Uncertainty-Propagation Tree Acquisition

Integrate this as an active-learning or data-collection controller around an existing neural predictor. Maintain an ensemble of M networks with identical architecture and different bootstrap samples or random seeds. For every unlabeled candidate batch or simulator trajectory a, evaluate its points S(a), and estimate predictive variance v_t(z) from the ensemble predictions. Build a shallow tree of depth H=2 or 3. At every node, score each candidate using the displayed discounted objective. To estimate v_{t+1}^a cheaply, use a Bayesian linear update on the final layer: compute feature vectors phi(z) from the shared network, update the final-layer covariance with the candidate features, and recompute predictive variance. A more faithful version performs one small gradient update per ensemble member on newly labeled observations and recalculates variance. Use 100-500 random rollouts with UCB child selection, execute only the first action of the best root path, acquire that batch, retrain, and repeat. Compute the weighted variance reduction and transition cost directly; estimate ensemble variance, hypothetical posterior updates, and candidate costs empirically. First experiment on CIFAR-10: start with 1,000 labels, create 20 candidate batches using uncertainty clustering, and compare random sampling, greedy ensemble-variance sampling, and MCTS with H=3. The prediction is that the second greedy batch becomes increasingly redundant, while MCTS improves cumulative weighted variance reduction per label by at least 10% when candidates overlap. The gain should disappear when candidate batches are statistically independent, confirming that propagated posterior state, rather than generic exploration, causes the improvement.