Approximation Algorithms for Action-Reward Query-Commit Matching

2026-03-13

AI Summary

This study addresses the query-commit matching problem with action selection: in a bipartite graph, a decision maker sequentially probes edges under node patience constraints (i.e., maximum allowable queries per node), and at each step may choose an action that influences both the success probability and the associated reward; upon success, the edge is irrevocably added to the matching and yields its reward. This framework strictly generalizes classical stochastic matching problems such as sequential pricing. By integrating techniques from stochastic optimization and combinatorial algorithms, the authors design polynomial-time approximation algorithms for both single-sided and double-sided patience settings, achieving approximation ratios of approximately 0.63 and 0.58, respectively—substantially improving upon the prior best-known guarantees of 0.426 and 0.395 for sequential pricing.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Matching problems under uncertainty arise in applications such as kidney exchange, hiring, and online marketplaces. A decision-maker must sequentially explore potential matches under local exploration constraints, while committing irrevocably to successful matches as they are revealed. The query-commit matching problem captures these challenges by modeling edges that succeed independently with known probabilities and must be accepted upon success, subject to vertex patience (time-out) constraints limiting the number of incident queries. In this work, we introduce the action-reward query-commit matching problem, a strict generalization of query-commit matching in which each query selects an action from a known action space, determining both the success probability and the reward of the queried edge. If an edge is queried using a chosen action and succeeds, it is irrevocably added to the matching, and the corresponding reward is obtained; otherwise, the edge is permanently discarded. We study the design of approximation algorithms for this problem on bipartite graphs. This model captures a broad class of stochastic matching problems, including the sequential pricing problem introduced by Pollner, Roghani, Saberi, and Wajc (EC~2022). On the positive side, Pollner et al. designed a polynomial-time approximation algorithm achieving a ratio of $0.426$ in the one-sided patience setting, which degrades to $0.395$ when both sides have bounded patience. In this work, we design computationally efficient algorithms for the action-reward query-commit in one-sided and two-sided patience settings, achieving approximation ratios of $1-1/e \approx 0.63$ and $\frac{1}{27}\!\left(19-67/e^3\right) \approx 0.58$ respectively. These results improve the state of the art for the sequential pricing problem, surpassing the previous guarantees of $0.426$ and $0.395$.

Problem

• query-commit matching
• action-reward
• stochastic matching
• patience constraints
• approximation algorithms

Innovation

• action-reward query-commit matching
• approximation algorithms
• stochastic matching
• patience constraints
• sequential pricing