The paper derives the efficient influence function for optimal policy values in MDPs, proves it does not exist under policy non-uniqueness, and proposes a sequential doubly robust estimator that provides valid conservative inference in such regimes.
Ψ˚pPq´E P “ QpPqpA,S;πqπpA|Sq ‰ “EP “ QpPqpA,S;π ˚pPqqπ˚pPqpA|Sq ‰ ´EP “ QpPqpA,S;πqπpA|Sq ‰ “EP “ QpPq ` A,S;π ˚pPq ˘` π˚pPqpA|Sq´πpA|Sq ˘‰ `EP
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Semiparametric Off-Policy Inference for Optimal Policy Values under Possible Non-Uniqueness
The paper derives the efficient influence function for optimal policy values in MDPs, proves it does not exist under policy non-uniqueness, and proposes a sequential doubly robust estimator that provides valid conservative inference in such regimes.