Performance of a Markovian neural network versus dynamic programming on a fishing control problem
Mathieu Laurière, NYU Shanghai, Shanghai, 200122, China, Gilles Pagès, Olivier Pironneau, LPMA, Sorbonne Université, 75006, Paris, France, LJLL, Sorbonne Université, 75006, Paris, France · Probability Uncertainty and Quantitative Risk · 2023
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 multi species model and shows that the Neural Network is usable in high dimensions.