Assortment optimization selects a subset of items to maximize expected revenue under a discrete choice model and is widely used in revenue management and online platforms. Its combinatorial nature creates a practical tension among generality, scalability, and provable guarantees: model-specific algorithms can be strong when their structural assumptions hold, but are hard to adapt across choice models; broadly applicable heuristics and learning-based methods scale to large instances but often come without near-optimality guarantees.
We propose Neural Assortment Optimization (NAO), a choice-model-agnostic optimization framework that only requires an oracle that evaluates the expected revenue of a candidate assortment.
NAO follows an “extend-particle search-round” pipeline: it constructs a tight continuous extension of the discrete objective, then optimizes a population of interacting particles using noisy subgradient descent, and finally rounds candidates back to discrete assortments. The particle objective admits a simple neural-network interpretation: each particle can be viewed as a hidden neuron, and an entropic-risk pooling layer emphasizes the best-performing candidates during optimization.
We establish global convergence and near-optimality guarantees under mild conditions, and extend the method to cardinality constraints via a capacity-aware rolling-window construction. Experiments on challenging Mixed ultinomial Logit and Nested Logit benchmarks show that NAO achieves near-optimal revenue with strong computational efficiency, consistently outperforming competitive heuristics and neural baselines and scaling well to large instances.