# Dynamic Local Regret for Non-convex Online Forecasting

arXiv: https://arxiv.org/abs/1910.07927 · HTML: https://mlsanity.com/paper/1910.07927/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Oct 2019.

## Built on by (most cited first, 17 of 17)

- [Learning Fast and Slow for Online Time Series Forecasting](https://mlsanity.com/paper/2202.11672/) (2022)
- [Online Bilevel Optimization: Regret Analysis of Online Alternating Gradient Methods](https://mlsanity.com/paper/2207.02829/) (2022)
- [Non-Convex Bilevel Optimization with Time-Varying Objective Functions](https://mlsanity.com/paper/2308.03811/) (2023)
- [Act Now: A Novel Online Forecasting Framework for Large-Scale Streaming Data](https://mlsanity.com/paper/2412.00108/) (2024)
- [Dynamic Regret Analysis for Online Meta-Learning](https://mlsanity.com/paper/2109.14375/) (2021)
- [Online Decision-Focused Learning](https://mlsanity.com/paper/2505.13564/) (2025)
- [Disentangling Long-Short Term State Under Unknown Interventions for Online Time Series Forecasting](https://mlsanity.com/paper/2502.12603/) (2025)
- [Online Nonconvex Bilevel Optimization with Bregman Divergences](https://mlsanity.com/paper/2409.10470/) (2024)
- [Evolving Multi-Scale Normalization for Time Series Forecasting under Distribution Shifts](https://mlsanity.com/paper/2409.19718/) (2024)
- [Online Time Series Forecasting with Theoretical Guarantees](https://mlsanity.com/paper/2510.18281/) (2025)
- [Achieving Better Local Regret Bound for Online Non-Convex Bilevel Optimization](https://mlsanity.com/paper/2602.06457/) (2026)
- [Compositional Spectral Prompts for LLM-based Online Time Series Forecasting](https://mlsanity.com/paper/2609.02093/) (2026)
- [Event-Driven Online Vertical Federated Learning](https://mlsanity.com/paper/2506.14911/) (2025)
- [Fed-REACT: Federated Representation Learning for Heterogeneous and Evolving Data](https://mlsanity.com/paper/2509.07198/) (2025)
- [Progressive Power Homotopy for Non-convex Optimization](https://mlsanity.com/paper/2601.15915/) (2026)
- [AdaWeather: Adaptively Mixing Probabilistic Weather Forecasts with Logarithmic Regret](https://mlsanity.com/paper/2606.02663/) (2026)
- [Online Optimization of Difference-of-Convex Compositions with Smooth Mappings](https://mlsanity.com/paper/2607.19553/) (2026)

## Abstract (arXiv)

We consider online forecasting problems for non-convex machine learning models. Forecasting introduces several challenges such as (i) frequent updates are necessary to deal with concept drift issues since the dynamics of the environment change over time, and (ii) the state of the art models are non-convex models. We address these challenges with a novel regret framework. Standard regret measures commonly do not consider both dynamic environment and non-convex models. We introduce a local regret for non-convex models in a dynamic environment. We present an update rule incurring a cost, according to our proposed local regret, which is sublinear in time T. Our update uses time-smoothed gradients. Using a real-world dataset we show that our time-smoothed approach yields several benefits when compared with state-of-the-art competitors: results are more stable against new data; training is more robust to hyperparameter selection; and our approach is more computationally efficient than the alternatives.