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Projection-free Online Learning

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arxiv 1206.4657 v1 pith:PLNVEA7M submitted 2012-06-18 cs.LG cs.DS

classification cs.LGcs.DS
keywords onlinealgorithmslearningoptimizationboundscomputationalconvexefficient
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The computational bottleneck in applying online learning to massive data sets is usually the projection step. We present efficient online learning algorithms that eschew projections in favor of much more efficient linear optimization steps using the Frank-Wolfe technique. We obtain a range of regret bounds for online convex optimization, with better bounds for specific cases such as stochastic online smooth convex optimization. Besides the computational advantage, other desirable features of our algorithms are that they are parameter-free in the stochastic case and produce sparse decisions. We apply our algorithms to computationally intensive applications of collaborative filtering, and show the theoretical improvements to be clearly visible on standard datasets.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Training Deep Learning Models with Norm-Constrained LMOs

    cs.LG 2025-02 unverdicted novelty 7.0 of 10

    Scion is a new stochastic LMO-based optimizer family that unifies existing methods, supports unconstrained problems, and delivers hyperparameter transferability plus speedups on nanoGPT training.

  2. Quantum Algorithms for Projection-Free Sparse Convex Optimization

    quant-ph 2025-07 conditional novelty 5.0 of 10

    Quantum Frank-Wolfe algorithms reduce dimension dependence in sparse convex optimization, from O(d) to O(sqrt d) function queries for vectors and from O(d^2) to O(d) per update step for matrices under certain assumptions.

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