Fairness, Efficiency and Privacy in Energy Resource Allocation: Incentive Design and Machine Learning for Distributed Agents

Abstract

The rapid proliferation of distributed energy resources (DERs) has fundamentally reshaped the energy landscape. While these technologies present opportunities for decentralized energy management, they have also introduced diverse and heterogeneous user groups, surpassing the capabilities of traditional efficiency-oriented allocation schemes. This growing complexity often leads to fairness concerns, with disproportionate payments or allocations disadvantaging certain user groups due to their utility formats, budgets or group sizes. Balancing fairness, efficiency, and protecting user privacy in energy resource allocation is a pressing challenge, essential for developing equitable, resilient, and stable energy systems, particularly in the context of decentralized agents and competitive energy markets. This dissertation develops principled approaches for coordinating distributed agents in energy systems through the design of decision-making frameworks leveraging optimization and learning. Drawing on methods from game theory, machine learning and dynamical systems, this work explores how fairness, efficiency, and privacy objectives can be achieved while ensuring system stability. The contributions of this dissertation are organized across three key areas: 1. Privacy-Preserving Adaptive Pricing Mechanisms: A two-time-scale incentive mechanism, that alternatively updates between the users and a system operator, is proposed to align user behavior with system-level social objectives that induce socially optimal energy usage without requiring private user information. The iterative pricing updates are proven to converge to the social welfare solution under mild assumptions, accommodating user behaviors driven by machine learning-based load control algorithms. 2. Fairness in Energy Systems through Aggregator Market Structures: This thesis formalizes the problem of fair energy resource allocation by introducing an aggregator-based framework that balances fairness and efficiency through principled trade-offs. By jointly optimizing total resources and individual allocations, this work develops schemes that achieve Pareto-optimal outcomes for diverse user groups. Extending to a multi-aggregator setting, a game-theoretical model is proposed to analyze strategic interactions among aggregators in energy markets, proving the existence of a Nash equilibrium. These contributions demonstrate how aggregator structures stabilize market outcomes, ensure equitable resource distribution, and optimize user surplus, providing a comprehensive foundation for fairness in energy systems. 3. Safe Learning-Based Control for Distributed Systems: This thesis develops a decentralized reinforcement learning framework for designing neural network-based controllers that ensure exponential stability and safety in distributed systems. By imposing Lipschitz constraints on control policies and engineering their structure to satisfy these constraints by design, the framework guarantees reliable performance under dynamic system conditions. This approach enables decentralized decision-making without requiring real-time centralized coordination, making it scalable and robust for modern energy systems. By integrating fairness, efficiency, and privacy into the design of energy allocation mechanisms, this dissertation advances the theoretical and practical understanding of decentralized energy systems. The proposed methods contribute to a sustainable, fair, and stable energy future by addressing fundamental challenges in modern energy systems.