# Smoothed Online Optimization for Regression and Control

arXiv: https://arxiv.org/abs/1810.10132 · HTML: https://mlsanity.com/paper/1810.10132/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2018.

## Built on by (most cited first, 26 of 26)

- [Non-stationary Online Learning with Memory and Non-stochastic Control](https://mlsanity.com/paper/2102.03758/) (2021)
- [Revisiting Smoothed Online Learning](https://mlsanity.com/paper/2102.06933/) (2021)
- [Optimal Dynamic Regret in Proper Online Learning with Strongly Convex Losses and Beyond](https://mlsanity.com/paper/2201.08905/) (2022)
- [Chasing Convex Bodies and Functions with Black-Box Advice](https://mlsanity.com/paper/2206.11780/) (2022)
- [Online Label Shift: Optimal Dynamic Regret meets Practical Algorithms](https://mlsanity.com/paper/2305.19570/) (2023)
- [Regret-optimal Estimation and Control](https://mlsanity.com/paper/2106.12097/) (2021)
- [Smoothed Online Optimization with Unreliable Predictions](https://mlsanity.com/paper/2202.03519/) (2022)
- [Competitive Control](https://mlsanity.com/paper/2107.13657/) (2021)
- [Second Order Path Variationals in Non-Stationary Online Learning](https://mlsanity.com/paper/2205.01921/) (2022)
- [Movement Penalized Bayesian Optimization with Application to Wind Energy Systems](https://mlsanity.com/paper/2210.08087/) (2022)
- [Online Convex Optimization with Continuous Switching Constraint](https://mlsanity.com/paper/2103.11370/) (2021)
- [Smoothed Online Convex Optimization Based on Discounted-Normal-Predictor](https://mlsanity.com/paper/2205.00741/) (2022)
- [Optimal Dynamic Regret in LQR Control](https://mlsanity.com/paper/2206.09257/) (2022)
- [Best of Both Worlds in Online Control: Competitive Ratio and Policy Regret](https://mlsanity.com/paper/2211.11219/) (2022)
- [Online Optimization with Feedback Delay and Nonlinear Switching Cost](https://mlsanity.com/paper/2111.00095/) (2021)
- [Efficient Online Linear Control with Stochastic Convex Costs and Unknown Dynamics](https://mlsanity.com/paper/2203.01170/) (2022)
- [Near-Optimal Adversarial Reinforcement Learning with Switching Costs](https://mlsanity.com/paper/2302.04374/) (2023)
- [Online Learning for Predictive Control with Provable Regret Guarantees](https://mlsanity.com/paper/2111.15041/) (2021)
- [Online Convex Optimization with Switching Cost and Delayed Gradients](https://mlsanity.com/paper/2310.11880/) (2023)
- [Optimal Competitive-Ratio Control](https://mlsanity.com/paper/2206.01782/) (2022)
- [Best of Both Worlds Guarantees for Smoothed Online Quadratic Optimization](https://mlsanity.com/paper/2311.00181/) (2023)
- [Parameter-free Dynamic Regret: Time-varying Movement Costs, Delayed Feedback, and Memory](https://mlsanity.com/paper/2602.06902/) (2026)
- [Online Convex Optimization with Switching Cost with Only One Single Gradient Evaluation](https://mlsanity.com/paper/2507.04133/) (2025)
- [Online estimation and control with optimal pathlength regret](https://mlsanity.com/paper/2110.12544/) (2021)
- [Capacity Provisioning Motivated Online Non-Convex Optimization Problem with Memory and Switching Cost](https://mlsanity.com/paper/2403.17480/) (2024)
- [SCaLE: Switching Cost aware Learning and Exploration](https://mlsanity.com/paper/2601.09042/) (2026)

## Abstract (arXiv)

We consider Online Convex Optimization (OCO) in the setting where the costs are m-strongly convex and the online learner pays a switching cost for changing decisions between rounds. We show that the recently proposed Online Balanced Descent (OBD) algorithm is constant competitive in this setting, with competitive ratio 3 + O(1/m), irrespective of the ambient dimension. Additionally, we show that when the sequence of cost functions is ε-smooth, OBD has near-optimal dynamic regret and maintains strong per-round accuracy. We demonstrate the generality of our approach by showing that the OBD framework can be used to construct competitive algorithms for a variety of online problems across learning and control, including online variants of ridge regression, logistic regression, maximum likelihood estimation, and LQR control.