Anantharam, V. ; Borkar, V. S. (2015) Rocking in two by two: From Collatz-Wielandt to Donsker-Varadhan In: 2015 Information Theory and Applications Workshop (ITA), San Diego, CA, USA, 01-06 February 2015.
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Official URL: http://doi.org/10.1109/ITA.2015.7308997
Related URL: http://dx.doi.org/10.1109/ITA.2015.7308997
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 state and action spaces, extending a formula of Donsker and Varadhan for the Perron-Frobenius eigenvalue of a positive operator. This can be viewed as an abstract version of the Collatz-Wielandt formula for the Perron-Frobenius eigenvalue of a non-negative matrix. This leads to a concave maximization formulation of the problem of determining the optimal growth rate of risk-sensitive reward.
| Item Type: | Conference or Workshop Item (Other) |
|---|---|
| Source: | Copyright of this article belongs to IEEE. |
| ID Code: | 135199 |
| Deposited On: | 20 Jan 2023 05:59 |
| Last Modified: | 20 Jan 2023 05:59 |
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