# Multi-Agent Reinforcement Learning on Active Particles¶

Ensemble of N point particles travelling at a fixed speed $$|u|=1$$.

The reinforcement learning agent $$i$$ that has available as state the distance $$r_{ij}$$, direction vector $$\boldsymbol{r}_{ij}$$, and angles $$\theta_{ij}$$ to the M nearest neighbours $$j=1,\dots,M$$. The action determines the wished new direction $$u=(u_x, u_y, u_z)$$ of the particle. The reward is computed as the sum of a pairwise potential between the neihest neighbours

$r_t=\sum_{i=0}^{M}V(r)$

As example potential is the Lennard-Jones potential as well as its harmonic approximation. The particles orientation is updated by rotating the current orientation by an angle $$\alpha$$ towards the wished new direction. Then it moves by updating the position as $$x\rightarrow x+\Delta t u$$.

## Example¶

Verbous example with Newton policy $$a=-dV(r)/dr / \|dV(r)/dr\|$$ and visualisation turned on can be run using

python main.py --visualize 1 --numIndividuals 10 --numTimesteps 100 --numNearestNeighbours 5