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We investigate online convex optimization in non-stationary environments and choose dynamic regret as the performance measure, defined as the difference between cumulative loss incurred by the online algorithm and that of any feasible…
In this paper, we investigate an online prediction strategy named as Discounted-Normal-Predictor (Kapralov and Panigrahy, 2010) for smoothed online convex optimization (SOCO), in which the learner needs to minimize not only the hitting cost…
In constrained convex optimization, existing methods based on the ellipsoid or cutting plane method do not scale well with the dimension of the ambient space. Alternative approaches such as Projected Gradient Descent only provide a…
This paper proposes a modular approach that combines the online convex optimization framework and reference governors to solve a constrained control problem featuring time-varying and a priori unknown cost functions. Compared to existing…
Unlike classical control theory, such as Linear Quadratic Control (LQC), real-world control problems are highly complex. These problems often involve adversarial perturbations, bandit feedback models, and non-quadratic, adversarially chosen…
Gradient-variation online learning has drawn increasing attention due to its deep connections to game theory, optimization, etc. It has been studied extensively in the full-information setting, but is underexplored with bandit feedback. In…
We study online learning problems in which a decision maker has to take a sequence of decisions subject to $m$ long-term constraints. The goal of the decision maker is to maximize their total reward, while at the same time achieving small…
We consider online convex optimization (OCO) with multi-slot feedback delay, where an agent makes a sequence of online decisions to minimize the accumulation of time-varying convex loss functions, subject to short-term and long-term…
In this paper, we consider online convex optimization (OCO) with time-varying loss and constraint functions. Specifically, the decision maker chooses sequential decisions based only on past information, meantime the loss and constraint…
We investigate the problem of online learning with monotone and continuous DR-submodular reward functions, which has received great attention recently. To efficiently handle this problem, especially in the case with complicated decision…
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…
We investigate bandit convex optimization (BCO) with delayed feedback, where only the loss value of the action is revealed under an arbitrary delay. Let $n,T,\bar{d}$ denote the dimensionality, time horizon, and average delay, respectively.…
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…
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…
This paper considers online convex optimization with time-varying constraint functions. Specifically, we have a sequence of convex objective functions $\{f_t(x)\}_{t=0}^{\infty}$ and convex constraint functions…
We consider an agent who is involved in a Markov decision process and receives a vector of outcomes every round. Her objective is to maximize a global concave reward function on the average vectorial outcome. The problem models applications…
The problem of constrained online convex optimization is considered, where at each round, once a learner commits to an action $x_t \in \mathcal{X} \subset \mathbb{R}^d$, a convex loss function $f_t$ and a convex constraint function $g_t$…
Many techniques for online optimization problems involve making decisions based solely on presently available information: fewer works take advantage of potential predictions. In this paper, we discuss the problem of online convex…
Universal online learning aims to achieve optimal regret guarantees without requiring prior knowledge of the curvature of online functions. Existing methods have established minimax-optimal regret bounds for universal online learning, where…
We consider a smoothed online convex optimization (SOCO) problem with predictions, where the learner has access to a finite lookahead window of time-varying stage costs, but suffers a switching cost for changing its actions at each stage.…