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arXiv · 2108.08502

A relaxed technical assumption for posterior sampling-based reinforcement learning for control of unknown linear systems

Mukul Gagrani·Sagar Sudhakara·Aditya Mahajan·Ashutosh Nayyar·Yi Ouyang
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Abstract

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 closed loop system. In this technical note, we show that by making a minor modification in the algorithm (in particular, ensuring that an episode does not end too soon), this technical assumption on the induced norm can be replaced by a milder assumption in terms of the spectral radius of the closed loop system. The modified algorithm has the same Bayesian regret of $\tilde{\mathcal{O}}(\sqrt{T})$, where $T$ is the time-horizon and the $\tilde{\mathcal{O}}(\cdot)$ notation hides logarithmic terms in~$T$.

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Mukul Gagrani, Sagar Sudhakara, Aditya Mahajan, Ashutosh Nayyar, Yi Ouyang. 2022-09-20. A relaxed technical assumption for posterior sampling-based reinforcement learning for control of unknown linear systems. https://arxiv.org/abs/2108.08502

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