From Infinite to Finite Programs: Explicit Error Bounds with Applications to Approximate Dynamic Programming
研究了无限维线性规划问题，通过随机优化和一阶方法构建了到有限凸规划的近似桥梁，并给出了显式的先验和后验性能保证，在马尔可夫决策过程的最优控制问题中验证了其通用性。
We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite dimensional LP to tractable finite convex programs in which the performance of the approximation is quantified explicitly. To this end, we adopt the recent developments in two areas of randomized optimization and first-order methods, leading to a priori as well as a posteriori performance guarantees. We illustrate the generality and implications of our theoretical results in the special case of the long-run average cost and discounted cost optimal control problems in the context of Markov decision processes on Borel spaces. The applicability of the theoretical results is demonstrated through a fisheries management problem.