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Query OracleRLGenerative ModelKnown Transition
Previous Upper Bounds
Exact linear Q* + DetMDP(Wen & Van Roy,2013)√√√
Exact linear Q* + Bellman-Rank (Jiang et al.,2017)√√√
Exact Linear Q* + Low Var + Gap (Du et al.,2019a)√√√
Exact Linear Q* + Gap (Open Problem /Theorem C.1)？√√
Exact Linear Q" for all π (Open Problem /Theorem D.1)？√√
Approx.Linear Q for all π+Concentratability (Munos,2005; Antos et al.,2008)×√√
Approx.Linear Q" for all π+Bounded Dist Mismatch Coeff (Kakade & Langford, 2002)×√√
Lower Bounds (this work)
Approx Linear Q* (Theorem 4.1)×××
Approx Linear Q" for all π (Theorem 4.1)×××
lApprox Linear MDP (Theorem 4.2)×××
Exact Linear π* + Margin + Gap + DetMDP (Theorem 4.3)×××
Exact Linear Q*(Open Problem)？？？
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