What bothers me in The Basic AI Drives is a complete lack of quantitativeness.
Temporal discount rate isn’t even mentioned. No analysis of self-improvement/getting-things-done tradeoff. Influence of explicit / implicit utility function dichotomy on self-improvement aren’t considered.
Probabilistic inference for general belief networks is NP-hard (see The Computational Complexity of Probabilistic Inference Using Bayesian Belief Networks (PDF)). Thus straitforward approach is not an option. The problem is more like finding computationally tractable yet sufficiently powerful subtype of belief networks.