Restarted Bayesian Online Change-point Detection for Non-Stationary Markov Decision Processes
This addresses the problem of adapting to abrupt changes in environments for reinforcement learning practitioners, though it is incremental as it builds on existing UCRL2 and change-point detection methods.
The paper tackles learning in non-stationary reinforcement learning environments by proposing R-BOCPD-UCRL2, an algorithm that achieves a regret bound of O(D O sqrt(A T K_T log(T/δ) + K_T log(K_T/δ)/min_ℓ KL(θ^(ℓ+1)||θ^(ℓ)))) and outperforms state-of-the-art methods in synthetic experiments.
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 $O\left(D O \sqrt{A T K_T \log\left (\frac{T}δ \right) + \frac{K_T \log \frac{K_T}δ}{\min\limits_\ell \: \mathbf{KL}\left( {\mathbfθ^{(\ell+1)}}\mid\mid{\mathbfθ^{(\ell)}}\right)}}\right)$, 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 $\mathbfθ^{(\ell)}$ 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.