# Adaptive Composite Online Optimization: Predictions in Static and Dynamic Environments

arXiv: https://arxiv.org/abs/2205.00446 · HTML: https://mlsanity.com/paper/2205.00446/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 54 references that are in the map.
- First posted on arXiv 1 May 2022.

## Builds on (most cited first, 28 of 28)

- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [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)
- [Online Optimization : Competing with Dynamic Comparators](https://mlsanity.com/paper/1501.06225/) (2015)
- [Online Control with Adversarial Disturbances](https://mlsanity.com/paper/1902.08721/) (2019)
- [The Nonstochastic Control Problem](https://mlsanity.com/paper/1911.12178/) (2019)
- [Dynamical Models and Tracking Regret in Online Convex Programming](https://mlsanity.com/paper/1301.1254/) (2013)
- [Online Optimal Control with Linear Dynamics and Predictions: Algorithms and Regret Analysis](https://mlsanity.com/paper/1906.11378/) (2019)
- [Logarithmic Regret for Online Control](https://mlsanity.com/paper/1909.05062/) (2019)
- [Online Learning with Imperfect Hints](https://mlsanity.com/paper/2002.04726/) (2020)
- [Distributed Online Optimization in Dynamic Environments Using Mirror Descent](https://mlsanity.com/paper/1609.02845/) (2016)
- [The Power of Predictions in Online Control](https://mlsanity.com/paper/2006.07569/) (2020)
- [An Online Learning Approach to Model Predictive Control](https://mlsanity.com/paper/1902.08967/) (2019)
- [Online Optimization with Predictions and Switching Costs: Fast Algorithms and the Fundamental Limit](https://mlsanity.com/paper/1801.07780/) (2018)
- [Temporal Variability in Implicit Online Learning](https://mlsanity.com/paper/2006.07503/) (2020)
- [Online Convex Optimization Using Predictions](https://mlsanity.com/paper/1504.06681/) (2015)
- [Robustness and Consistency in Linear Quadratic Control with Untrusted Predictions](https://mlsanity.com/paper/2106.09659/) (2021)
- [A closer look at temporal variability in dynamic online learning](https://mlsanity.com/paper/2102.07666/) (2021)
- [Online Optimization with Predictions and Non-convex Losses](https://mlsanity.com/paper/1911.03827/) (2019)
- [Leveraging Predictions in Smoothed Online Convex Optimization via Gradient-based Algorithms](https://mlsanity.com/paper/2011.12539/) (2020)
- [Exploiting Problem Structure in Optimization under Uncertainty via Online Convex Optimization](https://mlsanity.com/paper/1709.02490/) (2017)
- [Maximum Hands-Off Control: A Paradigm of Control Effort Minimization](https://mlsanity.com/paper/1408.3025/) (2014)
- [Fully Implicit Online Learning](https://mlsanity.com/paper/1809.09350/) (2018)
- [Predictive Online Convex Optimization](https://mlsanity.com/paper/1905.06263/) (2019)
- [Sparse Packetized Predictive Control for Networked Control over Erasure Channels](https://mlsanity.com/paper/1307.8242/) (2013)
- [Prediction in Online Convex Optimization for Parametrizable Objective Functions](https://mlsanity.com/paper/1901.11500/) (2019)

## Built on by (most cited first, 6 of 6)

- [An Optimistic Algorithm for Online Convex Optimization with Adversarial Constraints](https://mlsanity.com/paper/2412.08060/) (2024)
- [Triplets Better Than Pairs: Towards Stable and Effective Self-Play Fine-Tuning for LLMs](https://mlsanity.com/paper/2601.08198/) (2026)
- [SPACE: Noise Contrastive Estimation Stabilizes Self-Play Fine-Tuning for Large Language Models](https://mlsanity.com/paper/2512.07175/) (2025)
- [On the Dynamic Regret of Following the Regularized Leader: Optimism with History Pruning](https://mlsanity.com/paper/2505.22899/) (2025)
- [A Modular Algorithm for Non-Stationary Online Convex-Concave Optimization](https://mlsanity.com/paper/2509.07901/) (2025)
- [Optimistic Learning for Communication Networks](https://mlsanity.com/paper/2504.03499/) (2025)

## Abstract (arXiv)

In the past few years, Online Convex Optimization (OCO) has received notable attention in the control literature thanks to its flexible real-time nature and powerful performance guarantees. In this paper, we propose new step-size rules and OCO algorithms that simultaneously exploit gradient predictions, function predictions and dynamics, features particularly pertinent to control applications. The proposed algorithms enjoy static and dynamic regret bounds in terms of the dynamics of the reference action sequence, gradient prediction error, and function prediction error, which are generalizations of known regularity measures from the literature. We present results for both convex and strongly convex costs. We validate the performance of the proposed algorithms in a trajectory tracking case study, as well as portfolio optimization using real-world datasets.