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We study online learning problems in which a decision maker has to take a sequence of decisions subject to $m$ long-term constraints. The goal of the decision maker is to maximize their total reward, while at the same time achieving small…

Machine Learning · Computer Science 2022-09-16 Matteo Castiglioni , Andrea Celli , Alberto Marchesi , Giulia Romano , Nicola Gatti

We consider the online control problem with an unknown linear dynamical system in the presence of adversarial perturbations and adversarial convex loss functions. Although the problem is widely studied in model-based control, it remains…

Systems and Control · Electrical Eng. & Systems 2024-03-12 Zishun Liu , Yongxin Chen

Optimizing smooth convex functions in stochastic settings, where only noisy estimates of gradients and Hessians are available, is a fundamental problem in optimization. While first-order methods possess a low per-iteration cost, their…

Statistics Theory · Mathematics 2026-02-06 Antoine Godichon-Baggioni , Bruno Portier , Guillaume Sallé

The goal of a learner in standard online learning is to maintain an average loss close to the loss of the best-performing single function in some class. In many real-world problems, such as rating or ranking items, there is no single best…

Machine Learning · Computer Science 2013-03-18 Edward Moroshko , Koby Crammer

A natural goal when designing online learning algorithms for non-stationary environments is to bound the regret of the algorithm in terms of the temporal variation of the input sequence. Intuitively, when the variation is small, it should…

Machine Learning · Computer Science 2021-12-08 Gautam Goel , Babak Hassibi

We derive an online learning algorithm with improved regret guarantees for `easy' loss sequences. We consider two types of `easiness': (a) stochastic loss sequences and (b) adversarial loss sequences with small effective range of the…

Machine Learning · Computer Science 2019-08-28 Tobias Sommer Thune , Yevgeny Seldin

We consider online optimization with binary decision variables and convex loss functions. We design a new algorithm, binary online gradient descent (bOGD) and bound its expected dynamic regret. We provide a regret bound that holds for any…

Optimization and Control · Mathematics 2022-01-21 Antoine Lesage-Landry , Joshua A. Taylor , Duncan S. Callaway

Stochastic optimization methods encounter new challenges in the realm of streaming, characterized by a continuous flow of large, high-dimensional data. While first-order methods, like stochastic gradient descent, are the natural choice,…

Statistics Theory · Mathematics 2024-02-02 Antoine Godichon-Baggioni , Nicklas Werge

We consider a family of learning strategies for online optimization problems that evolve in continuous time and we show that they lead to no regret. From a more traditional, discrete-time viewpoint, this continuous-time approach allows us…

Optimization and Control · Mathematics 2014-02-28 Joon Kwon , Panayotis Mertikopoulos

We study the effectiveness of stochastic side information in deterministic online learning scenarios. We propose a forecaster to predict a deterministic sequence where its performance is evaluated against an expert class. We assume that…

Machine Learning · Computer Science 2023-03-13 Junzhang Jia , Xuetong Wu , Jingge Zhu , Jamie Evans

In this paper, we consider the problem of prediction with expert advice in dynamic environments. We choose tracking regret as the performance metric and develop two adaptive and efficient algorithms with data-dependent tracking regret…

Machine Learning · Computer Science 2020-02-11 Shiyin Lu , Lijun Zhang

In the random-order model for online learning, the sequence of losses is chosen upfront by an adversary and presented to the learner after a random permutation. Any random-order input is \emph{asymptotically} equivalent to a stochastic…

Machine Learning · Computer Science 2025-10-06 Martino Bernasconi , Andrea Celli , Riccardo Colini-Baldeschi , Federico Fusco , Stefano Leonardi , Matteo Russo

Sparse regression has been a popular approach to perform variable selection and enhance the prediction accuracy and interpretability of the resulting statistical model. Existing approaches focus on offline regularized regression, while the…

Machine Learning · Statistics 2023-01-03 Shuoguang Yang , Yuhao Yan , Xiuneng Zhu , Qiang Sun

Considering non-stationary environments in online optimization enables decision-maker to effectively adapt to changes and improve its performance over time. In such cases, it is favorable to adopt a strategy that minimizes the negative…

Systems and Control · Electrical Eng. & Systems 2024-04-05 Siyi Wang , Zifan Wang , Xinlei Yi , Michael M. Zavlanos , Karl H. Johansson , Sandra Hirche

We study the problems of offline and online contextual optimization with feedback information, where instead of observing the loss, we observe, after-the-fact, the optimal action an oracle with full knowledge of the objective function would…

Machine Learning · Computer Science 2023-07-04 Omar Besbes , Yuri Fonseca , Ilan Lobel

In the online non-stochastic control problem, an agent sequentially selects control inputs for a linear dynamical system when facing unknown and adversarially selected convex costs and disturbances. A common metric for evaluating control…

Optimization and Control · Mathematics 2025-04-24 Vijeth Hebbar , Cédric Langbort

This paper addresses safe distributed online optimization over an unknown set of linear safety constraints. A network of agents aims at jointly minimizing a global, time-varying function, which is only partially observable to each…

Optimization and Control · Mathematics 2023-02-27 Ting-Jui Chang , Sapana Chaudhary , Dileep Kalathil , Shahin Shahrampour

Maintaining predictive accuracy in non-stationary environments requires online model selection to adapt autonomously to unknown distribution shifts. However, existing tuning-free algorithms face a fundamental trade-off between robustness…

Machine Learning · Computer Science 2026-05-27 Kei Takemura , Ryuta Matsuno , Keita Sakuma

We improve the theoretical and empirical performance of neural-network(NN)-based active learning algorithms for the non-parametric streaming setting. In particular, we introduce two regret metrics by minimizing the population loss that are…

Machine Learning · Computer Science 2023-01-18 Yikun Ban , Yuheng Zhang , Hanghang Tong , Arindam Banerjee , Jingrui He

Constrained Online Convex Optimization (COCO) can be seen as a generalization of the standard Online Convex Optimization (OCO) framework. At each round, a cost function and constraint function are revealed after a learner chooses an action.…

Machine Learning · Computer Science 2025-05-30 Ricardo N. Ferreira , Cláudia Soares