A monotone semi-discrete policy iteration scheme with O(h) artificial viscosity for stationary discounted HJB equations converges geometrically for fixed h and achieves O(sqrt(h)) error to the viscosity solution.
Solving high-dimensional partial differen- tial equations using deep learning.Proceedings of the National Academy of Sciences, 115(34):8505–8510, 2018
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The authors prove a population L2 stability estimate and finite-sample certificate for one policy-evaluation step in a neural HJB solver with learned dynamics, plus multi-step propagation through greedy improvement, with experiments on high-dimensional control tasks.
A deep policy iteration method reformulates finite-horizon mean-field games as regenerative problems with deterministic cycles, using particle systems and one-step updates to handle dimensions up to 10,000 efficiently.
citing papers explorer
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Policy Iteration for Stationary Discounted Hamilton--Jacobi--Bellman Equations: A Viscosity Approach
A monotone semi-discrete policy iteration scheme with O(h) artificial viscosity for stationary discounted HJB equations converges geometrically for fixed h and achieves O(sqrt(h)) error to the viscosity solution.
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Stabilized neural Hamilton--Jacobi--Bellman solvers: Error analysis and applications in model-based reinforcement learning
The authors prove a population L2 stability estimate and finite-sample certificate for one policy-evaluation step in a neural HJB solver with learned dynamics, plus multi-step propagation through greedy improvement, with experiments on high-dimensional control tasks.
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Deep Policy Iteration for High-Dimensional Mean-Field Games with Regenerative Reformulation
A deep policy iteration method reformulates finite-horizon mean-field games as regenerative problems with deterministic cycles, using particle systems and one-step updates to handle dimensions up to 10,000 efficiently.