mlsanityData to 14 Oct 2026

Adaptive Regret of Convex and Smooth Functions

arXiv 1904.11681 ↗First posted 26 Apr 2019cs.LG stat.MLcited by 24

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Abstract (arXiv)

We investigate online convex optimization in changing environments, and choose the adaptive regret as the performance measure. The goal is to achieve a small regret over every interval so that the comparator is allowed to change over time. Different from previous works that only utilize the convexity condition, this paper further exploits smoothness to improve the adaptive regret. To this end, we develop novel adaptive algorithms for convex and smooth functions, and establish problem-dependent regret bounds over any interval. Our regret bounds are comparable to existing results in the worst case, and become much tighter when the comparator has a small loss.

Key facts. Cited by 24 papers in the map (data through 14 Oct 2026). First posted on arXiv 26 Apr 2019.

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Citing papers per year: 2021: 7; 2022: 7; 2023: 4; 2024: 2; 2025: 1; 2026: 3.

24 papers.

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  1. 2021Adaptivity and Non-stationarity: Problem-dependent Dynamic Regret for Online Convex Optimizationcited by 66
  2. 2021Regret and Cumulative Constraint Violation Analysis for Online Convex Optimization with Long Term Constraintscited by 39
  3. 2022Corralling a Larger Band of Bandits: A Case Study on Switching Regret for Linear Banditscited by 22
  4. 2022Online Bilevel Optimization: Regret Analysis of Online Alternating Gradient Methodscited by 15
  5. 2023Efficient Methods for Non-stationary Online Learningcited by 15
  6. 2021Adversarial Tracking Control via Strongly Adaptive Online Learning with Memorycited by 14
  7. 2022Online Control of Unknown Time-Varying Dynamical Systemscited by 13
  8. 2023Non-stationary Projection-free Online Learning with Dynamic and Adaptive Regret Guaranteescited by 13
  9. 2021Optimal and Efficient Algorithms for General Mixable Losses against Switching Oraclescited by 10
  10. 2022Adaptive Gradient Methods with Local Guaranteescited by 8
  11. 2022Adaptive Oracle-Efficient Online Learningcited by 7
  12. 2021Online Convex Optimization with Continuous Switching Constraintcited by 6
12 more
  1. 2022Smoothed Online Convex Optimization Based on Discounted-Normal-Predictorcited by 6
  2. 2023Adaptive, Doubly Optimal No-Regret Learning in Strongly Monotone and Exp-Concave Games with Gradient Feedbackcited by 6
  3. 2024Universal Online Convex Optimization with 1 Projection per Roundcited by 6
  4. 2021Universal Online Convex Optimization Meets Second-order Boundscited by 4
  5. 2022One Arrow, Two Kills: An Unified Framework for Achieving Optimal Regret Guarantees in Sleeping Banditscited by 3
  6. 2026Online Learning with Gradient-Variation Interval Regretcited by 2
  7. 2021Near-Linear Time Algorithm with Near-Logarithmic Regret Per Switch for Mixable/Exp-Concave Lossescited by 1
  8. 2026On the Relation Between Interval Regret and Dynamic Regretcited by 1
  9. 2023Nearly Optimal Algorithms with Sublinear Computational Complexity for Online Kernel Regressioncited by 0
  10. 2024Reciprocal Learningcited by 0
  11. 2025Distributed Dynamic Associative Memory via Online Convex Optimizationcited by 0
  12. 2026Small Gradient Norm Regret for Online Convex Optimizationcited by 0