Exploring the Pareto-Optimality between Quality and Diversity in Text Generation

Quality and diversity are two essential aspects for performance evaluation of text generation models. Quality indicates how likely the generated samples are to be real samples, and diversity indicates how much differences there are between generated samples. Though quality and diversity metrics have been widely used for evaluation, it is still not clear what the relationship is between them. In this paper, we give theoretical analysis of a multi-objective programming problem where quality and diversity are both expected to be maximized. We prove that there exists a family of Pareto-optimal solutions, giving an explanation of the widely observed tradeoff behavior between quality and diversity in practice. We also give the structure of such solutions, and show that a linear combination of quality and diversity is sufficient to measure the divergence between the generated distribution and the real distribution. Further, we derive an efficient algorithm to reach the Pareto-optimal solutions in practice, enabling a controllable quality-diversity tradeoff.