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We propose a Thompson sampling-based learning algorithm for the Linear Quadratic (LQ) control problem with unknown system parameters. The algorithm is called Thompson sampling with dynamic episodes (TSDE) where two stopping criteria determine the lengths of the dynamic episodes in Thompson sampling. The first stopping criterion controls the growth rate of episode length. The second stopping criterion is triggered when the determinant of the sample covariance matrix is less than half of the previous value. We show under some conditions on the prior distribution that the expected (Bayesian) regret of TSDE accumulated up to time T is bounded by O(sqrt{T}). Here O(.) hides constants and logarithmic factors. This is the first O(sqrt{T} ) bound on expected regret of learning in LQ control. By introducing a reinitialization schedule, we also show that the algorithm is robust to time-varying drift in model parameters. Numerical simulations are provided to illustrate the performance of TSDE.
We present a sample-based Learning Model Predictive Controller (LMPC) for constrained uncertain linear systems subject to bounded additive disturbances. The proposed controller builds on earlier work on LMPC for deterministic systems. First, we intro
We revisit the Thompson sampling algorithm to control an unknown linear quadratic (LQ) system recently proposed by Ouyang et al (arXiv:1709.04047). The regret bound of the algorithm was derived under a technical assumption on the induced norm of the
We consider the problem of designing control laws for stochastic jump linear systems where the disturbances are drawn randomly from a finite sample space according to an unknown distribution, which is estimated from a finite sample of i.i.d. observat
Robots performing manipulation tasks must operate under uncertainty about both their pose and the dynamics of the system. In order to remain robust to modeling error and shifts in payload dynamics, agents must simultaneously perform estimation and co
Thompson Sampling is one of the oldest heuristics for multi-armed bandit problems. It is a randomized algorithm based on Bayesian ideas, and has recently generated significant interest after several studies demonstrated it to have better empirical pe