Combinatorial Allocation Bandits with Nonlinear Arm Utility

TL;DR

This paper introduces Combinatorial Allocation Bandits, a new online learning framework focusing on maximizing arm satisfaction in matching platforms, with algorithms that achieve near-optimal regret bounds and demonstrate effectiveness in synthetic experiments.

Contribution

The paper formulates the novel CAB problem incorporating arm satisfaction, and develops UCB and TS algorithms with theoretical regret guarantees and empirical validation.

Findings

Proposed algorithms achieve near-optimal regret bounds.

Algorithms outperform existing methods in synthetic experiments.

Arm satisfaction maximization reduces participant churn.

Abstract

A matching platform is a system that matches different types of participants, such as companies and job-seekers. In such a platform, merely maximizing the number of matches can result in matches being concentrated on highly popular participants, which may increase dissatisfaction among other participants, such as companies, and ultimately lead to their churn, reducing the platform's profit opportunities. To address this issue, we propose a novel online learning problem, Combinatorial Allocation Bandits (CAB), which incorporates the notion of *arm satisfaction*. In CAB, at each round $t=1,\dots,T$, the learner observes $K$ feature vectors corresponding to $K$ arms for each of $N$ users, assigns each user to an arm, and then observes feedback following a generalized linear model (GLM). Unlike prior work, the learner's objective is not to maximize the number of positive feedback, but rather to maximize the arm satisfaction. For CAB, we provide an upper confidence bound algorithm that achieves an approximate regret upper bound, which matches the existing lower bound for the special case. Furthermore, we propose a TS algorithm and provide an approximate regret upper bound. Finally, we conduct experiments on synthetic data to demonstrate the effectiveness of the proposed algorithms compared to other methods.