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A variational formula for risk-sensitive reward (1501.00676v1)
Published 4 Jan 2015 in math.OC, cs.IT, math.IT, and math.PR
Abstract: We derive a variational formula for the optimal growth rate of reward in the infinite horizon risk-sensitive control problem for discrete time Markov decision processes with compact metric state and action spaces, extending a formula of Donsker and Varadhan for the Perron-Frobenius eigenvalue of a positive operator. This leads to a concave maximization formulation of the problem of determining this optimal growth rate.
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