Related papers: Gradient-Variation Regret Bounds for Unconstrained…
In the convex optimization approach to online regret minimization, many methods have been developed to guarantee a $O(\sqrt{T})$ bound on regret for subdifferentiable convex loss functions with bounded subgradients, by using a reduction to…
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 study optimal regret bounds for control in linear dynamical systems under adversarially changing strongly convex cost functions, given the knowledge of transition dynamics. This includes several well studied and fundamental frameworks…
We study the framework of universal dynamic regret minimization with strongly convex losses. We answer an open problem in Baby and Wang 2021 by showing that in a proper learning setup, Strongly Adaptive algorithms can achieve the near…
We study the problem of online learning and online regret minimization when samples are drawn from a general unknown non-stationary process. We introduce the concept of a dynamic changing process with cost $K$, where the conditional…
We consider an online learning process to forecast a sequence of outcomes for nonconvex models. A typical measure to evaluate online learning algorithms is regret but such standard definition of regret is intractable for nonconvex models…
Existing online learning algorithms for adversarial Markov Decision Processes achieve ${O}(\sqrt{T})$ regret after $T$ rounds of interactions even if the loss functions are chosen arbitrarily by an adversary, with the caveat that the…
We study online convex optimization with constraints consisting of multiple functional constraints and a relatively simple constraint set, such as a Euclidean ball. As enforcing the constraints at each time step through projections is…
We consider the problem of online learning in Linear Quadratic Control systems whose state transition and state-action transition matrices $A$ and $B$ may be initially unknown. We devise an online learning algorithm and provide guarantees…
We develop a reduction-based framework for online learning with delayed feedback that recovers and improves upon existing results for both first-order and bandit convex optimization. Our approach introduces a continuous-time model under…
In this work, we study the online convex optimization problem with curved losses and delayed feedback. When losses are strongly convex, existing approaches obtain regret bounds of order $d_{\max} \ln T$, where $d_{\max}$ is the maximum…
Nowadays, online learning is an appealing learning paradigm, which is of great interest in practice due to the recent emergence of large scale applications such as online advertising placement and online web ranking. Standard online…
We consider the problem of the Zinkevich (2003)-style dynamic regret minimization in online learning with exp-concave losses. We show that whenever improper learning is allowed, a Strongly Adaptive online learner achieves the dynamic regret…
We investigate the problem of online convex optimization with unknown delays, in which the feedback of a decision arrives with an arbitrary delay. Previous studies have presented a delayed variant of online gradient descent (OGD), and…
Some of the most compelling applications of online convex optimization, including online prediction and classification, are unconstrained: the natural feasible set is R^n. Existing algorithms fail to achieve sub-linear regret in this…
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…
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…
We study Online Convex Optimization in the unbounded setting where neither predictions nor gradient are constrained. The goal is to simultaneously adapt to both the sequence of gradients and the comparator. We first develop parameter-free…
Consider an online convex optimization problem where the loss functions are self-concordant barriers, smooth relative to a convex function $h$, and possibly non-Lipschitz. We analyze the regret of online mirror descent with $h$. Then, based…
This work introduces the first small-loss and gradual-variation regret bounds for online portfolio selection, marking the first instances of data-dependent bounds for online convex optimization with non-Lipschitz, non-smooth losses. The…