To make decisions organisms often accumulate information across multiple timescales. However, most experimental and modeling studies of decision-making focus on sequences of independent trials. On the other hand, natural environments are characterized by long temporal correlations, and evidence used to make a present choice is often relevant to future decisions. To understand decision-making under these conditions we analyze how a model ideal observer accumulates evidence to freely make choices across a sequence of correlated trials. We use principles of probabilistic inference to show that an ideal observer incorporates information obtained on one trial as an initial bias on the next. This bias decreases the time, but not the accuracy of the next decision. Furthermore, in finite sequences of trials the rate of reward is maximized when the observer deliberates longer for early decisions, but responds more quickly towards the end of the sequence. Our model also explains experimentally observed patterns in decision times and choices, thus providing a mathematically principled foundation for evidence-accumulation models of sequential decisions.

中文翻译：

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优化漂移扩散模型中的顺序决策

为了做出决策，生物体通常会在多个时间尺度上积累信息。然而，大多数决策的实验和建模研究都集中在独立试验的序列上。另一方面，自然环境的特点是长时间的相关性，用于做出当前选择的证据通常与未来的决策相关。为了理解这些条件下的决策，我们分析了模型理想观察者如何积累证据以在一系列相关试验中自由地做出选择。我们使用概率推理原理来表明理想的观察者会将在一次试验中获得的信息作为对下一次试验的初始偏差。这种偏差会减少时间，但不会减少下一个决策的准确性。此外，在有限的试验序列中，当观察者为早期决定考虑更长时间时，奖励率最大化，但在序列结束时反应更快。我们的模型还解释了实验观察到的决策时间和选择模式，从而为顺序决策的证据积累模型提供了数学原理基础。