Fel'dbaum's own exact Bayesian dynamic-programming solution to dual control is one he himself flagged as impractical beyond small examples, confirmed by two independent later sources

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In "Dual Control Theory. II," A.A. Fel'dbaum's exact solution proceeds by backward induction: derive the posterior density over unknown plant parameters given all past inputs and observations at each time step, then choose the control minimizing expected total future risk by working backward from the final step — an augmented physical-plus-information state solved via Bellman's dynamic programming. Fel'dbaum is explicit about the cost of exactness: determining the resulting sequence of functions in concrete examples "может оказаться чрезмерно громоздким" ("may prove excessively cumbersome"), and that even with computing aids, "можно решать пока лишь сравнительно простые задачи" ("one can currently solve only comparatively simple problems") — his own assessment of his own method.

Two independent modern sources, different author groups and venues, neither citing the other, confirm rather than dispute this. Meijer and Rantzer's 2026 survey states Fel'dbaum "recognized that solving Bellman's equation exactly poses computational challenges and emphasized the need for tractable approximations." Klenske and Hennig's 2016 peer-reviewed JMLR paper states it more bluntly: "It has been shown that optimal dual control is practically unsolvable for most cases (Aoki, 1967)." Fel'dbaum posed the Bayes-optimal exploration-exploitation problem in exact form; by his own account, and by later independent confirmation, he did not — and in general could not — solve it.

This intractability is the reason dual control's actual influence on later fields runs through approximations and reformulations rather than direct use of Fel'dbaum's own equations (see claim-mainstream-rl-exploration-traces-to-1933-bandit-lineage-not-feldbaum-dual-control).