非平稳环境下贝叶斯决策模型的Lévy行走
Lévy walks derived from a Bayesian decision-making model in non-stationary environments
摘要：
Lévy Walks在各种生物的迁移行为模式中被发现，这种现象的原因已经被广泛讨论。我们使用模拟来证明，学习导致在非平稳环境中的决策过程中的置信水平的变化，并导致Lévy-walk-like模式。一种涉及置信度的推理算法是贝叶斯推理。我们提出了一种算法，引入学习和遗忘的影响贝叶斯推理，并模拟模仿游戏中，两个决策代理将算法估计对方的内部模型，从他们的对手的观测数据。对于没有学习的遗忘，由于缺乏关于对方的信息，代理人的信心水平仍然很低，并且布朗行走发生在很宽的遗忘率范围内。相反，当学习被引入时，即使在高遗忘率的情况下，高置信水平偶尔也会出现，布朗漫步普遍成为通过高置信和低置信状态混合的列维漫步。
英文摘要：
Lévy walks are found in the migratory behaviour patterns of various organisms, and the reason for this phenomenon has been much discussed. We use simulations to demonstrate that learning causes the changes in confidence level during decision-making in non-stationary environments, and results in Lévy-walk-like patterns. One inference algorithm involving confidence is Bayesian inference. We propose an algorithm that introduces the effects of learning and forgetting into Bayesian inference, and simulate an imitation game in which two decision-making agents incorporating the algorithm estimate each other's internal models from their opponent's observational data. For forgetting without learning, agent confidence levels remained low due to a lack of information on the counterpart and Brownian walks occurred for a wide range of forgetting rates. Conversely, when learning was introduced, high confidence levels occasionally occurred even at high forgetting rates, and Brownian walks universally became Lévy walks through a mixture of high- and low-confidence states.
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