随机最短路问题的次优界
Suboptimality Bounds for Stochastic Shortest Path Problems
摘要：
我们考虑如何使用Bellman残差的动态规划运营商计算次优界的解决方案随机最短路问题。这种界限以前只在“所有策略都是适当的”的特殊情况下才建立起来，在这种情况下，动态规划算子被认为是一个收缩，并且已经被证明只在更有限的贴现特殊情况下才容易计算。在转移成本为正的条件下，我们证明了即使不是所有的政策都是正确的，次优性界限也可以很容易地计算出来。在一般情况下，如果对过渡成本没有限制，分析就比较复杂。但我们目前的初步结果表明，这种界限是可能的。
英文摘要：
We consider how to use the Bellman residual of the dynamic programming operator to compute suboptimality bounds for solutions to stochastic shortest path problems. Such bounds have been previously established only in the special case that "all policies are proper," in which case the dynamic programming operator is known to be a contraction, and have been shown to be easily computable only in the more limited special case of discounting. Under the condition that transition costs are positive, we show that suboptimality bounds can be easily computed even when not all policies are proper. In the general case when there are no restrictions on transition costs, the analysis is more complex. But we present preliminary results that show such bounds are possible.
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