Solving the ILWE problem serves as a tool for cryptographic analysis and finds widespread application in side-channel attacks against lattice-based post-quantum signature schemes following the “Fiat-Shamir with abort” paradigm such as BLISS, Dilithium and qTESLA. The existing method for solving the ILWE problem, least squares regression followed by rounding, involves computationally expensive operations like matrix-matrix multiplication and matrix inversion, resulting in poor performance when dealing with large inputs. In this paper, we first model the ILWE problem as a special case of linear regression, thus offering a more generalized perspective for solving it: parameter estimation. Then we propose a refinement named BGD-enhancement (short for “batch gradient descent-enhancement”) to solve the ILWE problem more efficiently, incorporating batch gradient descent as an iterative numerical optimization method during the parameter estimation process. This significantly lowers the runtime, and also reduces the memory usage required to solve the ILWE problem. Finally, we apply BGD-enhancement to a side-channel attack against the BLISS signature scheme, where the side-channel leakage forms an instance of the ILWE problem. It is shown that BGD-enhancement lowers the time and memory consumption of the attack, making side-channel attacks that may involve large-scale data inputs in similar scenarios more practical. To be specific, in comparison to previous works, our refinement achieves around a 90% relative speedup in runtime and also substantially lowers memory usage.