We consider how to construct state abstractions compatible with a given set of abstract actions, to obtain a well-formed abstract Markov decision process (MDP). We show that the Bellman equation suggests that abstract states should represent distributions over states in the ground MDP; we characterize the conditions under which the resulting process is Markov and approximately model-preserving, derive an algorithm for constructing the abstract MDP, and apply it to visual chain and maze tasks. We generalize these results to the factored actions case, characterize the conditions that lead to factored abstract states, and apply the resulting algorithm to a visual grid and Montezuma's Revenge. These results provide a principled, powerful framework for learning neurosymbolic abstract Markov decision processes.

However, in domains where precise and succinct expert state information is available, agents trained onsuchexpert state features usually outperform agents trained onrichobservations.

Incontrast,our work is concerned with an overall limit on the total amount of information an agent may acquire fromtheenvironment and,inturn,howthattranslates intoitsselection ofafeasible learning target.

Blind-spot mass is a Good-Turing framework for quantifying deployment coverage risk in machine learning. In modern ML systems, operational state distributions are often heavy-tailed, implying that a long tail of valid but rare states is structurally under-supported in finite training and evaluation data. This creates a form of 'coverage blindness': models can appear accurate on standard test sets yet remain unreliable across large regions of the deployment state space. We propose blind-spot mass B_n(tau), a deployment metric estimating the total probability mass assigned to states whose empirical support falls below a threshold tau. B_n(tau) is computed using Good-Turing unseen-species estimation and yields a principled estimate of how much of the operational distribution lies in reliability-critical, under-supported regimes. We further derive a coverage-imposed accuracy ceiling, decomposing overall performance into supported and blind components and separating capacity limits from data limits. We validate the framework in wearable human activity recognition (HAR) using wrist-worn inertial data. We then replicate the same analysis in the MIMIC-IV hospital database with 275 admissions, where the blind-spot mass curve converges to the same 95% at tau = 5 across clinical state abstractions. This replication across structurally independent domains - differing in modality, feature space, label space, and application - shows that blind-spot mass is a general ML methodology for quantifying combinatorial coverage risk, not an application-specific artifact. Blind-spot decomposition identifies which activities or clinical regimes dominate risk, providing actionable guidance for industrial practitioners on targeted data collection, normalization/renormalization, and physics- or domain-informed constraints for safer deployment.

All experiments are run on Intel Xeon ICX Platinum 8358 and GeForce RTX 3090.

Furthermore, the theoretical guarantees of the transitivity and aggregation error bound are justified.

Incontrast,our work is concerned with an overall limit on the total amount of information an agent may acquire fromtheenvironment and,inturn,howthattranslates intoitsselection ofafeasible learning target.