Learning in Probabilistic Boolean Networks via Structural Policy Gradients

We revisit Probabilistic Boolean Networks as trainable function approximators. The key obstacle, non-differentiable structural choices (which predictors to read and which Boolean operators to apply), is addressed by casting the PBN's structure as a stochastic policy whose parameters are optimized with score-function (REINFORCE) gradients. Continuous output heads (logistic/linear/softmax or policy logits) are trained with ordinary gradients. We call the resulting model a Learning PBN. We formalize the Learning Probabilistic Boolean Network, derive unbiased structural gradients with variance reduction, and prove a universal approximation property over discretized inputs. Empirically, Learning Probabilistic Boolean Networks approach ANN performance across classification (accuracy ↑), regression (RMSE ↓), representation quality via clustering (ARI ↑), and reinforcement learning (return ↑) while yielding interpretable, rule-like internal units. We analyze the effect of binning resolution, operator sets, and unit counts, and show how the learned logic stabilizes as training progresses. Our results indicate that PBNs can serve as general-purpose learners, competitive with ANNs in tabular/noisy regimes, without sacrificing interpretability.