Transcranial alternating current stimulation (tACS) can evoke illusory flash-like visual percepts known as phosphenes. The perception of phosphenes represents a major experimental challenge when studying tACS-induced effects on cognitive performance. Besides growing concerns that retinal phosphenes themselves could potentially have neuromodulatory effects, the perception of phosphenes may also modify the alertness of participants. Past research has shown that stimulation intensity, frequency and electrode montage affect phosphene perception. However, to date, the effect of an additional tACS parameter on phosphene perception has been completely overlooked: the relative phase difference between stimulation electrodes. This is a crucial and timely topic given the confounding nature of phosphene perception and the increasing number of studies reporting changes in cognitive function following tACS phase manipulations. However, studying phosphene perception for different frequencies and phases simultaneously is not tractable using standard approaches, as the physiologically plausible range of parameters results in a combinatorial explosion of experimental conditions, yielding impracticable experiment durations. To overcome this limitation, here we applied a Bayesian optimization approach to efficiently sample an exhaustive tACS parameter space. Moreover, unlike conventional methodology, which involves subjects judging the perceived phosphene intensity on a rating scale, our study leveraged the strength of human perception by having the optimization driven based on a subject's relative judgement.Applying Bayesian optimization for two different montages, we found that phosphene perception was affected by differences in the relative phase between cortical electrodes. The results were replicated in a second study involving new participants and validated using computational modelling. In summary, our results have important implications for the experimental design and conclusions drawn from future tACS studies investigating the effects of phase on cognition.