Learning to Solve Two-Stage Stochastic Unit Commitment Problems with Quality Guarantees
TL;DR
An Input Convex Neural Network architecture is proposed to learn a convex surrogate of the second-stage value function, enabling fast first-stage optimization while preserving convexity by construction.
Abstract
Two-stage stochastic Mixed-Integer Linear Programs are a canonical modeling tool to optimize power system operations under uncertainty, yet their extensive-form counterparts scale linearly with the number of scenarios and quickly become computationally prohibitive under day-ahead time constraints. We propose an Input Convex Neural Network architecture to learn a convex surrogate of the second-stage value function, enabling fast first-stage optimization while preserving convexity by construction. We couple the surrogate with a Neural-Benders correction loop that refines the first-stage solution a posteriori, recovering the exact optimum whether the network overestimates or underestimates the recourse cost, and certifying solution quality independently of surrogate accuracy. We evaluate the method on IEEE Stochastic Unit Commitment benchmarks (case9-case118) under both continuous and integer recourse. The proposed approach achieves solutions with zero optimality gap on the $K$-scenario instance across all test cases and scenario dimensions $K \in \{10, 50, 100\}$, with speedups up to $214\times$ over the Extensive Form in the integer setting. Solve times are stable across scenario realizations and compatible with day-ahead time windows on the tested benchmark instances.