• Corpus ID: 52823321

Fully Implicit Online Learning

@article{Song2018FullyIO,
  title={Fully Implicit Online Learning},
  author={Chaobing Song and Ji Liu and Han Liu and Yong Jiang and T. Zhang},
  journal={ArXiv},
  year={2018},
  volume={abs/1809.09350}
}
Regularized online learning is widely used in machine learning applications. In online learning, performing exact minimization ($i.e.,$ implicit update) is known to be beneficial to the numerical stability and structure of solution. In this paper we study a class of regularized online algorithms without linearizing the loss function or the regularizer, which we call \emph{fully implicit online learning} (FIOL). We show that for arbitrary Bregman divergence, FIOL has the $O(\sqrt{T})$ regret for… 

Tables from this paper

Implicit Parameter-free Online Learning with Truncated Linear Models
TLDR
New parameter-free algorithms that can take advantage of truncated linear models through a new update that has an “implicit” flavor are proposed that are efficient, efficient, requires only one gradient at each step, never overshoots the minimum of the truncated model, and retains the favorable parameter- free properties.
Temporal Variability in Implicit Online Learning
TLDR
It is shown that the regret can be constant if the temporal variability is constant and the learning rate is tuned appropriately, without the need of smooth losses, and a novel static regret bound is proved.
A closer look at temporal variability in dynamic online learning
TLDR
An adaptation of the Implicit version of Online Mirror Descent to the dynamic setting is proposed, which is adaptive not only to the temporal variability of the loss functions, but also to the path length of the sequence of comparators when an upper bound is known.
Adaptive Online Optimization with Predictions: Static and Dynamic Environments
TLDR
New step-size rules and OCO algorithms that simultaneously exploit gradient predictions, function predictions and dynamics, features particularly pertinent to control applications are proposed.
An Online Supervised Learning Framework for Crime Data
TLDR
The unfortunate, frequent nature of crime, and the fact that it often follows a geographic and demographic pattern which requires constant updation makes this data set an excellent choice for online learning based models for analytics.

References

SHOWING 1-10 OF 22 REFERENCES
Dual Averaging Methods for Regularized Stochastic Learning and Online Optimization
  • Lin Xiao
  • Computer Science
    J. Mach. Learn. Res.
  • 2009
TLDR
A new online algorithm is developed, the regularized dual averaging (RDA) method, that can explicitly exploit the regularization structure in an online setting and can be very effective for sparse online learning with l1-regularization.
Implicit Online Learning
TLDR
This paper analyzes a class of online learning algorithms based on fixed potentials and non-linearized losses, which yields algorithms with implicit update rules, and provides improved algorithms and bounds for the online metric learning problem, and shows improved robustness for online linear prediction problems.
Adaptive Subgradient Methods for Online Learning and Stochastic Optimization
TLDR
This work describes and analyze an apparatus for adaptively modifying the proximal function, which significantly simplifies setting a learning rate and results in regret guarantees that are provably as good as the best proximal functions that can be chosen in hindsight.
A Unified View of Regularized Dual Averaging and Mirror Descent with Implicit Updates
TLDR
The results demonstrate that FOBOS uses subgradient approximations to the L1 penalty from previous rounds, leading to less sparsity than RDA, which handles the cumulative penalty in closed form.
Efficient projections onto the l1-ball for learning in high dimensions
TLDR
Efficient algorithms for projecting a vector onto the l1-ball are described and variants of stochastic gradient projection methods augmented with these efficient projection procedures outperform interior point methods, which are considered state-of-the-art optimization techniques.
Towards Stability and Optimality in Stochastic Gradient Descent
TLDR
A new iterative procedure termed averaged implicit SGD (AI-SGD), which employs an implicit update at each iteration, which is related to proximal operators in optimization and achieves competitive performance with other state-of-the-art procedures.
Exact Soft Confidence-Weighted Learning
TLDR
A new Soft Confidence-Weighted online learning scheme is proposed, which enables the conventional confidence-weighted learning method to handle non-separable cases and generally achieves better or at least comparable predictive accuracy, but enjoys significant advantage of computational efficiency.
Stochastic dual coordinate ascent methods for regularized loss
TLDR
A new analysis of Stochastic Dual Coordinate Ascent (SDCA) is presented showing that this class of methods enjoy strong theoretical guarantees that are comparable or better than SGD.
Stochastic gradient descent methods for estimation with large data sets
TLDR
The sgd package in R offers the most extensive and robust implementation of stochastic gradient descent methods, which include the wide class of generalized linear models as well as M-estimation for robust regression.
Online Bayesian Passive-Aggressive Learning
TLDR
Online Bayesian Passive-Aggressive learning is presented, which subsumes the online PA and extends naturally to incorporate latent variables and perform nonparametric Bayesian inference, thus providing great flexibility for explorative analysis.
...
...