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We consider the problem of Online Convex Optimization (OCO) with two-point bandit feedback. In this setting, a player attempts to minimize a sequence of adversarially generated convex loss functions, while only observing the value of each…
We consider prediction with expert advice for strongly convex and bounded losses, and investigate trade-offs between regret and "variance" (i.e., squared difference of learner's predictions and best expert predictions). With $K$ experts,…
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…
We design and analyze algorithms for online linear optimization that have optimal regret and at the same time do not need to know any upper or lower bounds on the norm of the loss vectors. Our algorithms are instances of the Follow the…
In Online Convex Optimization (OCO), when the stochastic gradient has a finite variance, many algorithms provably work and guarantee a sublinear regret. However, limited results are known if the gradient estimate has a heavy tail, i.e., the…
We consider online reinforcement learning in episodic Markov decision process (MDP) with unknown transition function and stochastic rewards drawn from some fixed but unknown distribution. The learner aims to learn the optimal policy and…
In online convex optimization, the player aims to minimize regret, or the difference between her loss and that of the best fixed decision in hindsight over the entire repeated game. Algorithms that minimize (standard) regret may converge to…
We address the problem of learning in an online setting where the learner repeatedly observes features, selects among a set of actions, and receives reward for the action taken. We provide the first efficient algorithm with an optimal…
Online learning is a powerful tool for analyzing iterative algorithms. However, the classic adversarial setup sometimes fails to capture certain regularity in online problems in practice. Motivated by this, we establish a new setup, called…
This paper considers the stability of online learning algorithms and its implications for learnability (bounded regret). We introduce a novel quantity called {\em forward regret} that intuitively measures how good an online learning…
We present the first theoretical guarantees for zero constraint violation in Online Convex Optimization (OCO) across all rounds, addressing dynamic constraint changes. Unlike existing approaches in constrained OCO, which allow for…
Motivated by applications in machine learning and operations research, we study regret minimization with stochastic first-order oracle feedback in online constrained, and possibly non-smooth, non-convex problems. In this setting, the…
We consider the problem of unconstrained online convex optimization (OCO) with sub-exponential noise, a strictly more general problem than the standard OCO. In this setting, the learner receives a subgradient of the loss functions corrupted…
Motivated by the challenge of nonstationarity in sequential decision making, we study Online Convex Optimization (OCO) under the coupling of two problem structures: the domain is unbounded, and the comparator sequence $u_1,\ldots,u_T$ is…
Dictionary learning is a widely used unsupervised learning method in signal processing and machine learning. Most existing works of dictionary learning are in an offline manner. There are mainly two offline ways for dictionary learning. One…
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 consider the fundamental problem of prediction with expert advice where the experts are "optimizable": there is a black-box optimization oracle that can be used to compute, in constant time, the leading expert in retrospect at any point…
Making use of predictions is a crucial, but under-explored, area of online algorithms. This paper studies a class of online optimization problems where we have external noisy predictions available. We propose a stochastic prediction error…
This paper considers the distributed online convex-concave optimization with constraint sets over a multiagent network, in which each agent autonomously generates a series of decision pairs through a designable mechanism to cooperatively…
The online meta-learning framework is designed for the continual lifelong learning setting. It bridges two fields: meta-learning which tries to extract prior knowledge from past tasks for fast learning of future tasks, and online-learning…