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Introduction to Online Convex Optimization

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arxiv 1909.05207 v3 pith:X6T3JKKH submitted 2019-09-07 cs.LG math.OCstat.ML

Elad Hazan This is my paper · ORCID
classification cs.LGmath.OCstat.ML
keywords optimizationprocessalgorithmicalongapplicationsapplyingapproachaspects
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This manuscript portrays optimization as a process. In many practical applications the environment is so complex that it is infeasible to lay out a comprehensive theoretical model and use classical algorithmic theory and mathematical optimization. It is necessary as well as beneficial to take a robust approach, by applying an optimization method that learns as one goes along, learning from experience as more aspects of the problem are observed. This view of optimization as a process has become prominent in varied fields and has led to some spectacular success in modeling and systems that are now part of our daily lives.

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Cited by 6 Pith papers

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

  1. A Linearly Convergent Projection-Free Algorithm for Smooth Convex Sets

    math.OC 2026-08 accept novelty 8.0 of 10

    This paper presents a projection-free algorithm that converges linearly for strongly convex minimization over convex sets satisfying a uniform rolling-ball condition, using only membership queries.

  2. Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications

    cs.LG 2025-09 conditional novelty 8.0 of 10

    A new potential-based algorithm achieves instance-optimal O(sqrt(T·S(X||I/d))) regret for matrix LEA with the same complexity as MMWU, using a one-sided Jensen trace inequality.

  3. Blackwell's Approachability with Approximation Algorithms

    math.OC 2025-02 conditional novelty 8.0 of 10

    Blackwell approachability with approximation oracles for both players: the downward closure of α_X α_Y^{-1} S is efficiently approachable at rate O(1/sqrt(T)).

  4. Decoupling Corruption and Horizon in Robust Contextual Pricing

    cs.GT 2026-07 accept novelty 7.0 of 10

    Robust contextual pricing admits regret O(Cd + d² log T), the first bound that additively separates corruption budget C from horizon T.

  5. Lower Bound on the Cumulative Constrained Violation for the OGD+Projection algorithm for Constrained Online Convex Optimization (COCO)

    cs.LG 2026-07 accept novelty 6.0 of 10

    OGD+Projection for constrained online convex optimization has cumulative constraint violation Ω(T^{(d-1)/(2d)}) in dimension d, the first lower bound of this form.

  6. Rethinking Pricing in Energy Markets: Pay-as-Bid vs Pay-as-Clear

    cs.GT 2025-07 conditional novelty 6.0 of 10

    A game-theoretic comparison shows pay-as-bid's worst-case equilibrium price is at most pay-as-clear's, with strict gains in generic instances.

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