# Online (Non-)Convex Learning via Tempered Optimism

arXiv: https://arxiv.org/abs/2301.07530 · HTML: https://mlsanity.com/paper/2301.07530/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 46 references that are in the map.
- First posted on arXiv 18 Jan 2023.

## Builds on (most cited first, 23 of 23)

- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [Optimization, Learning, and Games with Predictable Sequences](https://mlsanity.com/paper/1311.1869/) (2013)
- [Non-stationary Stochastic Optimization](https://mlsanity.com/paper/1307.5449/) (2013)
- [Adaptive Online Learning in Dynamic Environments](https://mlsanity.com/paper/1810.10815/) (2018)
- [Dynamic Regret of Convex and Smooth Functions](https://mlsanity.com/paper/2007.03479/) (2020)
- [On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problems](https://mlsanity.com/paper/2006.11144/) (2020)
- [Tracking Slowly Moving Clairvoyant: Optimal Dynamic Regret of Online Learning with True and Noisy Gradient](https://mlsanity.com/paper/1605.04638/) (2016)
- [Improved Dynamic Regret for Non-degenerate Functions](https://mlsanity.com/paper/1608.03933/) (2016)
- [Dynamical Models and Tracking Regret in Online Convex Programming](https://mlsanity.com/paper/1301.1254/) (2013)
- [Online Learning with Imperfect Hints](https://mlsanity.com/paper/2002.04726/) (2020)
- [Optimal learning with Bernstein Online Aggregation](https://mlsanity.com/paper/1404.1356/) (2014)
- [Improved Analysis for Dynamic Regret of Strongly Convex and Smooth Functions](https://mlsanity.com/paper/2006.05876/) (2020)
- [Non-stationary Online Learning with Memory and Non-stochastic Control](https://mlsanity.com/paper/2102.03758/) (2021)
- [Online Learning with Optimism and Delay](https://mlsanity.com/paper/2106.06885/) (2021)
- [Online Non-Convex Learning: Following the Perturbed Leader is Optimal](https://mlsanity.com/paper/1903.08110/) (2019)
- [Online Forecasting of Total-Variation-bounded Sequences](https://mlsanity.com/paper/1906.03364/) (2019)
- [Simultaneous Model Selection and Optimization through Parameter-free Stochastic Learning](https://mlsanity.com/paper/1406.3816/) (2014)
- [Learning in Non-convex Games with an Optimization Oracle](https://mlsanity.com/paper/1810.07362/) (2018)
- [Stochastic Online Convex Optimization. Application to probabilistic time series forecasting](https://mlsanity.com/paper/2102.00729/) (2021)
- [Stochastic Gradient Descent on Nonconvex Functions with General Noise Models](https://mlsanity.com/paper/2104.00423/) (2021)
- [Dynamic Regret of Adaptive Gradient Methods for Strongly Convex Problems](https://mlsanity.com/paper/2209.01608/) (2022)

## 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.