Related papers: Online mirror descent and dual averaging: keeping …
In this paper, we consider the online proximal mirror descent for solving the time-varying composite optimization problems. For various applications, the algorithm naturally involves the errors in the gradient and proximal operator. We…
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…
We show that, for any sufficiently small fixed $\epsilon > 0$, when both players in a general-sum two-player (bimatrix) game employ optimistic mirror descent (OMD) with smooth regularization, learning rate $\eta = O(\epsilon^2)$ and $T =…
In this paper, we consider the problem of distributed online convex optimization, where a group of agents collaborate to track the global minimizers of a sum of time-varying objective functions in an online manner. Specifically, we propose…
We consider online convex optimization with stochastic constraints where the objective functions are arbitrarily time-varying and the constraint functions are independent and identically distributed (i.i.d.) over time. Both the objective…
In this paper, we consider an online distributed composite optimization problem over a time-varying multi-agent network that consists of multiple interacting nodes, where the objective function of each node consists of two parts: a loss…
In this work, we consider a distributed online convex optimization problem, with time-varying (potentially adversarial) constraints. A set of nodes, jointly aim to minimize a global objective function, which is the sum of local convex…
We consider prediction with expert advice when the loss vectors are assumed to lie in a set described by the sum of atomic norm balls. We derive a regret bound for a general version of the online mirror descent (OMD) algorithm that uses a…
Recently, much work has been done on extending the scope of online learning and incremental stochastic optimization algorithms. In this paper we contribute to this effort in two ways: First, based on a new regret decomposition and a…
Dual-based proportional-integral-derivative (PID) controllers are often employed in practice to solve online allocation problems with global constraints, such as budget pacing in online advertising. However, controllers are used in a…
This paper studies online optimization from a high-level unified theoretical perspective. We not only generalize both Optimistic-DA and Optimistic-MD in normed vector space, but also unify their analysis methods for dynamic regret. Regret…
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…
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…
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…
Dual averaging and gradient descent with their stochastic variants stand as the two canonical recipe books for first-order optimization: Every modern variant can be viewed as a descendant of one or the other. In the convex regime, these…
We study long-run market stability for repeated price competitions between two firms, where consumer demand depends on firms' posted prices and consumers' price expectations called reference prices. Consumers' reference prices vary over…
This work focuses on the setting of dynamic regret in the context of online learning with full information. In particular, we analyze regret bounds with respect to the temporal variability of the loss functions. By assuming that the…
It is well known that mirror descent may diverge or cycle on merely monotone variational inequalities. In this paper, we propose \emph{Target Mirror Descent} (TMD), a unified framework that stabilizes monotone flows via a target point…
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…
High-velocity streams of high-dimensional data pose significant "big data" analysis challenges across a range of applications and settings. Online learning and online convex programming play a significant role in the rapid recovery of…