Approximation Algorithms for Action-Reward Query-Commit Matching

TL;DR

This paper introduces a new stochastic matching problem model that generalizes query-commit matching by incorporating actions and rewards, and provides improved approximation algorithms for bipartite graphs under patience constraints.

Contribution

It develops efficient algorithms with better approximation ratios for the action-reward query-commit matching problem, extending prior work on sequential pricing and stochastic matching.

Findings

Achieved approximation ratios of approximately 0.63 and 0.58 for one-sided and two-sided patience settings.

Improved upon previous guarantees of 0.426 and 0.395 for related problems.

Provided computationally efficient algorithms for a broad class of stochastic matching problems.

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 $0.395$.