Related papers: Online Learning for Approximately-Convex Functions…
In this paper, we analyze the continuous armed bandit problems for nonconvex cost functions under certain smoothness and sublevel set assumptions. We first derive an upper bound on the expected cumulative regret of a simple bin splitting…
Learning paradigms based purely on offline data as well as those based solely on sequential online learning have been well-studied in the literature. In this paper, we consider combining offline data with online learning, an area less…
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…
In online marketing, the advertisers aim to balance achieving high volumes and high profitability. The companies' business units address this tradeoff by maximizing the volumes while guaranteeing a minimum Return On Investment (ROI) level.…
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…
This article investigates the problem of controlling linear time-invariant systems subject to time-varying and a priori unknown cost functions, state and input constraints, and exogenous disturbances. We combine the online convex…
In this paper, we propose an online convex optimization approach with two different levels of adaptivity. On a higher level, our approach is agnostic to the unknown types and curvatures of the online functions, while at a lower level, it…
This paper studies online convex optimization with unknown linear budget constraints, where only the gradient information of the objective and the bandit feedback of constraint functions are observed. We propose a safe and efficient…
Contextual bandit algorithms are at the core of many applications, including recommender systems, clinical trials, and optimal portfolio selection. One of the most popular problems studied in the contextual bandit literature is to maximize…
We study the placement of virtual functions aimed at minimizing the cost. We propose a novel algorithm, using ideas based on multi-armed bandits. We prove that these algorithms learn the optimal placement policy rapidly, and their regret…
This paper considers online convex optimization (OCO) with stochastic constraints, which generalizes Zinkevich's OCO over a known simple fixed set by introducing multiple stochastic functional constraints that are i.i.d. generated at each…
We consider an online stochastic game with risk-averse agents whose goal is to learn optimal decisions that minimize the risk of incurring significantly high costs. Specifically, we use the Conditional Value at Risk (CVaR) as a risk measure…
Spurred by the enthusiasm surrounding the "Big Data" paradigm, the mathematical and algorithmic tools of online optimization have found widespread use in problems where the trade-off between data exploration and exploitation plays a…
We consider the problem of online allocation subject to a long-term fairness penalty. Contrary to existing works, however, we do not assume that the decision-maker observes the protected attributes -- which is often unrealistic in practice.…
In this paper, we investigate the online allocation problem of maximizing the overall revenue subject to both lower and upper bound constraints. Compared to the extensively studied online problems with only resource upper bounds, the…
Online learning algorithms are designed to learn even when their input is generated by an adversary. The widely-accepted formal definition of an online algorithm's ability to learn is the game-theoretic notion of regret. We argue that the…
We study the online convex covering problem and online convex packing problem. The (offline) convex covering problem is modeled by the following convex program: $\min_{x \in R_+^n} f(x) \ \text{s.t}\ A x \ge 1$, where $f : R_+^n \mapsto…
We consider the adversarial convex bandit problem and we build the first $\mathrm{poly}(T)$-time algorithm with $\mathrm{poly}(n) \sqrt{T}$-regret for this problem. To do so we introduce three new ideas in the derivative-free optimization…
A stochastic combinatorial semi-bandit is an online learning problem where at each step a learning agent chooses a subset of ground items subject to constraints, and then observes stochastic weights of these items and receives their sum as…
The linear submodular bandit problem was proposed to simultaneously address diversified retrieval and online learning in a recommender system. If there is no uncertainty, this problem is equivalent to a submodular maximization problem under…