In some rate-distortion-type problems, the required fidelity of information is affected by past actions. As a result, the distortion function depends not only on the instantaneous distortion between a source symbol and its representation symbol, but also on past representations. In this paper, we give a formal definition of this problem and introduce both inner (achievable) and outer bounds on the rate-distortion tradeoff. We also discuss convexification of the problem, which makes it easier to find bounds. Problems of this type arise in biological information processing, as well as in recommendation engines; we provide an example applied to a simplified biological information processing problem.

翻译：在某些率失真类型的问题中，所需的信息保真度会受到过往行为的影响。因此，失真函数不仅取决于源符号与其表示符号之间的瞬时失真，还取决于过往的表示。本文中，我们给出了该问题的正式定义，并引入了率失真权衡的内界（可达界）与外界。我们还讨论了问题的凸化，这有助于更容易地找到边界。此类问题出现在生物信息处理以及推荐引擎中；我们提供了一个应用于简化生物信息处理问题的示例。