Restarted Bayesian Online Change-point Detection for Non-Stationary Markov Decision Processes

• URL: http://arxiv.org/abs/2304.00232v1
• Date: Sat, 1 Apr 2023 05:26:41 GMT
• Title: Restarted Bayesian Online Change-point Detection for Non-Stationary Markov Decision Processes
• Authors: Reda Alami, Mohammed Mahfoud, Eric Moulines
• Abstract summary: We introduce a variant of the Restarted Bayesian Online Change-Point Detection algorithm (R-BOCPD) We propose an improved version of the UCRL2 algorithm for MDPs with state transition kernel sampled from a multinomial distribution. We show that R-BOCPD-UCRL2 enjoys a favorable regret bound of $Oleft(D O sqrtA T K_T logleft (fracTdelta right) + fracK_Tdeltaminlimits_ell.
• Score: 12.229154524476405
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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