Related papers: Universal Online Learning with Gradient Variations…
Reflecting the greater significance of recent history over the distant past in non-stationary environments, $\lambda$-discounted regret has been introduced in online convex optimization (OCO) to gracefully forget past data as new…
In this work, we study online convex optimization with a fixed constraint function $g : \mathbb{R}^d \rightarrow \mathbb{R}$. Prior work on this problem has shown $O(\sqrt{T})$ regret and cumulative constraint satisfaction $\sum_{t=1}^{T}…
In this paper, we present an improved analysis for dynamic regret of strongly convex and smooth functions. Specifically, we investigate the Online Multiple Gradient Descent (OMGD) algorithm proposed by Zhang et al. (2017). The original…
Motivated by the stringent safety requirements that are often present in real-world applications, we study a safe online convex optimization setting where the player needs to simultaneously achieve sublinear regret and zero constraint…
Online minimization of an unknown convex function over the interval $[0,1]$ is considered under first-order stochastic bandit feedback, which returns a random realization of the gradient of the function at each query point. Without knowing…
We provide algorithms that guarantee regret $R_T(u)\le \tilde O(G\|u\|^3 + G(\|u\|+1)\sqrt{T})$ or $R_T(u)\le \tilde O(G\|u\|^3T^{1/3} + GT^{1/3}+ G\|u\|\sqrt{T})$ for online convex optimization with $G$-Lipschitz losses for any comparison…
We present new efficient \textit{projection-free} algorithms for online convex optimization (OCO), where by projection-free we refer to algorithms that avoid computing orthogonal projections onto the feasible set, and instead relay on…
We study monotone submodular maximization under general matroid constraints in the online setting. We prove that online optimization of a large class of submodular functions, namely, weighted threshold potential functions, reduces to online…
The projection operation is a critical component in a wide range of optimization algorithms, such as online gradient descent (OGD), for enforcing constraints and achieving optimal regret bounds. However, it suffers from computational…
This paper investigates online algorithms for smooth time-varying optimization problems, focusing first on methods with constant step-size, momentum, and extrapolation-length. Assuming strong convexity, precise results for the tracking…
We study unconstrained Online Linear Optimization with Lipschitz losses. Motivated by the pursuit of instance optimality, we propose a new algorithm that simultaneously achieves ($i$) the AdaGrad-style second order gradient adaptivity; and…
Recent literature on online learning has focused on developing adaptive algorithms that take advantage of a regularity of the sequence of observations, yet retain worst-case performance guarantees. A complementary direction is to develop…
Although online convex optimization (OCO) under arbitrary delays has received increasing attention recently, previous studies focus on stationary environments with the goal of minimizing static regret. In this paper, we investigate the…
This paper considers the problem of distributed bandit online convex optimization with time-varying coupled inequality constraints. This problem can be defined as a repeated game between a group of learners and an adversary. The learners…
This paper revisits the online learning approach to inverse linear optimization studied by B\"armann et al. (2017), where the goal is to infer an unknown linear objective function of an agent from sequential observations of the agent's…
This paper considers the distributed online bandit optimization problem with nonconvex loss functions over a time-varying digraph. This problem can be viewed as a repeated game between a group of online players and an adversary. At each…
A standard way to obtain convergence guarantees in stochastic convex optimization is to run an online learning algorithm and then output the average of its iterates: the actual iterates of the online learning algorithm do not come with…
Pairwise learning is essential in machine learning, especially for problems involving loss functions defined on pairs of training examples. Online gradient descent (OGD) algorithms have been proposed to handle online pairwise learning,…
We study various discrete nonlinear combinatorial optimization problems in an online learning framework. In the first part, we address the question of whether there are negative results showing that getting a vanishing (or even vanishing…
We consider online convex optimization with time-varying stage costs and additional switching costs. Since the switching costs introduce coupling across all stages, multi-step-ahead (long-term) predictions are incorporated to improve the…