# Augmented Lagrangian Methods for Time-varying Constrained Online Convex Optimization

arXiv: https://arxiv.org/abs/2205.09571 · HTML: https://mlsanity.com/paper/2205.09571/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 41 references that are in the map.
- First posted on arXiv 19 May 2022.

## Builds on (most cited first, 18 of 18)

- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Online Learning: A Comprehensive Survey](https://mlsanity.com/paper/1802.02871/) (2018)
- [Online Learning under Delayed Feedback](https://mlsanity.com/paper/1306.0686/) (2013)
- [Online Convex Optimization with Stochastic Constraints](https://mlsanity.com/paper/1708.03741/) (2017)
- [Stochastic (Approximate) Proximal Point Methods: Convergence, Optimality, and Adaptivity](https://mlsanity.com/paper/1810.05633/) (2018)
- [Online Convex Optimization with Time-Varying Constraints](https://mlsanity.com/paper/1702.04783/) (2017)
- [An Online Convex Optimization Approach to Dynamic Network Resource Allocation](https://mlsanity.com/paper/1701.03974/) (2017)
- [Distributed Online Convex Optimization with Time-Varying Coupled Inequality Constraints](https://mlsanity.com/paper/1903.04277/) (2019)
- [Online Learning with Inexact Proximal Online Gradient Descent Algorithms](https://mlsanity.com/paper/1806.00202/) (2018)
- [Distributed Bandit Online Convex Optimization with Time-Varying Coupled Inequality Constraints](https://mlsanity.com/paper/1912.03719/) (2019)
- [Online Proximal-ADMM For Time-varying Constrained Convex Optimization](https://mlsanity.com/paper/2005.03267/) (2020)
- [Second-order Online Nonconvex Optimization](https://mlsanity.com/paper/2001.10114/) (2020)
- [Prediction-Correction Interior-Point Method for Time-Varying Convex Optimization](https://mlsanity.com/paper/1608.07544/) (2016)
- [Online Primal-Dual Methods with Measurement Feedback for Time-Varying Convex Optimization](https://mlsanity.com/paper/1804.05159/) (2018)
- [Regrets of Proximal Method of Multipliers for Online Non-convex Optimization with Long Term Constraints](https://mlsanity.com/paper/2204.10986/) (2022)
- [Solving Stochastic Optimization with Expectation Constraints Efficiently by a Stochastic Augmented Lagrangian-Type Algorithm](https://mlsanity.com/paper/2106.11577/) (2021)
- [Online Optimization with Feedback Delay and Nonlinear Switching Cost](https://mlsanity.com/paper/2111.00095/) (2021)
- [Cluster-based Distributed Augmented Lagrangian Algorithm for a Class of Constrained Convex Optimization Problems](https://mlsanity.com/paper/1908.06634/) (2019)

## Abstract (arXiv)

In this paper, we consider online convex optimization (OCO) with time-varying loss and constraint functions. Specifically, the decision maker chooses sequential decisions based only on past information, meantime the loss and constraint functions are revealed over time. We first develop a class of model-based augmented Lagrangian methods (MALM) for time-varying functional constrained OCO (without feedback delay). Under standard assumptions, we establish sublinear regret and sublinear constraint violation of MALM. Furthermore, we extend MALM to deal with time-varying functional constrained OCO with delayed feedback, in which the feedback information of loss and constraint functions is revealed to decision maker with delays. Without additional assumptions, we also establish sublinear regret and sublinear constraint violation for the delayed version of MALM. Finally, numerical results for several examples of constrained OCO including online network resource allocation, online logistic regression and online quadratically constrained quadratical program are presented to demonstrate the efficiency of the proposed algorithms.