Supplementary Material from Searching for a source without gradients: how good is infotaxis and how to beat it

Infotaxis is a popular search algorithm designed to track a source of odour in a turbulent environment using information provided by odour detections. To exemplify its capabilities, the source-tracking task was framed as a partially observable Markov decision process consisting in finding, as fast as possible, a stationary target hidden in a two-dimensional grid using stochastic partial observations of the target location. Here, we provide an extended review of infotaxis, together with a toolkit for devising better strategies. We first characterize the performance of infotaxis in domains from one dimension to four dimensions. Our results show that, while being suboptimal, infotaxis is reliable (the probability of not reaching the source approaches zero), efficient (the mean search time scales as expected for the optimal strategy) and safe (the tail of the distribution of search times decays faster than any power law, though subexponentially). We then present three possible ways of beating infotaxis, all inspired by methods used in artificial intelligence: tree search, heuristic approximation of the value function, and deep reinforcement learning. The latter is able to find, without any prior human knowledge, the (near) optimal strategy. Altogether, our results provide evidence that the margin of improvement of infotaxis towards the optimal strategy gets smaller as the dimensionality increases.