# Robustness and Consistency in Linear Quadratic Control with Untrusted Predictions

arXiv: https://arxiv.org/abs/2106.09659 · HTML: https://mlsanity.com/paper/2106.09659/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jun 2021.

## Built on by (most cited first, 14 of 14)

- [Beyond Black-Box Advice: Learning-Augmented Algorithms for MDPs with Q-Value Predictions](https://mlsanity.com/paper/2307.10524/) (2023)
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- [Equipping Black-Box Policies with Model-Based Advice for Stable Nonlinear Control](https://mlsanity.com/paper/2206.01341/) (2022)
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- [Adaptive Online Non-stochastic Control](https://mlsanity.com/paper/2310.02261/) (2023)
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- [Optimistic Online Non-stochastic Control via FTRL](https://mlsanity.com/paper/2404.03309/) (2024)
- [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)
- [Anytime-Competitive Reinforcement Learning with Policy Prior](https://mlsanity.com/paper/2311.01568/) (2023)
- [Out-of-Distribution-Aware Electric Vehicle Charging](https://mlsanity.com/paper/2311.05941/) (2023)
- [Safe Exploitative Play with Untrusted Type Beliefs](https://mlsanity.com/paper/2411.07679/) (2024)
- [Constrained Online Convex Optimization with Memory and Predictions](https://mlsanity.com/paper/2603.21375/) (2026)

## Abstract (arXiv)

We study the problem of learning-augmented predictive linear quadratic control. Our goal is to design a controller that balances textit"consistency", which measures the competitive ratio when predictions are accurate, and textit"robustness", which bounds the competitive ratio when predictions are inaccurate. We propose a novel λ-confident policy and provide a competitive ratio upper bound that depends on a trust parameter λ∈ [0,1] set based on the confidence in the predictions and some prediction error varepsilon. Motivated by online learning methods, we design a self-tuning policy that adaptively learns the trust parameter λ with a competitive ratio that depends on varepsilon and the variation of system perturbations and predictions. We show that its competitive ratio is bounded from above by  1+O(varepsilon)/(Theta(1)+Theta(varepsilon))+O(μ_mathsfVar) where μ_mathsfVar measures the variation of perturbations and predictions. It implies that when the variations of perturbations and predictions are small, by automatically adjusting the trust parameter online, the self-tuning scheme ensures a competitive ratio that does not scale up with the prediction error varepsilon.