Reinforcement Learning in Switching Non-Stationary Markov Decision Processes: Algorithms and Convergence Analysis

Reinforcement learning in non-stationary environments is challenging due to abrupt and unpredictable changes in dynamics, often causing traditional algorithms to fail to converge. However, in many real-world cases, non-stationarity has some structure that can be exploited to develop algorithms and facilitate theoretical analysis. We introduce one such structure, Switching Non-Stationary Markov Decision Processes (SNS-MDP), where environments switch over time based on an underlying Markov chain. Under a fixed policy, the value function of an SNS-MDP admits a closed-form solution determined by the Markov chain's statistical properties, and despite the inherent non-stationarity, Temporal Difference (TD) learning methods still converge to the correct value function. Furthermore, policy improvement can be performed, and it is shown that policy iteration converges to the optimal policy. Moreover, since Q-learning converges to the optimal Q-function, it likewise yields the corresponding optimal policy. To illustrate the practical advantages of SNS-MDPs, we present an example in communication networks where channel noise follows a Markovian pattern, demonstrating how this framework can effectively guide decision-making in complex, time-varying contexts.

Closed-Loop Model Identification and MPC-based Navigation of Quadcopters: A Case Study of Parrot Bebop 2

The growing potential of quadcopters in various domains, such as aerial photography, search and rescue, and infrastructure inspection, underscores the need for real-time control under strict safety and operational constraints. This challenge is compounded by the inherent nonlinear dynamics of quadcopters and the on-board computational limitations they face. This paper aims at addressing these challenges. First, this paper presents a comprehensive procedure for deriving a linear yet efficient model to describe the dynamics of quadrotors, thereby reducing complexity without compromising efficiency. Then, this paper develops a steady-state-aware Model Predictive Control (MPC) to effectively navigate quadcopters, while guaranteeing constraint satisfaction at all times. The main advantage of the steady-state-aware MPC is its low computational complexity, which makes it an appropriate choice for systems with limited computing capacity, like quadcopters. This paper considers Parrot Bebop 2 as the running example, and experimentally validates and evaluates the proposed algorithms.