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This paper addresses the challenge of minimizing training time for the control of Heating, Ventilation, and Air-conditioning (HVAC) systems with online Reinforcement Learning (RL). This is done by developing a novel approach to Multi-Agent Reinforcement Learning (MARL) to HVAC systems. In this paper, the environment formed by the HVAC system is formulated as a Markov Game (MG) in a general sum setting. The MARL algorithm is designed in a decentralized structure, where only relevant states are shared between agents, and actions are shared in a sequence, which are sensible from a system's point of view. The simulation environment is a domestic house located in Denmark and designed to resemble an average house. The heat source in the house is an air-to-water heat pump, and the HVAC system is an Underfloor Heating system (UFH). The house is subjected to weather changes from a data set collected in Copenhagen in 2006, spanning the entire year except for June, July, and August, where heat is not required. It is shown that: (1) When comparing Single Agent Reinforcement Learning (SARL) and MARL, training time can be reduced by 70% for a four temperature-zone UFH system, (2) the agent can learn and generalize over seasons, (3) the cost of heating can be reduced by 19% or the equivalent to 750 kWh of electric energy per year for an average Danish domestic house compared to a traditional control method, and (4) oscillations in the room temperature can be reduced by 40% when comparing the RL control methods with a traditional control method. [ABSTRACT FROM AUTHOR]