Predictive Control and Regret Analysis of Non-Stationary MDP with Look-ahead Information

2024-09-13

Trans. Mach. Learn. Res.

AI Summary

Designing effective policies for non-stationary Markov decision processes (MDPs), where time-varying transition and reward functions undermine conventional reinforcement learning assumptions, remains challenging. Method: This paper proposes a low-regret online control framework that integrates forward-looking predictions—e.g., renewable generation and load forecasts—within a robust model predictive control (MPC) architecture. It introduces an online policy update mechanism resilient to model uncertainty and explicitly accounts for prediction inaccuracies. Contribution/Results: We establish, for the first time, an exponential decay relationship between lookahead horizon length and dynamic regret. Theoretically, we prove that dynamic regret remains strictly bounded under sub-exponential prediction error growth. Empirical evaluation in representative non-stationary environments demonstrates substantial performance gains over state-of-the-art baselines, validating both theoretical guarantees and practical efficacy.

Technology Category

• Machine Learning: Online Learning & Bandits
• Planning, Routing, and Scheduling: Planning with Markov Models (MDPs, POMDPs)
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

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.

Problem

• Designing policies for non-stationary MDPs with time-varying transitions and rewards
• Achieving low regret by incorporating look-ahead predictions in algorithm design
• Analyzing regret behavior under prediction errors and expanding forecast horizons

Innovation

• Uses look-ahead predictions for non-stationary MDP control
• Achieves low regret with expanding prediction windows
• Maintains regret stability under sub-exponential prediction errors