Mohammed El Mahfoud

Reda Alami, Mohammed Mahfoud, Eric Moulines

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.

Reda Alami, Mohammed Mahfoud, Mastane Achab

In a typical stochastic multi-armed bandit problem, the objective is often to maximize the expected sum of rewards over some time horizon $T$. While the choice of a strategy that accomplishes that is optimal with no additional information, it is no longer the case when provided additional environment-specific knowledge. In particular, in areas of high volatility like healthcare or finance, a naive reward maximization approach often does not accurately capture the complexity of the learning problem and results in unreliable solutions. To tackle problems of this nature, we propose a framework of adaptive risk-aware strategies that operate in non-stationary environments. Our framework incorporates various risk measures prevalent in the literature to map multiple families of multi-armed bandit algorithms into a risk-sensitive setting. In addition, we equip the resulting algorithms with the Restarted Bayesian Online Change-Point Detection (R-BOCPD) algorithm and impose a (tunable) forced exploration strategy to detect local (per-arm) switches. We provide finite-time theoretical guarantees and an asymptotic regret bound of order $\tilde O(\sqrt{K_T T})$ up to time horizon $T$ with $K_T$ the total number of change-points. In practice, our framework compares favorably to the state-of-the-art in both synthetic and real-world environments and manages to perform efficiently with respect to both risk-sensitivity and non-stationarity.