mlsanityData to 7 Oct 2026

Online Convex Optimization with Unconstrained Domains and Losses

arXiv 1703.02622 ↗First posted 7 Mar 2017cs.LG stat.MLcited by 14

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Abstract (arXiv)

We propose an online convex optimization algorithm (RescaledExp) that achieves optimal regret in the unconstrained setting without prior knowledge of any bounds on the loss functions. We prove a lower bound showing an exponential separation between the regret of existing algorithms that require a known bound on the loss functions and any algorithm that does not require such knowledge. RescaledExp matches this lower bound asymptotically in the number of iterations. RescaledExp is naturally hyperparameter-free and we demonstrate empirically that it matches prior optimization algorithms that require hyperparameter optimization.

Key facts. Cited by 14 papers in the map (data through 7 Oct 2026). First posted on arXiv 7 Mar 2017.

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Citing papers per year: 2021: 3; 2022: 2; 2023: 3; 2024: 4; 2025: 1; 2026: 1.

14 papers.

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  1. 2023Parameter-Agnostic Optimization under Relaxed Smoothnesscited by 29
  2. 2022PDE-Based Optimal Strategy for Unconstrained Online Learningcited by 27
  3. 2023Adaptive SGD with Polyak stepsize and Line-search: Robust Convergence and Variance Reductioncited by 23
  4. 2023Mechanic: A Learning Rate Tunercited by 20
  5. 2024Dealing with unbounded gradients in stochastic saddle-point optimizationcited by 15
  6. 2021SVRG Meets AdaGrad: Painless Variance Reductioncited by 13
  7. 2024Tuning-Free Stochastic Optimizationcited by 13
  8. 2024How Free is Parameter-Free Stochastic Optimization?cited by 12
  9. 2024Universal Online Convex Optimization with 1 Projection per Roundcited by 6
  10. 2021On the Initialization for Convex-Concave Min-max Problemscited by 4
  11. 2021Universal Online Convex Optimization Meets Second-order Boundscited by 4
  12. 2022Optimistic Optimisation of Composite Objective with Exponentiated Updatecited by 3
2 more
  1. 2025Decentralized Parameter-Free Online Learningcited by 1
  2. 2026Decentralized Parameter-Free Online Learning with Compressed Gossipcited by 0