mlsanityData to 14 Oct 2026

Data-Dependent Bounds for Online Portfolio Selection Without Lipschitzness and Smoothness

arXiv 2305.13946 ↗First posted 23 May 2023cs.LG math.OC stat.MLcited by 11

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Abstract (arXiv)

This work introduces the first small-loss and gradual-variation regret bounds for online portfolio selection, marking the first instances of data-dependent bounds for online convex optimization with non-Lipschitz, non-smooth losses. The algorithms we propose exhibit sublinear regret rates in the worst cases and achieve logarithmic regrets when the data is "easy," with per-iteration time almost linear in the number of investment alternatives. The regret bounds are derived using novel smoothness characterizations of the logarithmic loss, a local norm-based analysis of following the regularized leader (FTRL) with self-concordant regularizers, which are not necessarily barriers, and an implicit variant of optimistic FTRL with the log-barrier.

Key facts. Cited by 11 papers in the map (data through 14 Oct 2026). Builds on 13 of its 41 references that are in the map. First posted on arXiv 23 May 2023.

Builds on

13 of 41 references.

References · 13

  1. 2019Introduction to Online Convex Optimizationcited by 803
  2. 2019Online Learning: A Modern Introduction Using Convex Optimizationcited by 417
  3. 2013Optimization, Learning, and Games with Predictable Sequencescited by 188
  4. 2016Relatively-Smooth Convex Optimization by First-Order Methods, and Applicationscited by 108
  5. 2021Adaptivity and Non-stationarity: Problem-dependent Dynamic Regret for Online Convex Optimizationcited by 66
  6. 2017A Modular Analysis of Adaptive (Non-)Convex Optimization: Optimism, Composite Objectives, and Variational Boundscited by 23
  7. 2018Efficient Online Portfolio with Logarithmic Regretcited by 20
  8. 2022Pushing the Efficiency-Regret Pareto Frontier for Online Learning of Portfolios and Quantum Statescited by 15
  9. 2022Efficient and Near-Optimal Online Portfolio Selectioncited by 13
  10. 2019Soft-Bayes: Prod for Mixtures of Experts with Log-Losscited by 10
  11. 2022Damped Online Newton Step for Portfolio Selectioncited by 9
  12. 2022Online Self-Concordant and Relatively Smooth Minimization, With Applications to Online Portfolio Selection and Learning Quantum Statescited by 7
1 more
  1. 2023Minimizing Dynamic Regret on Geodesic Metric Spacescited by 6

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 2; 2024: 1; 2025: 5; 2026: 3.

11 papers.

  1. 2024Gradient-Variation Online Learning under Generalized Smoothnesscited by 11
  2. 2025On the Dynamic Regret of Following the Regularized Leader: Optimism with History Pruningcited by 5
  3. 2026Improved Dimension Dependence for Bandit Convex Optimization with Gradient Variationscited by 5
  4. 2025Optimistic Interior Point Methods for Sequential Hypothesis Testing by Bettingcited by 4
  5. 2026Online Learning with Gradient-Variation Interval Regretcited by 2
  6. 2023Fast Minimization of Expected Logarithmic Loss via Stochastic Dual Averagingcited by 1
  7. 2023Online Learning Quantum States with the Logarithmic Loss via VB-FTRLcited by 1
  8. 2025Optimistic Learning for Communication Networkscited by 0
  9. 2025Bayesian Ensembling: Insights from Online Optimization and Empirical Bayescited by 0
  10. 2025Duality and Policy Evaluation in Distributionally Robust Bayesian Diffusion Controlcited by 0
  11. 2026From Average Sensitivity to Small-Loss Regret Bounds under Random-Order Modelcited by 0