Robust-Adaptive Control of Linear Systems: beyond Quadratic Costs

• URL: http://arxiv.org/abs/2002.10816v2
• Date: Wed, 21 Oct 2020 15:15:40 GMT
• Title: Robust-Adaptive Control of Linear Systems: beyond Quadratic Costs
• Authors: Edouard Leurent and Denis Efimov and Odalric-Ambrym Maillard
• Abstract summary: We consider the problem of robust and adaptive model predictive control (MPC) of a linear system. We provide the first end-to-end suboptimal tractity analysis for this setting.
• Score: 14.309243378538012
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the problem of robust and adaptive model predictive control (MPC) of a linear system, with unknown parameters that are learned along the way (adaptive), in a critical setting where failures must be prevented (robust). This problem has been studied from different perspectives by different communities. However, the existing theory deals only with the case of quadratic costs (the LQ problem), which limits applications to stabilisation and tracking tasks only. In order to handle more general (non-convex) costs that naturally arise in many practical problems, we carefully select and bring together several tools from different communities, namely non-asymptotic linear regression, recent results in interval prediction, and tree-based planning. Combining and adapting the theoretical guarantees at each layer is non trivial, and we provide the first end-to-end suboptimality analysis for this setting. Interestingly, our analysis naturally adapts to handle many models and combines with a data-driven robust model selection strategy, which enables to relax the modelling assumptions. Last, we strive to preserve tractability at any stage of the method, that we illustrate on two challenging simulated environments.

Related papers

• Smart Predict-then-Optimize Method with Dependent Data: Risk Bounds and Calibration of Autoregression [7.369846475695131]
  We present an autoregressive SPO method directly targeting the optimization problem at the decision stage. We conduct experiments to demonstrate the effectiveness of the SPO+ surrogate compared to the absolute loss and the least squares loss.
  arXiv  Detail & Related papers  (2024-11-19T17:02:04Z)
• Optimization-Driven Adaptive Experimentation [7.948144726705323]
  Real-world experiments involve batched & delayed feedback, non-stationarity, multiple objectives & constraints, and (often some) personalization. Tailoring adaptive methods to address these challenges on a per-problem basis is infeasible, and static designs remain the de facto standard. We present a mathematical programming formulation that can flexibly incorporate a wide range of objectives, constraints, and statistical procedures.
  arXiv  Detail & Related papers  (2024-08-08T16:29:09Z)
• Learning Deterministic Surrogates for Robust Convex QCQPs [0.0]
  We propose a double implicit layer model for training prediction models with respect to robust decision loss. The first layer solves a deterministic version of the problem, the second layer evaluates the worst case realisation for an uncertainty set. This enables us to learn model parameterisations that lead to robust decisions while only solving a simpler deterministic problem at test time.
  arXiv  Detail & Related papers  (2023-12-19T16:56:13Z)
• Likelihood Ratio Confidence Sets for Sequential Decision Making [51.66638486226482]
  We revisit the likelihood-based inference principle and propose to use likelihood ratios to construct valid confidence sequences. Our method is especially suitable for problems with well-specified likelihoods. We show how to provably choose the best sequence of estimators and shed light on connections to online convex optimization.
  arXiv  Detail & Related papers  (2023-11-08T00:10:21Z)
• A Novel Plug-and-Play Approach for Adversarially Robust Generalization [38.72514422694518]
  We propose a robust framework that employs adversarially robust training to safeguard the ML models against perturbed testing data. Our contributions can be seen from both computational and statistical perspectives.
  arXiv  Detail & Related papers  (2022-08-19T17:02:55Z)
• Time varying regression with hidden linear dynamics [74.9914602730208]
  We revisit a model for time-varying linear regression that assumes the unknown parameters evolve according to a linear dynamical system. Counterintuitively, we show that when the underlying dynamics are stable the parameters of this model can be estimated from data by combining just two ordinary least squares estimates.
  arXiv  Detail & Related papers  (2021-12-29T23:37:06Z)
• A Surrogate Objective Framework for Prediction+Optimization with Soft Constraints [29.962390392493507]
  Decision-focused prediction approaches, such as SPO+ and direct optimization, have been proposed to fill this gap. This paper proposes a novel analytically differentiable surrogate objective framework for real-world linear and semi-definite negative quadratic programming problems.
  arXiv  Detail & Related papers  (2021-11-22T17:09:57Z)
• Modeling the Second Player in Distributionally Robust Optimization [90.25995710696425]
  We argue for the use of neural generative models to characterize the worst-case distribution. This approach poses a number of implementation and optimization challenges. We find that the proposed approach yields models that are more robust than comparable baselines.
  arXiv  Detail & Related papers  (2021-03-18T14:26:26Z)
• Stein Variational Model Predictive Control [130.60527864489168]
  Decision making under uncertainty is critical to real-world, autonomous systems. Model Predictive Control (MPC) methods have demonstrated favorable performance in practice, but remain limited when dealing with complex distributions. We show that this framework leads to successful planning in challenging, non optimal control problems.
  arXiv  Detail & Related papers  (2020-11-15T22:36:59Z)
• The Risks of Invariant Risk Minimization [52.7137956951533]
  Invariant Risk Minimization is an objective based on the idea for learning deep, invariant features of data. We present the first analysis of classification under the IRM objective--as well as these recently proposed alternatives--under a fairly natural and general model. We show that IRM can fail catastrophically unless the test data are sufficiently similar to the training distribution--this is precisely the issue that it was intended to solve.
  arXiv  Detail & Related papers  (2020-10-12T14:54:32Z)
• Adaptive Control and Regret Minimization in Linear Quadratic Gaussian (LQG) Setting [91.43582419264763]
  We propose LqgOpt, a novel reinforcement learning algorithm based on the principle of optimism in the face of uncertainty. LqgOpt efficiently explores the system dynamics, estimates the model parameters up to their confidence interval, and deploys the controller of the most optimistic model.
  arXiv  Detail & Related papers  (2020-03-12T19:56:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.