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Cascading Bandits Robust to Adversarial Corruptions

Jize Xie, Cheng Chen, Zhiyong Wang, Shuai Li

TL;DR

This work introduces CBAC, the problem of cascading bandits under adaptive adversarial corruptions, and proposes two robust algorithms built on a novel Position-based Elimination framework. CascadeRKC targets known corruption levels, while CascadeRAC handles agnostic corruptions by deploying multiple robustness layers; both achieve $O(\log T)$ regret in stochastic regimes and exhibit regret that grows linearly with the corruption level when attacked. The authors provide rigorous high-probability regret bounds and demonstrate, through extensive synthetic and real-world experiments, that the proposed methods are robust to various corruption mechanisms and levels. The methods advance online learning to rank under adversarial conditions, with practical implications for reliable recommendations in environments prone to feedback manipulation.

Abstract

Online learning to rank sequentially recommends a small list of items to users from a large candidate set and receives the users' click feedback. In many real-world scenarios, users browse the recommended list in order and click the first attractive item without checking the rest. Such behaviors are usually formulated as the cascade model. Many recent works study algorithms for cascading bandits, an online learning to rank framework in the cascade model. However, the performance of existing methods may drop significantly if part of the user feedback is adversarially corrupted (e.g., click fraud). In this work, we study how to resist adversarial corruptions in cascading bandits. We first formulate the ``\textit{Cascading Bandits with Adversarial Corruptions}" (CBAC) problem, which assumes that there is an adaptive adversary that may manipulate the user feedback. Then we propose two robust algorithms for this problem, which assume the corruption level is known and agnostic, respectively. We show that both algorithms can achieve logarithmic regret when the algorithm is not under attack, and the regret increases linearly with the corruption level. The experimental results also verify the robustness of our methods.

Cascading Bandits Robust to Adversarial Corruptions

TL;DR

This work introduces CBAC, the problem of cascading bandits under adaptive adversarial corruptions, and proposes two robust algorithms built on a novel Position-based Elimination framework. CascadeRKC targets known corruption levels, while CascadeRAC handles agnostic corruptions by deploying multiple robustness layers; both achieve regret in stochastic regimes and exhibit regret that grows linearly with the corruption level when attacked. The authors provide rigorous high-probability regret bounds and demonstrate, through extensive synthetic and real-world experiments, that the proposed methods are robust to various corruption mechanisms and levels. The methods advance online learning to rank under adversarial conditions, with practical implications for reliable recommendations in environments prone to feedback manipulation.

Abstract

Online learning to rank sequentially recommends a small list of items to users from a large candidate set and receives the users' click feedback. In many real-world scenarios, users browse the recommended list in order and click the first attractive item without checking the rest. Such behaviors are usually formulated as the cascade model. Many recent works study algorithms for cascading bandits, an online learning to rank framework in the cascade model. However, the performance of existing methods may drop significantly if part of the user feedback is adversarially corrupted (e.g., click fraud). In this work, we study how to resist adversarial corruptions in cascading bandits. We first formulate the ``\textit{Cascading Bandits with Adversarial Corruptions}" (CBAC) problem, which assumes that there is an adaptive adversary that may manipulate the user feedback. Then we propose two robust algorithms for this problem, which assume the corruption level is known and agnostic, respectively. We show that both algorithms can achieve logarithmic regret when the algorithm is not under attack, and the regret increases linearly with the corruption level. The experimental results also verify the robustness of our methods.

Paper Structure

This paper contains 26 sections, 4 theorems, 22 equations, 5 figures, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. Relatet Works
  3. Cascading Bandits
  4. Bandits Robust to Adversarial Corruptions
  5. Problem Setup
  6. Algorithms
  7. The Position-based Elimination Algorithm
  8. The CascadeRKC Algorithm
  9. The CascadeRAC Algorithm
  10. Theoretical Analysis
  11. Regret Analysis of CascadeRKC
  12. Regret Analysis of CascadeRAC
  13. Discussions
  14. Experiments
  15. Experiments in Synthetic Datasets
  16. ...and 11 more sections

Key Result

Lemma 1

With probability at least $1-\delta$, when sampled with probability $1/C$, the corruption $C_{S}$ of $S$ instance in CascadeRKC can be bounded by $\log(1/\delta) + 3$ during its exploration phase.

Figures (5)

  • Figure 1: Comparison of cumulative regrets on the synthetic dataset with $L=500$ and $K=5$.
  • Figure 2: Cumulative regret on the real datasets. (a) shows the results in the Yelp dataset, (b) shows the results in the Movielens dataset, and (c) shows the results in the Yandex dataset.
  • Figure 3: Cumulative regret under different $\Delta$ between optimal items and the target item. (a) exhibits the results when $\Delta=0.1$, (b) exhibits the results when $\Delta=0.2$, and (c) exhibits the results when $\Delta=0.4$.
  • Figure 4: Cumulative regret under different corruption levels in the synthetic dataset.
  • Figure 5: Cumulative regret under different corruption levels in the Movielens dataset.

Theorems & Definitions (8)

  • Lemma 1
  • Lemma 2
  • Theorem 3
  • Theorem 4
  • proof
  • proof
  • proof
  • proof