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Computer Science > Systems and Control

Title: Robustness to Incorrect System Models and Application to Data-Driven Learning in Stochastic Control

Abstract: We study the continuity properties of stochastic control problems with respect to transition kernels and applications of these to the robustness of optimal control policies applied to systems with incomplete or incorrect probabilistic models. We study both fully observed and partially observed Markov Decision Processes. We show that for infinite horizon discounted cost setup, continuity and robustness cannot be established under weak convergence and set-wise convergence of transition kernels in general, but that the optimal cost is continuous in the transition kernels under the convergence in total variation under mild conditions. By imposing further assumptions on the measurement models and on the kernel itself, we also show that the optimal cost can be made continuous under weak convergence of transition kernels. Using these continuity results we find bounds on the mismatch error that occurs due to the application of a control policy which is designed for an incorrectly estimated system model in terms of a distance measure between true model and the incorrect one. In particular, compared to the existing literature, we obtain strictly refined and strong robustness results that are applicable even under the errors that can be investigated under weak convergence criteria, in addition to total variation criteria. These lead to practically important results on empirical learning in (data-driven) stochastic control since often, in engineering applications, system models are learned through training data.
Subjects: Systems and Control (cs.SY)
Cite as: arXiv:1803.06046 [cs.SY]
  (or arXiv:1803.06046v1 [cs.SY] for this version)

Submission history

From: Ali Devran Kara [view email]
[v1] Fri, 16 Mar 2018 01:04:42 GMT (51kb)