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We propose a framework for designing adaptive choice-based conjoint questionnaires that are robust to response error. It is developed based on a combination of experimental design and statistical learning theory principles. We implement and test a specific case of this framework using Regularization Networks. We also formalize within this framework the polyhedral methods recently proposed in marketing. We use simulations as well as an online market research experiment with 500 participants to compare the proposed method to benchmark methods. Both experiments show that the proposed adaptive questionnaires outperform existing ones in most cases. This work also indicates the potential of using machine learning methods in marketing.