A Minimax Optimization Model for Virtual Reality Experiential Learning

Abstract

This study develops a minimax optimization model for evaluating virtual reality experiential learning when an intervention is expected to improve several educational outcomes at the same time. Conventional evaluations usually test each outcome separately or combine outcomes through arbitrary weights. Both approaches can conceal a weak result in one domain. The proposed model instead selects the instructional strategy that maximizes the worst standardized lower-bound gain across outcomes. An empirical demonstration uses a supplied pretest-posttest dataset containing 100 observations, two groups, and composite scores for cultural competence and emotional intelligence. The data contain no missing values. The baseline profiles of the two groups are pairwise identical, so the analysis combines heteroskedasticity-robust analysis of covariance with pair-based bootstrap and sensitivity procedures. Adjusted posttest differences favor the virtual reality group for cultural competence (0.602, 95% CI [0.522, 0.683]) and emotional intelligence (0.600, 95% CI [0.527, 0.673]). After baseline-standardization, the estimated gains are 1.271 and 1.350 standard deviations. The conservative minimax lower-bound score is 1.087, with cultural competence defining the binding outcome. The same strategy is selected under change-score, paired, rank-based, trimmed-mean, and leave-one-pair-out analyses. The model offers a transparent alternative to weighted composite evaluation while preserving outcome balance and uncertainty for instructional decisions.