A unified POMDP algorithm for sequential decisions under deep uncertainty: Robust satisficing, directed learning, and real options

Sequential decisions under deep uncertainty demand frameworks that enforce epistemic caution under model ambiguity, direct information acquisition toward critical unknowns, and preserve strategic flexibility before irreversible commitments. Standard Bayesian Decision Theory (BDT) assumes a well-specified prior, maximises expected utility myopically, and ignores the option to delay irreversible actions. We critically analyse three BDT extensions --- prescriptive Bayesian optimisation, robust and info-gap methods, and adaptive POMDP frameworks --- and expose a persistent integration gap: no single architecture simultaneously embeds all three properties within a Bellman recursion. Robust methods over-conserve without learning; adaptive methods explore without viability guarantees; real-options approaches delay without belief updating. We propose a unified POMDP framework combining robust satisficing for cross-model viability assurance, non-myopic value-of-information for directed learning, and real-options valuation for optimal commitment timing, embedded within a single sequential belief-update loop (Algorithm~1). Monte Carlo validation on ERA5-calibrated Biscayne Aquifer parameters (South Florida, n=1{,}000 trials) demonstrates 0.0% saltwater intrusion failure (95% CI [0%, 0.37%]) versus 59.1% under BDT and 9.5% under Dynamic Adaptive Policy Pathways (DAPP), at 91% lower total cost. The DAPP shortfall stems from reactive signpost lag (41% commit barrier after intrusion begins), which the unified framework avoids through proactive real-options timing. The framework generalises to capital allocation, supply chain management, and multi-stage investment scheduling, contributing a unified stochastic dynamic programming architecture to operations research under deep uncertainty.