## 1 Introduction
### Related Works  
To achieve the goal of zero carbon in building systems, each step of the carbon trail needs to be addressed, including carbon capture, utilization, and emissions. In integrated energy systems that include Combined Heat and Power (CHP), Carbon Capture and Storage (CCS) is commonly used as an important device, which can capture the CO\({}_{2}\) generated by CHP for storage or transportation. Ref. [11] integrates Power to Gas (P2G) and CCS with CHP in the integrated energy system, avoiding the costs of transportation and storage through the direct utilization of carbon while also improving the consumption of renewable energy. Ref. [12] utilizes post-combustion methods with monoethanolamine to capture CO\({}_{2}\) in a hybrid wind-solar system. In daily energy scheduling, carbon emission constraints are considered to derive the optimal strategy. CCS is also used as a carbon capture device in virtual power plant networks with electric vehicles. Through deep learning methods, it simultaneously leverages the flexibility of electric vehicles while achieving emission reduction targets [13]. In building energy systems, CCS is also used, as in [14], where it is employed to establish a low-carbon model to reduce carbon emissions to the atmosphere. Through non-cooperative game theory, the overall optimal solution for the common interests of multiple building systems is achieved. However, it is important to note that the efficiency of carbon capture by CCS and carbon utilization by P2G cannot reach 100%, so some CO\({}_{2}\) will inevitably be emitted into the atmosphere. If energy-consuming units participate in the carbon market, excessive carbon emissions compared to the given carbon quota will increase the energy costs, whereas a lower level of emissions may present potential benefits. This aspect has been less discussed in the aforementioned studies. Compared to traditional building systems, the introduction of zero-carbon technology will make it more complex due to the integration of various subsystems, with the most critical aspect being the existence of multiple types of uncertainty. From an energy perspective, the sources of uncertainty include both the energy supply side and the energy demand side. This has been studied by several scholars. Ref. [15] studied zero-carbon buildings powered by renewable energy and energy storage systems, analyzing the seasonal variation characteristics and uncertainties of energy supply. Solar and hydro energy are modeled using a Gaussian distribution, and the system stability is guaranteed through hydrogen storage and fuel cells. Similar research is also conducted in [16], where the uncertainties of photovoltaics and electric vehicles are analyzed and modeled to adjust the scale of battery storage in smart homes, achieving the optimal storage capacity to reduce costs. The changes in energy demand within the building system directly affect energy costs. Meanwhile, for consumers, variations in energy costs influence energy consumption habits, thereby altering the energy demand. These two factors are interrelated over time. If optimization can be combined with building occupants' energy consumption habits and comfort zones, it is bound to yield results that are closer to real-world scenarios, which is relatively studied in existing research. Traditional optimization approaches for addressing uncertainty include stochastic optimization (SO) [17], scenario reduction (SG) [18], chance-constrained (CC) optimization [19], robust optimization (RO) [20], and distributed robust optimization (DRO) [21]. However, these approaches either require detailed distribution information about uncertain parameters or result in optimization outcomes with noticeable conservatism. In contrast,data-driven approaches [22] are entirely based on the samples of uncertain parameters that can be collected. Through specific data analysis techniques, parameter information can be effectively extracted.