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- W2108293203 abstract "This paper addresses the problem of sensitivity analysis for finite-horizon performance measures of general Markov chains. We derive closed-form expressions and associated unbiased gradient estimators for the derivatives of finite products of Markov kernels by measure-valued differentiation (MVD). In the MVD setting, the derivatives of Markov kernels, called $mathcal{D}$ -derivatives, are defined with respect to a class of performance functions $mathcal{D}$ such that, for any performance measure $ginmathcal{D}$ , the derivative of the integral of g with respect to the one-step transition probability of the Markov chain exists. The MVD approach (i) yields results that can be applied to performance functions out of a predefined class, (ii) allows for a product rule of differentiation, that is, analyzing the derivative of the transition kernel immediately yields finite-horizon results, (iii) provides an operator language approach to the differentiation of Markov chains and (iv) clearly identifies the trade-off between the generality of the performance classes that can be analyzed and the generality of the classes of measures (Markov kernels). The $mathcal{D}$ -derivative of a measure can be interpreted in terms of various (unbiased) gradient estimators and the product rule for $mathcal {D}$ -differentiation yields a product-rule for various gradient estimators." @default.
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- W2108293203 date "2007-10-30" @default.
- W2108293203 modified "2023-09-26" @default.
- W2108293203 title "Measure-Valued Differentiation for Markov Chains" @default.
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- W2108293203 doi "https://doi.org/10.1007/s10957-007-9297-7" @default.
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