Distribution-Free One-Pass Learning

Zhao, Peng; Wang, Xinqiang; Xie, Siyu; Guo, Lei; Zhou, Zhi‐Hua

doi:10.1109/tkde.2019.2937078

Cited by 20 publications

(7 citation statements)

References 44 publications

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“…In our simulation, we set Γ = 1, D = 2, d = 5, T = 50000, and S = 1000. Next, we employ a real-world dataset called Sulfur recovery unit (SRU) (Zhao et al, 2021b), which is a regression dataset with slowly evolving distribution changes. There are in total 10,081 data samples representing the records of gas diffusion, where the feature consists of five different chemical and physical indexes and the label is the concentration of SO 2 .…”

Section: Methodsmentioning

confidence: 99%

“…Dynamic regret enforces the player to compete with time-varying comparators, and thus is favored in online learning in non-stationary environments (Sugiyama and Kawanabe, 2012;Zhao et al, 2021b). The notion of dynamic regret is also referred to as tracking regret or shifting regret in the prediction with expert advice setting Warmuth, 1998, 2001).…”

Section: Dynamic Regretmentioning

confidence: 99%

See 1 more Smart Citation

Adaptivity and Non-stationarity: Problem-dependent Dynamic Regret for Online Convex Optimization

Zhao¹,

Zhang²,

Zhang³

et al. 2021

Preprint

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We investigate online convex optimization in non-stationary environments and choose the dynamic regret as the performance measure, defined as the difference between cumulative loss incurred by the online algorithm and that of any feasible comparator sequence. Let T be the time horizon and P T be the path-length that essentially reflects the non-stationarity of environments, the state-of-theart dynamic regret is O( T (1 + P T )). Although this bound is proved to be minimax optimal for convex functions, in this paper, we demonstrate that it is possible to further enhance the guarantee for some easy problem instances, particularly when online functions are smooth. Specifically, we propose novel online algorithms that can leverage smoothness and replace the dependence on T in the dynamic regret by problem-dependent quantities: the variation in gradients of loss functions, the cumulative loss of the comparator sequence, and the minimum of the previous two terms. These quantities are at most O(T ) while could be much smaller in benign environments. Therefore, our results are adaptive to the intrinsic difficulty of the problem, since the bounds are tighter than existing results for easy problems and meanwhile guarantee the same rate in the worst case. Notably, our algorithm requires only one gradient per iteration, which shares the same gradient query complexity with the methods developed for optimizing the static regret. As a further application, we extend the results from the full-information setting to bandit convex optimization with two-point feedback and thereby attain the first problem-dependent dynamic regret for such bandit tasks.

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Section: Methodsmentioning

confidence: 99%

Section: Dynamic Regretmentioning

confidence: 99%

Adaptivity and Non-stationarity: Problem-dependent Dynamic Regret for Online Convex Optimization

Zhao¹,

Zhang²,

Zhang³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…In order to have an algorithm that adapts to non-stationary data, it is common to use a forgetting factor. For the recursive least squares, [14] analyzed the effect of the forgetting factor in terms of the tracking error covariance matrix, and [15] made the tracking error analysis with the assumptions that the noise is sub-Gaussian and the parameter follows a drifting model. However, none of the analysis mentioned is done in terms of the regret, which eliminates any noise assumption.…”

Section: Arxiv:190903118v2 [Cslg] 21 Nov 2019mentioning

confidence: 99%

Trading-Off Static and Dynamic Regret in Online Least-Squares and Beyond

Yuan

Lamperski

2020

AAAI

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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 Newton algorithms. For exp-concave and strongly convex objectives, the algorithms achieve the dynamic regret of max{O(log T),O(√TV)}, where V is a bound on the path length of the comparison sequence. In particular, we show how classic recursive least-squares with a forgetting factor achieves this dynamic regret bound. By varying V, we obtain a trade-off between static and dynamic regret. In order to obtain more computationally efficient algorithms, our second contribution is a novel gradient descent step size rule for strongly convex functions. Our gradient descent rule recovers the order optimal dynamic regret bounds described above. For smooth problems, we can also obtain static regret of O(T1-β) and dynamic regret of O(Tβ V*), where β ∈ (0,1) and V* is the path length of the sequence of minimizers. By varying β, we obtain a trade-off between static and dynamic regret.

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“…Although equipped with rich theories, the notion of regret defined in Eqn. ( 2) is not always the right objective to minimize, especially in dynamic environments where the underlying decision function can vary over time (Zhao, Cai, and Zhou 2019;Zhao et al 2019b) and there is no single fixed decision function doing well overall. To overcome this limitation, it is natural to consider a more stringent measure, i.e., dynamic regret (Hall and Willett 2013;Besbes, Gur, and Zeevi 2015;Mokhtari et al 2016;Yang et al 2016;Zhao et al 2019a), defined as the difference between the cumulative loss of the learner and that of a sequence of local minimizers:…”

Section: Dynamic Environmentsmentioning

confidence: 99%

“…Note that the standard cross-validation in the batch learning settings is not suitable here, due to inherent temporal relationships of the streaming data. Therefore, following the setup of previous works (Gama et al 2014;Zhao et al 2019b), for the data set with T instances, we select 10 different subsets with consecutive instances starting from {T /50, T/25, . .…”

Section: Settingsmentioning

confidence: 99%

Optimal Margin Distribution Learning in Dynamic Environments

Zhang

Zhao

Jin

2020

AAAI

Self Cite

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Recently a promising research direction of statistical learning has been advocated, i.e., the optimal margin distribution learning with the central idea that instead of the minimal margin, the margin distribution is more crucial to the generalization performance. Although the superiority of this new learning paradigm has been verified under batch learning settings, it remains open for online learning settings, in particular, the dynamic environments in which the underlying decision function varies over time. In this paper, we propose the dynamic optimal margin distribution machine and theoretically analyze its regret. Although the obtained bound has the same order with the best known one, our method can significantly relax the restrictive assumption that the function variation should be given ahead of time, resulting in better applicability in practical scenarios. We also derive an excess risk bound for the special case when the underlying decision function only evolves several discrete changes rather than varying continuously. Extensive experiments on both synthetic and real data sets demonstrate the superiority of our method.

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Distribution-Free One-Pass Learning

Cited by 20 publications

References 44 publications

Adaptivity and Non-stationarity: Problem-dependent Dynamic Regret for Online Convex Optimization

Adaptivity and Non-stationarity: Problem-dependent Dynamic Regret for Online Convex Optimization

Trading-Off Static and Dynamic Regret in Online Least-Squares and Beyond

Optimal Margin Distribution Learning in Dynamic Environments

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