We present a complete theoretical characterization of Latent Posterior Factors (LPF), a principled framework for aggregating multiple heterogeneous evidence items in probabilistic prediction tasks. Multi-evidence reasoning arises pervasively in high-stakes domains including healthcare diagnosis, financial risk assessment, legal case analysis, and regulatory compliance, yet existing approaches either lack formal guarantees or fail to handle multi-evidence scenarios architecturally. LPF encodes each evidence item into a Gaussian latent posterior via a variational autoencoder, converting posteriors to soft factors through Monte Carlo marginalization, and aggregating factors via exact Sum-Product Network inference (LPF-SPN) or a learned neural aggregator (LPF-Learned). We prove seven formal guarantees spanning the key desiderata for trustworthy AI: Calibration Preservation (ECE <= epsilon + C/sqrt(K_eff)); Monte Carlo Error decaying as O(1/sqrt(M)); a non-vacuous PAC-Bayes bound with train-test gap of 0.0085 at N=4200; operation within 1.12x of the information-theoretic lower bound; graceful degradation as O(epsilon*delta*sqrt(K)) under corruption, maintaining 88% performance with half of evidence adversarially replaced; O(1/sqrt(K)) calibration decay with R^2=0.849; and exact epistemic-aleatoric uncertainty decomposition with error below 0.002%. All theorems are empirically validated on controlled datasets spanning up to 4,200 training examples. Our theoretical framework establishes LPF as a foundation for trustworthy multi-evidence AI in safety-critical applications.

Learning reliably safe autonomous control is one of the core problems in trustworthy autonomy.

We consider the problem of Imitation Learning (IL) by actively querying noisy expert for feedback.

Hierarchical Bayesian bandit refers to the multi-task bandit problem in which bandit tasks are assumed to be drawn from the same distribution.

This approach is often preferable when using "standard" parametric5 regression algorithms, as the weighted p-norm can be directly minimized at learning time (e.g., in least-squares6 regression,the`2-normisminimized). This is not surprising as in the worst case the inherent Bellman error may12 be unbounded and standard AVI tends to diverge. Recent work (Jinglin Chen, Nan Jiang,Information-Theoretic13 Considerations in Batch Reinforcement Learning, ICML 2019, Conjecture 8) has even conjectured an exponential14 lower bound in case of unbounded Bellman error. In the paper we propose afirst heuristic algorithm to automatically construct aset22 ofanchor points (see beginning ofpage 6). Akeybenefit ofourapproach isthat itdoes notmodify theunderlying (linear) feature51 representation, allowing theuser tousethelinear representation with, forexample, approximate value iteration, and52 should this fail, the user can switch toour algorithm and progressively increase the number of support points while53 keeping the same feature representation.