Research map / Bandits and online learning / Online convex optimization and games
Constrained and unconstrained OCO algorithms
Design online convex optimization algorithms handling constraints, unbounded domains, and switching costs.
85 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Online convex optimization and games, keyword cluster “convex optimization · online convex · functions”
State History Tried Preprints Who Export
Where it stands
Not enough benchmark data Fewer than four papers report the same benchmark, so there is no record to follow.
19 papers in 2023–24 and 27 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic grew, from 8.3% to 9.8%.
How this is decided
A benchmark is tracked when at least four papers of this approach report their own method on the same dataset and metric in at least two different years. Its record is the best number reported up to 2024 compared with the best reported in 2025–26: still improving means at least 1% better, flat means at most 0.2% better with at least two papers from 2025–26 trying. Numbers on a different scale from the rest (a fraction among percentages) and far outliers are left out. Results come from different papers with different setups, so they are signals, not head-to-head comparisons. The share of papers is counted at ICML, NeurIPS, ICLR, CVPR and AAAI.
How it got here
Most cited paper of each year
- 2016 · Adaptive Algorithms for Online Convex Optimization with Long-term Constraints (ICML 2016 · 82 citations)
- 2017 · Online Convex Optimization with Stochastic Constraints (NeurIPS 2017 · 28 citations)
- 2018 · Online convex optimization for cumulative constraints (NeurIPS 2018 · 72 citations)
- 2019 · Beyond Online Balanced Descent: An Optimal Algorithm for Smoothed Online Optimization (NeurIPS 2019 · 40 citations)
- 2020 · Online Optimization with Memory and Competitive Control (NeurIPS 2020 · 26 citations)
- 2021 · Online Optimal Control with Affine Constraints (AAAI 2021 · 24 citations)
- 2022 · Safe Online Convex Optimization with Unknown Linear Safety Constraints (AAAI 2022 · 14 citations)
- 2023 · Distributed Projection-Free Online Learning for Smooth and Convex Losses (AAAI 2023 · 6 citations)
- 2024 · Optimal Algorithms for Online Convex Optimization with Adversarial Constraints (NeurIPS 2024 · 7 citations)
- 2025 · Doubly-Bounded Queue for Constrained Online Learning: Keeping Pace with Dynamics of Both Loss and Constraint (AAAI 2025 · 3 citations)
- 2026 · Upper-Linearizability of Online Non-Monotone DR-Submodular Maximization over Down-Closed Convex Sets (ICML 2026 · 0 citations)
Earliest papers here
- Adaptive Algorithms for Online Convex Optimization with Long-term Constraints (ICML 2016 · 82 citations)
- Delay-Tolerant Online Convex Optimization: Unified Analysis and Adaptive-Gradient Algorithms (AAAI 2016 · 34 citations)
- Online Convex Optimization with Unconstrained Domains and Losses (NeurIPS 2016 · 11 citations)
What has been tried
61 papers here report 359 measured changes (a component added, removed or swapped, compared with a baseline): helped 72%, no clear effect 6%, hurt 15%, mixed 7%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| use adaptive rather than constant or delay-total-specific learning-rate tuning | Exp-concave OCO with delayed feedback · regret bound | \min\{d (\max) n\ln T, \sqrt{d_{\mathrm{tot}}}\} | Helped | Exploiting Curvature in Online Convex Optimization with Delayed Feedback (ICML 2025 · 0 citations) |
| Increase quadratic regularization to obtain constant regret at the origin | Unconstrained OCO · regret | \|u\|^2 (k+1)^2; constant regret at the origin no matter what k is | Mixed | Unconstrained Robust Online Convex Optimization (ICML 2025 · 0 citations) |
| Use fixed φ₂ instead of adaptive regularisation | High-dimensional OCO · regret | R_T \geq L \cdot \min\Brb{\frac{T}{16}, \frac{1}{8}\sqrt{T d^{1-2/p}}} | Hurt | On the necessity of adaptive regularisation: Optimal anytime online learning on $\boldsymbol{\ell_p}$-balls (NeurIPS 2025 · 0 citations) |
| Use Mt+1 = ∇ft(ˆxt+1) with the original general-convex configuration instead of Mt+1 = ∇ft(xt) | Composite SEA, general convex · expected regret bound | O(√σ²₁:T + √Σ²₁:T) -> O(√˜σ²₁:T + √Σ²₁:T) | Hurt | Online Composite Optimization Between Stochastic and Adversarial Environments (NeurIPS 2024 · 0 citations) |
Recent preprints
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Who publishes on it
Institutions on the most papers of this approach since 2023 (of 46 papers; from OpenAlex and the papers' affiliations).
- Nanjing University · 7 papers
- Zhejiang University · 6 papers
- Tata Institute of Fundamental Research · 3 papers
- Boston University · 2 papers
- Google · 2 papers
- Purdue University · 2 papers
Use it
Download BibTeX of 39 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Dynamic and adaptive regret (57 papers)
- Parameter-free non-stationary online learning (45 papers)
Elsewhere in the topic
- Online learning with feedback graphs (155 papers)
- Best-of-both-worlds bandit algorithms (125 papers)
- Learning for pricing and auctions (101 papers)
- Online decision-making with feedback structure (81 papers)
- Online allocation with constraints (77 papers)
- Learning-augmented online algorithms (73 papers)
- Last-iterate convergence in games (65 papers)
- Fast no-regret dynamics in games (37 papers)
Benchmark numbers, ablations and baseline numbers are extracted by AI from each paper's full text and can be wrong; the paper is the authority. Data: results index of 2026-11-02, citation counts from OpenAlex (2026-10-09).