. Existing regret bounds for this setting scale as $\sqrt{T}$ unless strong stochastic assumptions are imposed on the…
Online learning and model reference adaptive control have many interesting intersections. One area where they differ however is in how the algorithms are analyzed and what objective or metric is used to discriminate "good" algorithms from…
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…
In citep{Hazan-2008-extract}, the authors showed that the regret of online linear optimization can be bounded by the total variation of the cost vectors. In this paper, we extend this result to general online convex optimization. We first…
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…
Some of the most compelling applications of online convex optimization, including online prediction and classification, are unconstrained: the natural feasible set is R^n. Existing algorithms fail to achieve sub-linear regret in this…