论文标题
纯跳跃最佳厄神控制问题的扩散极限近似
Diffusive limit approximation of pure jump optimal ergodic control problems
论文作者
论文摘要
通过快速增强学习算法的设计，我们研究了一类纯赤道随机控制问题的扩散极限。我们表明，每当跳跃强度足够大时，近似误差都由解决方案的Hessian矩阵的h {Ö} lder连续性控制，以极限麦片偏差偏微分方程。这扩展到此上下文，对于有限的地平线问题获得的[1]的结果。我们还解释了如何在适当的平滑度假设下构建一阶误差校正项。最后，我们通过使用与极限扩散问题相关的数值有限差异方案构建的马尔可夫控制策略所引起的错误，这在文献及其自身利益中似乎是新的。这种方法允许大大降低数值分辨率成本。
Motivated by the design of fast reinforcement learning algorithms, we study the diffusive limit of a class of pure jump ergodic stochastic control problems. We show that, whenever the intensity of jumps is large enough, the approximation error is governed by the H{ö}lder continuity of the Hessian matrix of the solution to the limit ergodic partial differential equation. This extends to this context the results of [1] obtained for finite horizon problems. We also explain how to construct a first order error correction term under appropriate smoothness assumptions. Finally, we quantify the error induced by the use of the Markov control policy constructed from the numerical finite difference scheme associated to the limit diffusive problem, this seems to be new in the literature and of its own interest. This approach permits to reduce very significantly the numerical resolution cost.
