Primal--Dual Alternating Neural Learning for Timely Classification with Performance Guarantees

This paper introduces Timely Decisions with Primal–dual Alternating Neural Learning, or TD-PANL, for sequential classification when decisions must balance sensitivity, specificity, and monitoring cost. It formulates the task as a constrained Neyman–Pearson problem: maximize specificity while enforcing user-specified sensitivity and cost targets. The optimal rule uses a Bellman-style value recursion, stopping when the immediate benefit of classifying exceeds the expected benefit of collecting more observations. TD-PANL estimates conditional risk and continuation value with shared recurrent neural networks, specifically gated recurrent units, while alternating primal gradient updates for the value network with dual ascent on Lagrange multipliers; this avoids costly grid searches over constraint weights. In simulations with sequence length T=5 and 50 repeated experiments, the method nearly recovered the optimal Pareto frontier in Markov and probit settings, consistently outperforming fixed-time myopic classification and exceeding FIRMBOUND in the more difficult bi-modal setting. In continuous glucose monitoring, the study used 201 participants and 8,192 bootstrapped monitoring windows, each containing T=13 five-minute measurements. Under a sensitivity target of 0.95, TD-PANL reached near-maximal specificity of 0.8 at an average normalized cost of 0.7, corresponding to an approximately 18-minute lead time, while the myopic baseline required the full one-hour window. The result is an interpretable early-warning policy with explicit empirical performance guarantees rather than an accuracy–earliness trade-off alone.