For non-rectangular Lp transition uncertainty, the worst-case return equals the nominal return minus a penalty that can be found by binary search on a fixed-point equation.
Lightning Does Not Strike Twice: Robust MDPs with Coupled Uncertainty
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abstract
We consider Markov decision processes under parameter uncertainty. Previous studies all restrict to the case that uncertainties among different states are uncoupled, which leads to conservative solutions. In contrast, we introduce an intuitive concept, termed "Lightning Does not Strike Twice," to model coupled uncertain parameters. Specifically, we require that the system can deviate from its nominal parameters only a bounded number of times. We give probabilistic guarantees indicating that this model represents real life situations and devise tractable algorithms for computing optimal control policies using this concept.
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Dual Formulation for Non-Rectangular Lp Robust Markov Decision Processes
For non-rectangular Lp transition uncertainty, the worst-case return equals the nominal return minus a penalty that can be found by binary search on a fixed-point equation.