Almost Surely $\sqrt{T}$ Regret for Adaptive LQR
The Linear-Quadratic Regulation (LQR) problem with unknown system parameters has been widely studied, but it has remained unclear whether $\tilde{ \mathcal{O}}(\sqrt{T})$ regret, which is the best known dependence on time, can be achieved almost surely. In this paper, we propose an adaptive LQR controller with almost surely $\tilde{ \mathcal{O}}(\sqrt{T})$ regret upper bound. The controller features a circuit-breaking mechanism, which circumvents potential safety breach and guarantees the convergence of the system parameter estimate, but is shown to be triggered only finitely often and hence has negligible effect on the asymptotic performance of the controller. The proposed controller is also validated via simulation on Tennessee Eastman Process~(TEP), a commonly used industrial process example.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
True Self-Avoiding Walk for Accelerating Markov-Chain Monte Carlo Integration
We study true self-avoiding walk (TSAW) as a mechanism for improving empirical integral estimation via Markov chain Monte Carlo (MCMC). We consider finite-state adaptive sampling dynamics associated with an irreducible M…
An algorithm with nearly optimal pseudo-regret for both stochastic and adversarial bandits
We present an algorithm that achieves almost optimal pseudo-regret bounds against adversarial and stochastic bandits. Against adversarial bandits the pseudo-regret is $O(K\sqrt{n \log n})$ and against stochastic bandits …
First-Order Bayesian Regret Analysis of Thompson Sampling
We address online combinatorial optimization when the player has a prior over the adversary's sequence of losses. In this framework, Russo and Van Roy proposed an information-theoretic analysis of Thompson Sampling based…
Combinatorial OptimizationThompson SamplingThompson Sampling for Infinite-Horizon Discounted Decision Processes
We model a Markov decision process, parametrized by an unknown parameter, and study the asymptotic behavior of a sampling-based algorithm, called Thompson sampling. The standard definition of regret is not always suitabl…
Thompson SamplingDifferentially Private Stochastic Linear Bandits: (Almost) for Free
In this paper, we propose differentially private algorithms for the problem of stochastic linear bandits in the central, local and shuffled models. In the central model, we achieve almost the same regret as the optimal n…