English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We consider robust Markov Decision Processes with Borel state and actionspaces, unbounded cost and finite time horizon. Our formulation leads to aStackelberg game against nature. Under integrability, continuity andcompactness assumptions we derive a robust cost iteration for a fixed policy ofthe decision maker and a value iteration for the robust optimization problem.Moreover, we show the existence of deterministic optimal policies for bothplayers. This is in contrast to classical zero-sum games. In case the statespace is the real line we show under some convexity assumptions that theinterchange of supremum and infimum is possible with the help of Sion's minimaxTheorem. Further, we consider the problem with special ambiguity sets. Inparticular we are able to derive some cases where the robust optimizationproblem coincides with the minimization of a coherent risk measure. In thefinal section we discuss two applications: A robust LQ problem and a robustproblem for managing regenerative energy.

Distributionally Robust Markov Decision Processes and their Connection to Risk Measures