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We consider the framework of non-stationary Online Convex Optimization where a learner seeks to control its dynamic regret against an arbitrary sequence of comparators. When the loss functions are strongly convex or exp-concave, we…
Online optimization has emerged as powerful tool in large scale optimization. In this pa- per, we introduce efficient online optimization algorithms based on the alternating direction method (ADM), which can solve online convex optimization…
Online convex optimization (OCO) with time-varying constraints is a critical framework for sequential decision-making in dynamic networked systems, where learners must minimize cumulative loss while satisfying regions of feasibility that…
In citep{Hazan-2008-extract}, the authors showed that the regret of online linear optimization can be bounded by the total variation of the cost vectors. In this paper, we extend this result to general online convex optimization. We first…
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…
In online learning, the data is provided in a sequential order, and the goal of the learner is to make online decisions to minimize overall regrets. This note is concerned with continuous-time models and algorithms for several online…
In this paper, we present a novel nonlinear programming-based approach to fine-tune pre-trained neural networks to improve robustness against adversarial attacks while maintaining high accuracy on clean data. Our method introduces…
We propose the algorithms for online convex optimization which lead to cumulative squared constraint violations of the form $\sum\limits_{t=1}^T\big([g(x_t)]_+\big)^2=O(T^{1-\beta})$, where $\beta\in(0,1)$. Previous literature has focused…
We present safe control of partially-observed linear time-varying systems in the presence of unknown and unpredictable process and measurement noise. We introduce a control algorithm that minimizes dynamic regret, i.e., that minimizes the…
We propose a data-driven online convex optimization algorithm for controlling dynamical systems. In particular, the control scheme makes use of an initially measured input-output trajectory and behavioral systems theory which enable it to…
We study Online Convex Optimization with adversarial constraints (COCO). At each round a learner selects an action from a convex decision set and then an adversary reveals a convex cost and a convex constraint function. The goal of the…
In this paper, we investigate the online non-convex optimization problem which generalizes the classic {online convex optimization problem by relaxing the convexity assumption on the cost function. For this type of problem, the classic…
We consider the problem of tracking the minimum of a time-varying convex optimization problem over a dynamic graph. Motivated by target tracking and parameter estimation problems in intermittently connected robotic and sensor networks, the…
Time-varying systems are a challenge in many scientific and engineering areas. Usually, estimation of time-varying parameters or signals must be performed online, which calls for the development of responsive online algorithms. In this…
The constrained version of the standard online convex optimization (OCO) framework, called COCO is considered, where on every round, a convex cost function and a convex constraint function are revealed to the learner after it chooses the…
Recursive least-squares algorithms often use forgetting factors as a heuristic to adapt to non-stationary data streams. The first contribution of this paper rigorously characterizes the effect of forgetting factors for a class of online…
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…
We study the problem of controlling a linear dynamical system with adversarial perturbations where the only feedback available to the controller is the scalar loss, and the loss function itself is unknown. For this problem, with either a…
We study a class of adversarial bandit optimization problems in which the loss functions may be non-convex and non-smooth. In each round, the learner observes a loss that consists of an underlying linear component together with an…
In this paper, we study fundamental problems of maximizing DR-submodular continuous functions that have real-world applications in the domain of machine learning, economics, operations research and communication systems. It captures a…