Related papers: Second-order Online Nonconvex Optimization
The regret bound of dynamic online learning algorithms is often expressed in terms of the variation in the function sequence ($V_T$) and/or the path-length of the minimizer sequence after $T$ rounds. For strongly convex and smooth…
Bandit algorithms have been predominantly analyzed in the convex setting with function-value based stationary regret as the performance measure. In this paper, motivated by online reinforcement learning problems, we propose and analyze…
We introduce an online convex optimization algorithm which utilizes projected subgradient descent with optimal adaptive learning rates. Our method provides second-order minimax-optimal dynamic regret guarantee (i.e. dependent on the sum of…
Non-stationary online learning has drawn much attention in recent years. In particular, dynamic regret and adaptive regret are proposed as two principled performance measures for online convex optimization in non-stationary environments. To…
In online convex optimization (OCO), a decision-maker is confronted with an unknown environment and seeks to play an optimal sequence of decisions on a short time-scale using only past information. Recent advances in second-order OCO…
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…
Online optimization has emerged as powerful tool in large scale optimization. In this pa- per, we introduce efficient online optimization algorithms based on the alternating direction method (ADM), which can solve online convex optimization…
Online optimization has emerged as powerful tool in large scale optimization. In this paper, we introduce efficient online algorithms based on the alternating directions method (ADM). We introduce a new proof technique for ADM in the batch…
In this work, we study the online convex optimization problem with curved losses and delayed feedback. When losses are strongly convex, existing approaches obtain regret bounds of order $d_{\max} \ln T$, where $d_{\max}$ is the maximum…
This paper considers the problem of online optimization where the objective function is time-varying. In particular, we extend coordinate descent type algorithms to the online case, where the objective function varies after a finite number…
Bandit convex optimization (BCO) is a general framework for online decision making under uncertainty. While tight regret bounds for general convex losses have been established, existing algorithms achieving these bounds have prohibitive…
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…
We introduce a new online convex optimization algorithm that adaptively chooses its regularization function based on the loss functions observed so far. This is in contrast to previous algorithms that use a fixed regularization function…
Hoffman's classical result gives a bound on the distance of a point from a convex and compact polytope in terms of the magnitude of violation of the constraints. Recently, several results showed that Hoffman's bound can be used to derive…
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, the online variants of the classical Frank-Wolfe algorithm are considered. We consider minimizing the regret with a stochastic cost. The online algorithms only require simple iterative updates and a non-adaptive step size…
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…
Recently, several universal methods have been proposed for online convex optimization which can handle convex, strongly convex and exponentially concave cost functions simultaneously. However, most of these algorithms have been designed…
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…
We investigate online convex optimization in non-stationary environments and choose the dynamic regret as the performance measure, defined as the difference between cumulative loss incurred by the online algorithm and that of any feasible…