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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…
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 consider distributed online learning for joint regret with communication constraints. In this setting, there are multiple agents that are connected in a graph. Each round, an adversary first activates one of the agents to issue a…
We consider the problem of online control of systems with time-varying linear dynamics. This is a general formulation that is motivated by the use of local linearization in control of nonlinear dynamical systems. To state meaningful…
We study the problem of full-information online learning in the "bounded recall" setting popular in the study of repeated games. An online learning algorithm $\mathcal{A}$ is $M$-$\textit{bounded-recall}$ if its output at time $t$ can be…
Stochastic optimization algorithms using exponential moving averages of the past gradients, such as ADAM, RMSProp and AdaGrad, have been having great successes in many applications, especially in training deep neural networks. ADAM in…
We consider an online learning problem in environments with multiple change points. In contrast to the single change point problem that is widely studied using classical "high confidence" detection schemes, the multiple change point…
We study dynamic regret minimization in non-stationary online learning, with a primary focus on follow-the-regularized-leader (FTRL) methods. FTRL is important for curved losses and for understanding adaptive optimizers such as Adam, yet…
Much of the work in online learning focuses on the study of sublinear upper bounds on the regret. In this work, we initiate the study of best-case lower bounds in online convex optimization, wherein we bound the largest improvement an…
A natural goal when designing online learning algorithms for non-stationary environments is to bound the regret of the algorithm in terms of the temporal variation of the input sequence. Intuitively, when the variation is small, it should…
Adaptive gradient methods have become recently very popular, in particular as they have been shown to be useful in the training of deep neural networks. In this paper we have analyzed RMSProp, originally proposed for the training of deep…
In this paper, we propose a learning approach to analyze dynamic systems with asymmetric information structure. Instead of adopting a game theoretic setting, we investigate an online quadratic optimization problem driven by system noises…
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…
To expand the applicability of decentralized online learning, previous studies have proposed several algorithms for decentralized online continuous submodular maximization (D-OCSM) -- a non-convex/non-concave setting with continuous…
We study a robust online convex optimization framework, where an adversary can introduce outliers by corrupting loss functions in an arbitrary number of rounds k, unknown to the learner. Our focus is on a novel setting allowing unbounded…
Stochastic and adversarial data are two widely studied settings in online learning. But many optimization tasks are neither i.i.d. nor fully adversarial, which makes it of fundamental interest to get a better theoretical understanding 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…
Online advertising has recently grown into a highly competitive and complex multi-billion-dollar industry, with advertisers bidding for ad slots at large scales and high frequencies. This has resulted in a growing need for efficient…
This paper considers distributed online optimization with time-varying coupled inequality constraints. The global objective function is composed of local convex cost and regularization functions and the coupled constraint function is the…
We consider online allocation problems with concave revenue functions and resource constraints, which are central problems in revenue management and online advertising. In these settings, requests arrive sequentially during a finite horizon…