\section{Related work}\label{sec:related}

\paragraph{ARM--EBM equivalence.} \citet{blondel2025} establish an explicit function-space bijection, connect it to the soft Bellman equation, and analyze EBM-to-ARM distillation. We retain their reference-measure logic but type the sequence into actions and events. This reveals that the factorization that is correct for generation is generally not the operator required for control.

\paragraph{Regularized control and control as inference.} Maximum-entropy inverse RL \citep{ziebart2008}, energy-based policies \citep{haarnoja2017}, and the general theory of regularized MDPs \citep{geist2019} connect exponential tilting, convex regularization, and Bellman operators. \citet{levine2018} explains why naive inference can be optimistic under stochastic dynamics, and \citet{arriojas2023} gives a Bayesian-inference construction consistent with the fixed-dynamics constraint. Our gap recursion complements these results by separating local entropic optimism and its downstream propagation inside an alternating sequence factorization. Stochastic GFlowNets likewise isolate environmental stochasticity from agent choices \citep{pan2023}.

\paragraph{Sequence models for decisions.} Decision Transformer conditions sequence generation on return \citep{chen2021}, while Trajectory Transformer performs model-based sequence search \citep{janner2021}; world-model approaches learn dynamics before controller optimization \citep{ha2018}. We focus on a different boundary: teacher forcing remains an estimator of the observational law, and the normative change is made explicitly in the readout operator.

\paragraph{Risk sensitivity and stochastic attribution.} Entropic utility and risk-sensitive MDPs are classical \citep{howard1972,bauerle2011}. Modern analyses quantify the statistical cost of exponential-utility objectives \citep{fei2021}. Martingale-based decompositions have also been used to separate reward uncertainty \citep{vadori2020}. Our $g_\tau$ is a diagnostic of generative/control mismatch, not a proposal that users should be risk-seeking. The pathwise innovation identity is specialized to typed action--event sequences and the same reference-policy control value.

\paragraph{Offline support and causal interpretation.} Off-policy evaluation quantifies policy-shift error \citep{precup2000,jiang2016,thomas2015}; support-constrained offline RL trades extrapolation control against conservatism \citep{mao2023,kim2023}. Corollary~\ref{cor:gate} makes this trade-off explicit for the present finite-horizon model comparison. Moving from conditional $P(e\mid s,a)$ to intervention claims requires the assumptions of longitudinal causal inference \citep{pearl2009,hernan2020}.

