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A Stochastic Control Problem can be solved by Dynamic Programming orDistributed Optimal Control with the Kolmogorov equation for the probabilitydensity of the Markov process of the problem. It can be solved also withSupervised Learning. We shall compare these two classes of methods for thecontrol of fisheries.  Fishing quotas are unpleasant but efficient to control the productivity of afishing site. A popular model has a vector-valued stochastic differentialequation for the biomass of the different species. Optimization of quota willbe obtained by a gradient method applied to the least square difference with anideal state weighted by the probability density of the biomasses. Alternativelya deep neural network which preserves the Markov property of the problem can betrained with a stochastic gradient algorithm. The model is extended todistributed fishing sites and biomass is stabilized by adjusting the quota toits time derivative.

Optimal Quota for a Multi-species Fishing Models