# Leveraging Predictions in Smoothed Online Convex Optimization via Gradient-based Algorithms

arXiv: https://arxiv.org/abs/2011.12539 · HTML: https://mlsanity.com/paper/2011.12539/

## Key facts

- Cited by 12 papers in the map (data through 7 Oct 2026).
- First posted on arXiv 25 Nov 2020.

## Built on by (most cited first, 12 of 12)

- [Revisiting Smoothed Online Learning](https://mlsanity.com/paper/2102.06933/) (2021)
- [Smoothed Online Optimization with Unreliable Predictions](https://mlsanity.com/paper/2202.03519/) (2022)
- [Expert-Calibrated Learning for Online Optimization with Switching Costs](https://mlsanity.com/paper/2204.08572/) (2022)
- [Adaptive Composite Online Optimization: Predictions in Static and Dynamic Environments](https://mlsanity.com/paper/2205.00446/) (2022)
- [Smoothed Online Convex Optimization Based on Discounted-Normal-Predictor](https://mlsanity.com/paper/2205.00741/) (2022)
- [Robustified Learning for Online Optimization with Memory Costs](https://mlsanity.com/paper/2305.00677/) (2023)
- [Reinforcement Learning with Imperfect Transition Predictions: A Bellman-Jensen Approach](https://mlsanity.com/paper/2510.18687/) (2025)
- [Partially Lazy Gradient Descent for Smoothed Online Learning](https://mlsanity.com/paper/2601.15984/) (2026)
- [A Survey on Distributed Online Optimization and Game](https://mlsanity.com/paper/2205.00473/) (2022)
- [Smoothed Online Combinatorial Optimization Using Imperfect Predictions](https://mlsanity.com/paper/2204.10979/) (2022)
- [Smoothed Online Optimization for Target Tracking: Robust and Learning-Augmented Algorithms](https://mlsanity.com/paper/2509.05930/) (2025)
- [Fairness-Regularized Online Optimization with Switching Costs](https://mlsanity.com/paper/2512.11131/) (2025)

## Abstract (arXiv)

We consider online convex optimization with time-varying stage costs and additional switching costs. Since the switching costs introduce coupling across all stages, multi-step-ahead (long-term) predictions are incorporated to improve the online performance. However, longer-term predictions tend to suffer from lower quality. Thus, a critical question is: how to reduce the impact of long-term prediction errors on the online performance? To address this question, we introduce a gradient-based online algorithm, Receding Horizon Inexact Gradient (RHIG), and analyze its performance by dynamic regrets in terms of the temporal variation of the environment and the prediction errors. RHIG only considers at most W-step-ahead predictions to avoid being misled by worse predictions in the longer term. The optimal choice of W suggested by our regret bounds depends on the tradeoff between the variation of the environment and the prediction accuracy. Additionally, we apply RHIG to a well-established stochastic prediction error model and provide expected regret and concentration bounds under correlated prediction errors. Lastly, we numerically test the performance of RHIG on quadrotor tracking problems.