Predictive Control and Regret Analysis of Non-Stationary MDP with Look-ahead Information
This work addresses the challenge of optimizing actions in time-varying systems like energy management, offering a method to reduce regret with available predictions, though it is incremental as it builds on existing MDP frameworks.
The paper tackles policy design in non-stationary Markov Decision Processes by leveraging look-ahead predictions, such as forecasts in energy systems, to propose an algorithm that achieves low regret. The theoretical analysis shows that regret decreases exponentially with longer look-ahead windows and remains stable even with sub-exponentially growing prediction errors, validated through simulations.
Policy design in non-stationary Markov Decision Processes (MDPs) is inherently challenging due to the complexities introduced by time-varying system transition and reward, which make it difficult for learners to determine the optimal actions for maximizing cumulative future rewards. Fortunately, in many practical applications, such as energy systems, look-ahead predictions are available, including forecasts for renewable energy generation and demand. In this paper, we leverage these look-ahead predictions and propose an algorithm designed to achieve low regret in non-stationary MDPs by incorporating such predictions. Our theoretical analysis demonstrates that, under certain assumptions, the regret decreases exponentially as the look-ahead window expands. When the system prediction is subject to error, the regret does not explode even if the prediction error grows sub-exponentially as a function of the prediction horizon. We validate our approach through simulations, confirming the efficacy of our algorithm in non-stationary environments.