What is the action sequence aaá" that was likely responsible for reaching state s"' (from state s) in 3 steps? Addressing such questions is important in causal reasoning and in reinforcement learning. Inverse "MDP" models p(aaá"|ss"') can be used to answer them. In the traditional "forward" view, transition "matrix" p(s'|sa) and policy {\pi}(a|s) uniquely determine "everything": the whole dynamics p(asá's"a"...|s), and with it, the action-conditional state process p(s's"...|saaá"), the multi-step inverse models p(aaá"...|ss^i), etc. If the latter is our primary concern, a natural question, analogous to the forward case is to which extent 1-step inverse model p(a|ss') plus policy {\pi}(a|s) determine the multi-step inverse models or even the whole dynamics. In other words, can forward models be inferred from inverse models or even be side-stepped. This work addresses this question and variations thereof, and also whether there are efficient decision/inference algorithms for this.
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