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Online (Non-)Convex Learning via Tempered Optimism

arXiv 2301.07530 ↗First posted 18 Jan 2023cs.LG math.OC stat.MLcited by 0

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Abstract (arXiv)

Optimistic Online Learning aims to exploit experts conveying reliable information to predict the future. However, such implicit optimism may be challenged when it comes to practical crafting of such experts. A fundamental example consists in approximating a minimiser of the current problem and use it as expert. In the context of dynamic environments, such an expert only conveys partially relevant information as it may lead to overfitting. To tackle this issue, we introduce in this work the optimistically tempered (OT) online learning framework designed to handle such imperfect experts. As a first contribution, we show that tempered optimism is a fruitful paradigm for Online Non-Convex Learning by proposing simple, yet powerful modification of Online Gradient and Mirror Descent. Second, we derive a second OT algorithm for convex losses and third, evaluate the practical efficiency of tempered optimism on real-life datasets and a toy experiment.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 23 of its 46 references that are in the map. First posted on arXiv 18 Jan 2023.

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References · 23

  1. 2017Visualizing the Loss Landscape of Neural Netscited by 1,126
  2. 2019Introduction to Online Convex Optimizationcited by 793
  3. 2013Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programmingcited by 716
  4. 2013Optimization, Learning, and Games with Predictable Sequencescited by 187
  5. 2013Non-stationary Stochastic Optimizationcited by 173
  6. 2018Adaptive Online Learning in Dynamic Environmentscited by 130
  7. 2020Dynamic Regret of Convex and Smooth Functionscited by 90
  8. 2020On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problemscited by 79
  9. 2016Tracking Slowly Moving Clairvoyant: Optimal Dynamic Regret of Online Learning with True and Noisy Gradientcited by 65
  10. 2016Improved Dynamic Regret for Non-degenerate Functionscited by 46
  11. 2013Dynamical Models and Tracking Regret in Online Convex Programmingcited by 42
  12. 2020Online Learning with Imperfect Hintscited by 37
11 more
  1. 2014Optimal learning with Bernstein Online Aggregationcited by 35
  2. 2020Improved Analysis for Dynamic Regret of Strongly Convex and Smooth Functionscited by 33
  3. 2021Non-stationary Online Learning with Memory and Non-stochastic Controlcited by 33
  4. 2021Online Learning with Optimism and Delaycited by 33
  5. 2019Online Non-Convex Learning: Following the Perturbed Leader is Optimalcited by 31
  6. 2019Online Forecasting of Total-Variation-bounded Sequencescited by 30
  7. 2014Simultaneous Model Selection and Optimization through Parameter-free Stochastic Learningcited by 27
  8. 2018Learning in Non-convex Games with an Optimization Oraclecited by 24
  9. 2021Stochastic Online Convex Optimization. Application to probabilistic time series forecastingcited by 8
  10. 2021Stochastic Gradient Descent on Nonconvex Functions with General Noise Modelscited by 7
  11. 2022Dynamic Regret of Adaptive Gradient Methods for Strongly Convex Problemscited by 3

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