In this letter we provide several informative tight error bounds when using value function approximators for the risk-sensitive cost setting for a given policy represented using exponential utility. The novelty of our approach is that we make use of the irreducibility of the underlying Markov chain (resulting in better bounds using Perron–Frobenius eigenvectors) to derive new bounds whereas the earlier work used primarily the spectral variation bound which holds for any matrix, hence did not make use of the irreducibility. All our bounds have a perturbation term for large state spaces. We also present examples where we show that the new bounds perform 90-100% better than the earlier proposed spectral variation bound.

在这封信中，当将价值函数逼近器用于使用指数效用表示的给定策略的风险敏感成本设置时，我们提供了一些有用的严格误差范围。我们方法的新颖性在于，我们利用了潜在的马尔可夫链的不可约性（使用Perron-Frobenius特征向量产生更好的界）来推导新的界，而早期的工作主要使用了适用于任何矩阵的频谱变化界，因此没有利用不可约性。我们所有的边界都有一个针对大状态空间的扰动项。我们还提供了一些示例，这些示例表明新边界的性能比早期提出的频谱变化边界好90-100％。