Information Aggregation for Constrained Online Control

Li, Tongxin; Chen, Yue; Sun, Bo; Wierman, Adam; Low, Steven H.

doi:10.1145/3460085

Cited by 7 publications

(3 citation statements)

References 33 publications

(58 reference statements)

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“…which in turns implies dist( Kt , K * t ) ≤ αdist( Kt−1 , K * t ) based on Eq (26). Proof: When t = 0, we have dist( K0 , K * 1 ) = dist(K 1 , K * 1 ) ≤ α (L H L 2 /m 3 ) .…”

Section: Appendixmentioning

confidence: 85%

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On Online Optimization: Dynamic Regret Analysis of Strongly Convex and Smooth Problems

Chang

Shahrampour

2021

AAAI

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The regret bound of dynamic online learning algorithms is often expressed in terms of the variation in the function sequence (V_T) and/or the path-length of the minimizer sequence after T rounds. For strongly convex and smooth functions, Zhang et al. (2017) establish the squared path-length of the minimizer sequence (C*_{2,T}) as a lower bound on regret. They also show that online gradient descent (OGD) achieves this lower bound using multiple gradient queries per round. In this paper, we focus on unconstrained online optimization. We first show that a preconditioned variant of OGD achieves O(min{C*_T,C*_{2,T}}) with one gradient query per round (C*_T refers to the normal path-length). We then propose online optimistic Newton (OON) method for the case when the first and second order information of the function sequence is predictable. The regret bound of OON is captured via the quartic path-length of the minimizer sequence (C*_{4,T}), which can be much smaller than C*_{2,T}. We finally show that by using multiple gradients for OGD, we can achieve an upper bound of O(min{C*_{2,T},V_T}) on regret.

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“…which in turns implies dist( Kt , K * t ) ≤ αdist( Kt−1 , K * t ) based on Eq (26). Proof: When t = 0, we have dist( K0 , K * 1 ) = dist(K 1 , K * 1 ) ≤ α (L H L 2 /m 3 ) .…”

Section: Appendixmentioning

confidence: 85%

“…A different setup with linear time-varying systems was studied and the corresponding dynamic bound was proposed in [24]. Motivated by the safety concern, the setup where constraints are imposed on states and controls was also studied in the literature [25], [26].…”

Section: Related Workmentioning

confidence: 99%

On Online Optimization: Dynamic Regret Analysis of Strongly Convex and Smooth Problems

Chang

Shahrampour

2021

AAAI

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“…The competitive analysis of the consistent and robust control scheme in this work makes use of this fact in the analysis of the more challenging case of untrusted predictions. Other related regret and competitive ratio results for MPC include [18,24,30].…”

Section: Introductionmentioning

confidence: 99%

Robustness and Consistency in Linear Quadratic Control with Untrusted Predictions

Yang

et al. 2022

SIGMETRICS Perform. Eval. Rev.

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We study the problem of learning-augmented predictive linear quadratic control. Our goal is to design a controller that balances "consistency'', which measures the competitive ratio when predictions are accurate, and "robustness'', which bounds the competitive ratio when predictions are inaccurate. We propose a novel λ-confident controller and prove that it maintains a competitive ratio upper bound of 1 + min {O(λ2ε)+ O(1-λ)2,O(1)+O(λ2)} where λ∈ [0,1] is a trust parameter set based on the confidence in the predictions, and ε is the prediction error. Further, 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 ε and the variation of system perturbations and predictions. We show that its competitive ratio is bounded from above by 1+O(ε) /(Θ)(1)+Θ(ε))+O(μVar) where μVar measures the variation of perturbations and predictions. It implies that by automatically adjusting the trust parameter online, the self-tuning scheme ensures a competitive ratio that does not scale up with the prediction error ε.

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