斑块介质中的随机记忆搜索：探索-利用权衡
Random Search with Memory in Patchy Media: Exploration-Exploitation Tradeoff
摘要：
如何最好地利用零散资源？这个长期存在的问题属于广泛研究的探索/利用问题，这些问题出现在广泛的情况下，从动物觅食，到机器人探索，再到人类决策过程。尽管其广泛的相关性，最佳利用的问题以前只解决了两个典型的限制模型-补丁使用和随机搜索-不占斑块内的运动和资源枯竭之间的相互作用。在这里，我们通过引入一个最小的补丁开发模型，结合这种耦合来弥合这一差距：在一个补丁内的随机行走轨迹耗尽资源和旅行到一个新的补丁后，它需要$\mathcal{S}$连续步骤没有找到资源。我们计算的资源量的分布$F_t$消耗时间$t$这个非马尔可夫随机步行者，并显示，探索多个补丁是有益的。在一个维度上，我们解析地推导出最大化$F_t$的最优策略。我们表明，这种策略是强大的补丁内的资源分布和离开一个给定的补丁的标准。我们还表明，$F_t$可以优化的生态相关的情况下，二维斑块环境。
英文摘要：
How to best exploit patchy resources? This long-standing question belongs to the extensively studied class of explore/exploit problems that arise in a wide range of situations, from animal foraging, to robotic exploration, and to human decision processes. Despite its broad relevance, the issue of optimal exploitation has previously only been tackled through two paradigmatic limiting models---patch-use and random search---that do not account for the interplay between searcher motion within patches and resource depletion. Here, we bridge this gap by introducing a minimal patch exploitation model that incorporates this coupling: the searcher depletes the resources along its random-walk trajectory within a patch and travels to a new patch after it takes $\mathcal{S}$ consecutive steps without finding resources. We compute the distribution of the amount of resources $F_t$ consumed by time $t$ for this non-Markovian random walker and show that exploring multiple patches is beneficial. In one dimension, we analytically derive the optimal strategy to maximize $F_t$. We show that this strategy is robust with respect to the distribution of resources within patches and the criterion for leaving a given patch. We also show that $F_t$ can be optimized in the ecologically-relevant case of two-dimensional patchy environments.
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