Performance of a Markovian neural network versus dynamic programming on a fishing control problem

Mathieu Laurière (1) , Gilles Pagès (2) , Olivier Pironneau (3)

1 Princeton University
2 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation
3 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions

Fishing quotas are unpleasant but efficient to control the productivity of a fishing site. A popular model has a stochastic differential equation for the biomass on which a stochastic dynamic programming or a Hamilton-Jacobi-Bellman algorithm can be used to find the stochastic control-the fishing quota. We compare the solutions obtained by dynamic programming against those obtained with a neural network which preserves the Markov property of the solution. The method is extended to a similar multi species model to check its robustness in high dimension.

Mots clés: Stochastic optimal control partial differential equations neural networks; Stochastic optimal control; partial differential equations; neural networks

Domaines: Probabilités [math.PR]

Mathieu Laurière, Gilles Pagès, Olivier Pironneau. Performance of a Markovian neural network versus dynamic programming on a fishing control problem. Probability, Uncertainty and Quantitative Risk, In press, ⟨10.48550/arXiv.2109.06856⟩. ⟨hal-03891220⟩