# Robust Learning for Smoothed Online Convex Optimization with Feedback Delay

arXiv: https://arxiv.org/abs/2310.20098 · HTML: https://mlsanity.com/paper/2310.20098/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 56 references that are in the map.
- First posted on arXiv 31 Oct 2023.

## Builds on (most cited first, 30 of 34)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [Projection-Based Constrained Policy Optimization](https://mlsanity.com/paper/2010.03152/) (2020)
- [Competitive caching with machine learned advice](https://mlsanity.com/paper/1802.05399/) (2018)
- [Do Differentiable Simulators Give Better Policy Gradients?](https://mlsanity.com/paper/2202.00817/) (2022)
- [Neural Lander: Stable Drone Landing Control using Learned Dynamics](https://mlsanity.com/paper/1811.08027/) (2018)
- [Conservative Offline Distributional Reinforcement Learning](https://mlsanity.com/paper/2107.06106/) (2021)
- [Online metric algorithms with untrusted predictions](https://mlsanity.com/paper/2003.02144/) (2020)
- [Optimal Robustness-Consistency Trade-offs for Learning-Augmented Online Algorithms](https://mlsanity.com/paper/2010.11443/) (2020)
- [Online Optimal Control with Linear Dynamics and Predictions: Algorithms and Regret Analysis](https://mlsanity.com/paper/1906.11378/) (2019)
- [Smoothed Online Convex Optimization in High Dimensions via Online Balanced Descent](https://mlsanity.com/paper/1803.10366/) (2018)
- [Beyond Online Balanced Descent: An Optimal Algorithm for Smoothed Online Optimization](https://mlsanity.com/paper/1905.12776/) (2019)
- [Revisiting Smoothed Online Learning](https://mlsanity.com/paper/2102.06933/) (2021)
- [Online Optimization with Predictions and Switching Costs: Fast Algorithms and the Fundamental Limit](https://mlsanity.com/paper/1801.07780/) (2018)
- [Memory Bounds for the Experts Problem](https://mlsanity.com/paper/2204.09837/) (2022)
- [Chasing Convex Bodies and Functions with Black-Box Advice](https://mlsanity.com/paper/2206.11780/) (2022)
- [Robustness and Consistency in Linear Quadratic Control with Untrusted Predictions](https://mlsanity.com/paper/2106.09659/) (2021)
- [Online Optimization with Predictions and Non-convex Losses](https://mlsanity.com/paper/1911.03827/) (2019)
- [Robust Learning-Augmented Caching: An Experimental Study](https://mlsanity.com/paper/2106.14693/) (2021)
- [A Regression Approach to Learning-Augmented Online Algorithms](https://mlsanity.com/paper/2205.08717/) (2022)
- [Online Learning with Local Permutations and Delayed Feedback](https://mlsanity.com/paper/1703.04274/) (2017)
- [Deep Policies for Online Bipartite Matching: A Reinforcement Learning Approach](https://mlsanity.com/paper/2109.10380/) (2021)
- [Smoothed Online Optimization with Unreliable Predictions](https://mlsanity.com/paper/2202.03519/) (2022)
- [A Reduction-Based Framework for Conservative Bandits and Reinforcement Learning](https://mlsanity.com/paper/2106.11692/) (2021)
- [Adversarial Deep Learning for Online Resource Allocation](https://mlsanity.com/paper/2111.10285/) (2021)
- [Learning Robust Algorithms for Online Allocation Problems Using Adversarial Training](https://mlsanity.com/paper/2010.08418/) (2020)
- [Expert-Calibrated Learning for Online Optimization with Switching Costs](https://mlsanity.com/paper/2204.08572/) (2022)
- [Equipping Black-Box Policies with Model-Based Advice for Stable Nonlinear Control](https://mlsanity.com/paper/2206.01341/) (2022)

## Built on by (most cited first, 3 of 3)

- [Online Budgeted Matching with General Bids](https://mlsanity.com/paper/2411.04204/) (2024)
- [Safe Exploitative Play with Untrusted Type Beliefs](https://mlsanity.com/paper/2411.07679/) (2024)
- [Fairness-Regularized Online Optimization with Switching Costs](https://mlsanity.com/paper/2512.11131/) (2025)

## Abstract (arXiv)

We study a challenging form of Smoothed Online Convex Optimization, a.k.a. SOCO, including multi-step nonlinear switching costs and feedback delay. We propose a novel machine learning (ML) augmented online algorithm, Robustness-Constrained Learning (RCL), which combines untrusted ML predictions with a trusted expert online algorithm via constrained projection to robustify the ML prediction. Specifically,we prove that RCL is able to guarantee(1+λ)-competitiveness against any given expert for anyλ>0, while also explicitly training the ML model in a robustification-aware manner to improve the average-case performance. Importantly,RCL is the first ML-augmented algorithm with a provable robustness guarantee in the case of multi-step switching cost and feedback delay.We demonstrate the improvement of RCL in both robustness and average performance using battery management for electrifying transportationas a case study.