  We apply machine-learning techniques to the effective-field-theory analysis
of the $e^+e^- \to W^+W^-$ processes at future lepton colliders, and
demonstrate their advantages in comparison with conventional methods, such as
optimal observables. Compared to traditional algorithms, we show that
simulation-based inference methods are more robust to detector effects and
backgrounds, and could in principle produce unbiased results with sufficient
Monte Carlo simulation samples that accurately describe experiments. This is
crucial for the analyses at future lepton colliders given the outstanding
precision of the $e^+e^- \to W^+W^-$ measurement ($\sim 10^{-4}$ in terms of
anomalous triple gauge couplings or even better) that can be reached. Our
framework can be generalized to other effective-field-theory analyses, such as
the one of $e^+e^- \to t\bar{t}$ or similar processes at muon colliders.
