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Online bilevel optimization (OBO) has emerged as a powerful framework for many machine learning problems. Prior works have developed several algorithms that minimize the standard bilevel local regret or the window-averaged bilevel local…
This work aims to provide understandings on the remarkable success of deep convolutional neural networks (CNNs) by theoretically analyzing their generalization performance and establishing optimization guarantees for gradient descent based…
We present regret minimization algorithms for the contextual multi-armed bandit (CMAB) problem over $K$ actions in the presence of delayed feedback, a scenario where loss observations arrive with delays chosen by an adversary. As a…
We consider the problem of online nonparametric regression with arbitrary deterministic sequences. Using ideas from the chaining technique, we design an algorithm that achieves a Dudley-type regret bound similar to the one obtained in a…
We consider the problem of online adaptive control of the linear quadratic regulator, where the true system parameters are unknown. We prove new upper and lower bounds demonstrating that the optimal regret scales as…
In this paper, we study the problem of learning Kalman filtering with unknown system model in partially observed linear dynamical systems. We propose a unified algorithmic framework based on online optimization that can be used to solve…
This paper considers the distributed online convex optimization problem with time-varying constraints over a network of agents. This is a sequential decision making problem with two sequences of arbitrarily varying convex loss and…
This paper considers the distributed bandit convex optimization problem with time-varying constraints. In this problem, the global loss function is the average of all the local convex loss functions, which are unknown beforehand. Each agent…
In this work, we explore online convex optimization (OCO) and introduce a new condition and analysis that provides fast rates by exploiting the curvature of feasible sets. In online linear optimization, it is known that if the average…
We study online linear optimization with matrix variables constrained by the operator norm, a setting where the geometry renders designing data-dependent and efficient adaptive algorithms challenging. The best-known adaptive regret bounds…
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…
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 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…
We present an algorithm guaranteeing dynamic regret bounds for online omniprediction with long term constraints. The goal in this recently introduced problem is for a learner to generate a sequence of predictions which are broadcast to a…
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…
Given a sequence of $n$ independent random variables with common continuous distribution, we propose a simple adaptive online policy that selects a monotone increasing subsequence. We show that the expected number of monotone increasing…
We prove new upper and lower bounds for the Online Orthogonal Vectors Problem ($\mathsf{OnlineOV}_{n,d}$). In this problem, a preprocessing algorithm receives $n$ vectors $x_1,\ldots,x_n\in\{0,1\}^d$ and constructs a data structure of size…
We study the control of an \emph{unknown} linear dynamical system under general convex costs. The objective is minimizing regret vs. the class of disturbance-feedback-controllers, which encompasses all stabilizing…
We investigate the online bandit learning of the monotone multi-linear DR-submodular functions, designing the algorithm $\mathtt{BanditMLSM}$ that attains $O(T^{2/3}\log T)$ of $(1-1/e)$-regret. Then we reduce submodular bandit with…
This paper studies an online optimization problem with a finite prediction window of cost functions and additional switching costs on decisions. We propose two gradient-based online algorithms: Receding Horizon Gradient Descent (RHGD), and…