  We consider the problem of learning in a non-stationary reinforcement
learning (RL) environment, where the setting can be fully described by a
piecewise stationary discrete-time Markov decision process (MDP). We introduce
a variant of the Restarted Bayesian Online Change-Point Detection algorithm
(R-BOCPD) that operates on input streams originating from the more general
multinomial distribution and provides near-optimal theoretical guarantees in
terms of false-alarm rate and detection delay. Based on this, we propose an
improved version of the UCRL2 algorithm for MDPs with state transition kernel
sampled from a multinomial distribution, which we call R-BOCPD-UCRL2. We
perform a finite-time performance analysis and show that R-BOCPD-UCRL2 enjoys a
favorable regret bound of $O\left(D O \sqrt{A T K_T \log\left (\frac{T}{\delta}
\right) + \frac{K_T \log \frac{K_T}{\delta}}{\min\limits_\ell \:
\mathbf{KL}\left(
{\mathbf{\theta}^{(\ell+1)}}\mid\mid{\mathbf{\theta}^{(\ell)}}\right)}}\right)$,
where $D$ is the largest MDP diameter from the set of MDPs defining the
piecewise stationary MDP setting, $O$ is the finite number of states (constant
over all changes), $A$ is the finite number of actions (constant over all
changes), $K_T$ is the number of change points up to horizon $T$, and
$\mathbf{\theta}^{(\ell)}$ is the transition kernel during the interval
$[c_\ell, c_{\ell+1})$, which we assume to be multinomially distributed over
the set of states $\mathbb{O}$. Interestingly, the performance bound does not
directly scale with the variation in MDP state transition distributions and
rewards, ie. can also model abrupt changes. In practice, R-BOCPD-UCRL2
outperforms the state-of-the-art in a variety of scenarios in synthetic
environments. We provide a detailed experimental setup along with a code
repository (upon publication) that can be used to easily reproduce our
experiments.
