Optimal designs are usually model-dependent and likely to be sub-optimal if the postulated model is not correctly specified. In practice, it is common that a researcher has a list of candidate models at hand and a design has to be found that is efficient for selecting the true model among the competing candidates and is also efficient (optimal, if possible) for estimating the parameters of the true model. In this article, we use a reinforced learning approach to address this problem. We develop a sequential algorithm, which generates a sequence of designs which have asymptotically, as the number of stages increases, the same efficiency for estimating the parameters in the true model as an optimal design if the true model would have correctly been specified in advance. A lower bound is established to quantify the relative efficiency between such a design and an optimal design for the true model in finite stages. Moreover, the resulting designs are also efficient for discriminating between the true model and other rival models from the candidate list. Some connections with other state-of-the-art algorithms for model discrimination and parameter estimation are discussed and the methodology is illustrated by a small simulation study.

翻译：最优设计通常依赖于预设模型，若假定模型设定有误则可能产生次优效果。实践中，研究者常面临候选模型集合，需构建既能高效区分真实模型与竞争模型，又能准确估计真实模型参数（在可能条件下达到最优）的设计方案。本文采用强化学习框架解决该问题，提出一种序贯算法。该算法生成的设计序列在阶段数趋于无穷时，渐近达到与预先正确指定真实模型时最优设计相同的参数估计效率。我们建立了有限阶段下该设计与真实模型最优设计之间相对效率的下界。此外，所得设计在区分真实模型与候选列表中其他竞争模型方面同样高效。本文讨论了该方法与当前最优的模型区分及参数估计算法之间的关联，并通过小型仿真研究验证了其有效性。