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• A safe reinforcement learning method for smart home energy management is proposed. • The operation of the components in a multi-energy smart home is modeled as a CMDP. • The approach minimizes total energy cost and avoids constraints violations. This paper proposes a data-driven approach for multi-energy management of a smart home with different types of appliances, including battery energy storage system (BESS), thermal energy storage system (TES), micro combined heat and power system (mCHP), electrical heat pump (EHP), rooftop photovoltaics (PV) and electrical vehicle (EV). Firstly, home energy management (HEM) is formulated as a cost minimization problem with hard constraints to optimize energy generation, storage, and consumption. Secondly, this paper proposes a safe reinforcement learning (SRL) approach with Primal-Dual Optimization (PDO) policy search-based algorithm to solve the HEM problem. Unlike existing DRL methods, the proposed approach learns to minimize costs from accumulated cost functions and automatically tunes the cost function coefficients to achieve zero constraints violation. Besides, a dynamic electricity price forecasting model based on CNN-LSTM neural network is designed to deal with the uncertainties in future prices. To verify the performance of the proposed HEM method, simulations are conducted using Singapore wholesale electricity price data. Numerical results demonstrate that the proposed method has a better ability to minimize energy costs and satisfy constraints compared to existing methods. [ABSTRACT FROM AUTHOR]