Thermostatically controlled load (TCL, such as heating, ventilation, and air conditioning system) is a desirable demand-side flexibility source in distribution networks. It can participate in regulation services and mitigate power imbalances from fluctuating distributed renewable generation. To effectively utilize the load flexibility from spatially and temporally distributed TCLs in a distribution network, it is necessary to consider power flow constraints to avoid possible voltage or current violations. Published works usually adopt optimal power flow models (OPF) to describe these constraints. However, these models require accurate topology of the distribution network that is often unobservable in practice. To bypass this challenge, this paper proposes a novel learning-based OPF to optimize TCLs for regulation services. This method trains three regression multi-layer perceptrons (MLPs) based on the distribution network's historical operation data to replicate its power flow constraints. The trained MLPs are further equivalently reformulated into linear constraints with binary variables so that the optimization problem becomes a mixed-integer linear program that can be effectively solved. Numerical experiments based on the IEEE 123-bus system validate that the proposed method can achieve better TCL power scheduling performance with guaranteed feasibility and optimality than other state-of-art models.