These literature consider using the causal effect of an intervention on a surrogate outcome (e.g., patients' short-term health) as a proxy for its treatment effect on the outcome of primary interest (e.g., long-term health). To this end, many criteria have been proposed to ensure the validity of the surrogate outcome. Examples include the statistical surrogate criterion [Prentice, 1989], principal surrogate criterion [Frangakis and Rubin, 2002], consistent surrogate criterion [Chen et al., 2007], among many others. However, these criteria can easily run into logic paradox [Chen et al., 2007] or rely on unidentifiable quantities, showing the challenge of causal inference when the primary outcome is completely missing. When multiple surrogates are available, , Price et al. [2018] consider transforming these surrogates to optimally approximate the primary outcome. Their approaches can avoid the surrogate paradox discussed in Chen et al. [2007]. Nevertheless, learning surrogate transformations requires experimental **data** with long-term outcome observations in the first place, which can be very demanding in practice.