Christophe Eloy

Selim Mecanna, Aurore Loisy, Christophe Eloy

Navigating in a fluid flow while being carried by it, using only information accessible from on-board sensors, is a problem commonly faced by small planktonic organisms. It is also directly relevant to autonomous robots deployed in the oceans. In the last ten years, the fluid mechanics community has widely adopted reinforcement learning, often in the form of its simplest implementations, to address this challenge. But it is unclear how good are the strategies learned by these algorithms. In this paper, we perform a quantitative assessment of reinforcement learning methods applied to navigation in partially observable flows. We first introduce a well-posed problem of directional navigation for which a quasi-optimal policy is known analytically. We then report on the poor performance and robustness of commonly used algorithms (Q-Learning, Advantage Actor Critic) in flows regularly encountered in the literature: Taylor-Green vortices, Arnold-Beltrami-Childress flow, and two-dimensional turbulence. We show that they are vastly surpassed by PPO (Proximal Policy Optimization), a more advanced algorithm that has established dominance across a wide range of benchmarks in the reinforcement learning community. In particular, our custom implementation of PPO matches the theoretical quasi-optimal performance in turbulent flow and does so in a robust manner. Reaching this result required the use of several additional techniques, such as vectorized environments and generalized advantage estimation, as well as hyperparameter optimization. This study demonstrates the importance of algorithm selection, implementation details, and fine-tuning for discovering truly smart autonomous navigation strategies in complex flows.

Mario Geiger, Christophe Eloy, Matthieu Wyart

Reinforcement learning is generally difficult for partially observable Markov decision processes (POMDPs), which occurs when the agent's observation is partial or noisy. To seek good performance in POMDPs, one strategy is to endow the agent with a finite memory, whose update is governed by the policy. However, policy optimization is non-convex in that case and can lead to poor training performance for random initialization. The performance can be empirically improved by constraining the memory architecture, then sacrificing optimality to facilitate training. Here we study this trade-off in a two-hypothesis testing problem, akin to the two-arm bandit problem. We compare two extreme cases: (i) the random access memory where any transitions between $M$ memory states are allowed and (ii) a fixed memory where the agent can access its last $m$ actions and rewards. For (i), the probability $q$ to play the worst arm is known to be exponentially small in $M$ for the optimal policy. Our main result is to show that similar performance can be reached for (ii) as well, despite the simplicity of the memory architecture: using a conjecture on Gray-ordered binary necklaces, we find policies for which $q$ is exponentially small in $2^m$, i.e. $q\simα^{2^m}$ with $α< 1$. In addition, we observe empirically that training from random initialization leads to very poor results for (i), and significantly better results for (ii) thanks to the constraints on the memory architecture.