Deep neural networks algorithms for stochastic control problems on finite horizon: numerical applications

Bachouch, Achref; Huré, Côme; Langrené, Nicolas; Pham, Huyen

doi:10.48550/arxiv.1812.05916

Cited by 19 publications

(50 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This strategy has been used previously in the optimal control literature, see e.g. [12], [14], [10], [3]. Given an activation function ψ : R → R (e.g.…”

Section: Optimisation With Markovian Feedback Neural Network Controlsmentioning

confidence: 99%

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

Laurière

Pagès²,

Pironneau

2021

Preprint

View full text Add to dashboard Cite

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.

show abstract

“…This strategy has been used previously in the optimal control literature, see e.g. [12], [14], [10], [3]. Given an activation function ψ : R → R (e.g.…”

Section: Optimisation With Markovian Feedback Neural Network Controlsmentioning

confidence: 99%

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

Laurière

Pagès²,

Pironneau

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…The widest studied problem is that of optimal stopping (aka American option pricing) initiated by [40,34] and studied continuously to this day [35]. Stochastic control problems were first addressed in [28] using control randomisation techniques and later studied in [2] using regress later approach and in [1] employing deep neural networks. Numerical methods designed in our paper are closest in their spirit to regress later ideas of [2] (see also [1]).…”

Section: Related Literaturementioning

confidence: 99%

“…Stochastic control problems were first addressed in [28] using control randomisation techniques and later studied in [2] using regress later approach and in [1] employing deep neural networks. Numerical methods designed in our paper are closest in their spirit to regress later ideas of [2] (see also [1]).…”

Section: Related Literaturementioning

confidence: 99%

Automatic model training under restrictive time constraints

Cironis¹,

Palczewski²,

Aivaliotis³

2021

Preprint

View full text Add to dashboard Cite

We develop a hyperparameter optimisation algorithm, Automated Budget Constrained Training (AutoBCT), which balances the quality of a model with the computational cost required to tune it. The relationship between hyperparameters, model quality and computational cost must be learnt and this learning is incorporated directly into the optimisation problem. At each training epoch, the algorithm decides whether to terminate or continue training, and, in the latter case, what values of hyperparameters to use. This decision weighs optimally potential improvements in the quality with the additional training time and the uncertainty about the learnt quantities. The performance of our algorithm is verified on a number of machine learning problems encompassing random forests and neural networks. Our approach is rooted in the theory of Markov decision processes with partial information and we develop a numerical method to compute the value function and an optimal strategy.

show abstract

“…Hence when n is larger than 2 it is very unlikely that simple finite differences methods can be used to solve numerically (HJB) α,γ . To tackle this issue one has to use other numerical methods such as neural networks, see [4,16] for example, or probabilistic method, see [14]. In this article we propose to use the later method for numerical applications.…”

Section: Conclusion On Approaching the Optimal Controlmentioning

confidence: 99%

Optimal market making with persistent order flow

Jusselin¹

2020

Preprint

View full text Add to dashboard Cite

We address the issue of market making on electronic markets when taking into account the self exciting property of market order flow. We consider a market with order flows driven by Hawkes processes where one market maker operates, aiming at optimizing its profit. We characterize an optimal control solving this problem by proving existence and uniqueness of a viscosity solution to the associated Hamilton Jacobi Bellman equation. Finally we propose a methodology to approximate the optimal strategy.

show abstract

Deep neural networks algorithms for stochastic control problems on finite horizon: numerical applications

Cited by 19 publications

References 9 publications

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

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

Automatic model training under restrictive time constraints

Optimal market making with persistent order flow

Contact Info

Product

Resources

About