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This paper introduces consensus-based primal-dual methods for distributed online optimization where the time-varying system objective function $f_t(\mathbf{x})$ is given as the sum of local agents' objective functions, i.e.,…
To deal with changing environments, a new performance measure -- adaptive regret, defined as the maximum static regret over any interval, was proposed in online learning. Under the setting of online convex optimization, several algorithms…
Optimization of convex functions under stochastic zeroth-order feedback has been a major and challenging question in online learning. In this work, we consider the problem of optimizing second-order smooth and strongly convex functions…
We consider the global minimization of smooth functions based solely on function evaluations. Algorithms that achieve the optimal number of function evaluations for a given precision level typically rely on explicitly constructing an…
We consider the setting of online logistic regression and consider the regret with respect to the 2-ball of radius B. It is known (see [Hazan et al., 2014]) that any proper algorithm which has logarithmic regret in the number of samples…
To address the uncertainty in function types, recent progress in online convex optimization (OCO) has spurred the development of universal algorithms that simultaneously attain minimax rates for multiple types of convex functions. However,…
We propose a novel approach for analyzing dynamic regret of first-order constrained online convex optimization algorithms for strongly convex and Lipschitz-smooth objectives. Crucially, we provide a general analysis that is applicable to a…
We consider the closely related problems of bandit convex optimization with two-point feedback, and zero-order stochastic convex optimization with two function evaluations per round. We provide a simple algorithm and analysis which is…
We study online optimization of smoothed piecewise constant functions over the domain [0, 1). This is motivated by the problem of adaptively picking parameters of learning algorithms as in the recently introduced framework by Gupta and…
For decision making under uncertainty, min-max regret has been established as a popular methodology to find robust solutions. In this approach, we compare the performance of our solution against the best possible performance had we known…
Calibration is a fundamental concept that aims at ensuring the reliability of probabilistic predictions by aligning them with real-world outcomes. There is a surge of studies on new calibration measures that are easier to optimize compared…
In this paper, we consider an online optimization process, where the objective functions are not convex (nor concave) but instead belong to a broad class of continuous submodular functions. We first propose a variant of the Frank-Wolfe…
The k-regret query aims to return a size-k subset S of a database D such that, for any query user that selects a data object from this size-k subset S rather than from database D, her regret ratio is minimized. The regret ratio here is…
In this paper, Lipschitz univariate constrained global optimization problems where both the objective function and constraints can be multiextremal are considered. The constrained problem is reduced to a discontinuous unconstrained problem…
We analyze the minimax regret of the adversarial bandit convex optimization problem. Focusing on the one-dimensional case, we prove that the minimax regret is $\widetilde\Theta(\sqrt{T})$ and partially resolve a decade-old open problem. Our…
In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…
Achieving sample efficiency in online episodic reinforcement learning (RL) requires optimally balancing exploration and exploitation. When it comes to a finite-horizon episodic Markov decision process with $S$ states, $A$ actions and…
Symmetry arises in many optimization and decision-making problems, and has attracted considerable attention from the optimization community: By utilizing the existence of such symmetries, the process of searching for optimal solutions can…
Recently, several universal methods have been proposed for online convex optimization which can handle convex, strongly convex and exponentially concave cost functions simultaneously. However, most of these algorithms have been designed…
Universal online learning aims to achieve optimal regret guarantees without requiring prior knowledge of the curvature of online functions. Existing methods have established minimax-optimal regret bounds for universal online learning, where…