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

TL;DR

This paper compares the effectiveness of a Markovian neural network approach with traditional dynamic programming methods in solving stochastic control problems related to fishing quotas, including multi-species models.

Contribution

It introduces a neural network method that preserves the Markov property and demonstrates its application to high-dimensional fishing control problems.

Findings

Neural network approach performs comparably to dynamic programming.

Method extends effectively to multi-species, high-dimensional models.

Neural network offers a promising alternative to classical stochastic control techniques.

Abstract

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.