Cascading Bandits: Learning to Rank in the Cascade Model

TL;DR

This paper introduces cascading bandits, a learning model for ranking in the cascade user behavior model, proposing algorithms with proven regret bounds and demonstrating strong empirical performance.

Contribution

It formulates cascading bandits as a stochastic combinatorial partial monitoring problem and proposes two algorithms with matching regret bounds.

Findings

CascadeKL-UCB achieves near-optimal regret bounds.

Algorithms perform well even with model assumption violations.

Proposed methods effectively identify attractive items in ranking tasks.

Abstract

A search engine usually outputs a list of $K$ web pages. The user examines this list, from the first web page to the last, and chooses the first attractive page. This model of user behavior is known as the cascade model. In this paper, we propose cascading bandits, a learning variant of the cascade model where the objective is to identify $K$ most attractive items. We formulate our problem as a stochastic combinatorial partial monitoring problem. We propose two algorithms for solving it, CascadeUCB1 and CascadeKL-UCB. We also prove gap-dependent upper bounds on the regret of these algorithms and derive a lower bound on the regret in cascading bandits. The lower bound matches the upper bound of CascadeKL-UCB up to a logarithmic factor. We experiment with our algorithms on several problems. The algorithms perform surprisingly well even when our modeling assumptions are violated.