AI 中文总结
本文提出活性布朗粒子集体适应模型，通过分散式策略调整与邻居信息交换学习目标宏观状态，并揭示学习时间与目标频率决定集体振荡及解锁转变。
AI 中文摘要
我们考虑一个活性智能体的最小模型，该模型通过分散式适应过程集体学习达到目标宏观状态。智能体被建模为活性布朗粒子，通过翻滚事件随机重定向到给定方向。平均目标状态被编码进每个智能体评估的奖励函数中。智能体可以调整其微观动力学参数之一，称为“策略”（例如速度或重定向方向），以通过与邻近智能体的信息交换来优化其奖励函数。我们在适应过程相对于物理动力学缓慢的假设下，用动力学理论描述策略分布在整个智能体群体中的演化。适应过程在几个学习协议上得到说明，这些协议具有固定或时间相关的目标速度。一个结合教学和突变的特征学习时间$\tau$从动力学中涌现。对于角频率为$\omega$的时间振荡目标，集体动力学随时间振荡，振荡幅度和相移由乘积$\omega \tau$决定。对于旋转目标速度，还观察到向不可适应状态的解锁转变。
英文摘要
We consider a minimal model of active agents which collectively learn to reach a target macroscopic state via a decentralized adaptation process. Agents are modeled as active Brownian particles which randomly reorient to a given direction through tumbling events. An average target state is encoded into a reward function evaluated by each agent. Agents can tune one of the parameters of their microscopic dynamics, called `policy' (e.g., speed or reorientation direction), to optimize their reward function thanks to information exchange with neighboring agents. We describe the evolution of the policy distribution across the agent population with a kinetic theory, under the assumption that the adaptation process is slow with respect to the physical dynamics. The adaptation process is illustrated on several learning protocols with either fixed or time-dependent target velocities. A characteristic learning time $τ$ combining teaching and mutations emerges from the dynamics. For time-oscillating targets at angular frequency $ω$, the collective dynamics oscillates in time, with an oscillation amplitude and phase shift determined by the product $ωτ$. An unlocking transition to a non-adaptable state is also observed for a rotating target velocity.
