UDuo: Universal Dual Optimization Framework for Online Matching

TL;DR

The paper tackles online matching under budget constraints in nonstationary environments by formulating a dual optimization problem with a temporal arrival representation $v(lambda) = \sum_i \max_j (r_{ij} - lambda c_{ij})$ and the corresponding objective $L(lambda) = lambda B + v(lambda)$. It introduces UDuo, a general-purpose framework combining time-series forecasting of future arrival representations, budget pacing (temporal-aware and generative), and a cross-scenario forecasting core (MiFormer) to maintain feasibility while optimizing resource use. The approach is validated with real-world dynamic pricing data from a large food-delivery platform, showing improved efficiency and faster convergence over stochastic arrival-based baselines, and MiFormer demonstrates an 8% reduction in forecasting error across multiple UAV benchmarks and production datasets. Overall, UDuo provides a principled, transferable method for proactive, constraint-feasible online allocation in environments with distribution shifts, with broad applicability to online matching and budgeted optimization problems.

Abstract

Online resource allocation under budget constraints critically depends on proper modeling of user arrival dynamics. Classical approaches employ stochastic user arrival models to derive near-optimal solutions through fractional matching formulations of exposed users for downstream allocation tasks. However, this is no longer a reasonable assumption when the environment changes dynamically. In this work, We propose the Universal Dual optimization framework UDuo, a novel paradigm that fundamentally rethinks online allocation through three key innovations: (i) a temporal user arrival representation vector that explicitly captures distribution shifts in user arrival patterns and resource consumption dynamics, (ii) a resource pacing learner with adaptive allocation policies that generalize to heterogeneous constraint scenarios, and (iii) an online time-series forecasting approach for future user arrival distributions that achieves asymptotically optimal solutions with constraint feasibility guarantees in dynamic environments. Experimental results show that UDuo achieves higher efficiency and faster convergence than the traditional stochastic arrival model in real-world pricing while maintaining rigorous theoretical validity for general online allocation problems.

Figures (1)

• Figure 1: Illustration of the UDuo framework. Take the food delivery scenario as an example: When a user initiates a coupon redemption request, we first apply a pretrained uplift model with frozen parameters to generate response scores for multi-treatment coupon denominations, capturing each user's incremental response propensity to different discounts. Subsequently, the target user cohort is aggregated into temporal sequences of user arrival representation vectors via Eq. \ref{['vlambda']}. Next, our online solver module performs a binary search over future time slots using pacing-adjusted budgets and predicted $v(\lambda)$ vectors to derive optimal dual solutions. Finally, these dual solutions feed into the decision Eq. \ref{['rank_eq']} to finalize the ranking and allocation of coupon denominations.