  System identification is a fundamental problem in reinforcement learning,
control theory and signal processing, and the non-asymptotic analysis of the
corresponding sample complexity is challenging and elusive, even for linear
time-varying (LTV) systems. To tackle this challenge, we develop an episodic
block model for the LTV system where the model parameters remain constant
within each block but change from block to block. Based on the observation that
the model parameters across different blocks are related, we treat each
episodic block as a learning task and then run meta-learning over many blocks
for system identification, using two steps, namely offline meta-learning and
online adaptation. We carry out a comprehensive non-asymptotic analysis of the
performance of meta-learning based system identification. To deal with the
technical challenges rooted in the sample correlation and small sample sizes in
each block, we devise a new two-scale martingale small-ball approach for
offline meta-learning, for arbitrary model correlation structure across blocks.
We then quantify the finite time error of online adaptation by leveraging
recent advances in linear stochastic approximation with correlated samples.
