# A Small-Sample Scenario Optimization Scheduling Method Based on Multidimensional Data Expansion
## 1 Introduction  
With the growing prominence of energy crises and environmental issues, countries worldwide are actively restructuring their energy systems to reduce dependence on fossil fuels [1, 2]. Integrated energy systems (IES), through multi-energy coupling, have emerged as an effective solution to enhance energy utilization efficiency and address these challenges [3, 4]. The optimal scheduling of IES currently represents a key research focus in this field. Currently, there have been a large number of studies for integrated energy system dispatch, mostly offline optimization problems for day-ahead dispatch [5, 6, 7, 8, 9, 10]. Stochastic programming [11, 12] and robust optimization [13] have been used to deal with uncertainties caused by fluctuations in renewable energy sources, loads, and real-time tariffs [14] in thesystem. Traditional optimization methods for dealing with uncertainty rely on predicting day-ahead renewable energy output, load, and other data. A better optimal dispatch solution can be obtained by transforming the problem into a deterministic one, which can be solved by modeling the uncertainty. The above methods are mainly based on physical modeling approaches, and more accurate modeling of the integrated energy system is needed to obtain more dispatch information. This paper considers another class of optimal scheduling methods: data-driven optimal scheduling. Methods such as reinforcement learning (RL) and deep RL (DRL) [15] have gained widespread attention since the success of AlphaGo [16]. RL learns through interactive trial-and-error [17], allowing model-free algorithms to handle system factors that are difficult to accurately model, and exhibits better real-time decision-making performance, which can be utilized in IES online real-time scheduling. There have been studies applying DRL to IES optimal scheduling studies. [PERSON] [18] proposed a real-time battery storage control model based on reinforcement learning by describing the problem as a Markov decision process (MDP), solving it using the Q-learning algorithm, and analyzing the effect of the discrete degree of the action space on the algorithm's performance. However, discretizing continuous variables will significantly increase the computation time and error for continuous space problems, such as integrated energy system scheduling. Current mainstream DRL algorithms include the Deep Deterministic Policy Gradient (DDPG), Proximal Policy Optimization (PPO), and the Twin-Delayed Deep Deterministic Policy Gradient algorithm (TD3), among others [19; 20; 21; 22]. [PERSON] [23] utilized the DDPG algorithm to solve continuous space problems, verifying the effectiveness and robustness of the algorithm. There is extensive literature on improving the method and enhancing the algorithm performance for the problems of convergence difficulty and unstable convergence in deep reinforcement learning algorithms. Reference [24] tuned the proportional-integral differential controller parameters based on an improved reinforcement learning agent with Double-Delayed Deep Deterministic Policy Gradients and trained multiple deep reinforcement learning agents under stochastic load perturbations and nonlinear power generation models to obtain the optimal controller gain for a multi-area interconnected system. Deep reinforcement learning has been widely applied to energy system optimization and scheduling. However, the DRL method relies more heavily on historical data, and few existing studies have considered scenarios with insufficient data. The lack of historical operation data in the newly built integrated energy system leads to insufficient DRL training samples, which are prone to the problems of underfitting and inadequate exploration of the decision space. It thus reduces the accuracy of the scheduling plan.