Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Online Learning to Rank under Corruption: A Robust Cascading Bandits Approach

Fatemeh Ghaffari, Siddarth Sitaraman, Xutong Liu, Xuchuang Wang, Mohammad Hajiesmaili

TL;DR

This work tackles online learning to rank under corrupted feedback by developing M2UCB-V, a corruption-robust cascading bandit algorithm. It fuses a calibrated mean-of-medians estimator with a variance-aware UCB and a model-selection wrapper to adapt automatically to unknown corruption levels, achieving near-optimal regret in the corruption-free setting and additive $O(KC)$ regret under corruption. Theoretical guarantees are complemented by extensive experiments on Yelp, MovieLens, and LastFM, where M2UCB-V consistently outperforms strong baselines across diverse corruption levels. The practical impact is a robust OLTR method capable of maintaining performance in real-world, fraud-prone environments without prior knowledge of the corruption budget. The paper also extends CBARBAR to the cascading setting as CascadeCBARBAR for comparison. Overall, M2UCB-V represents the first corruption-robust cascading bandit method that attains stochastic-optimal performance while adapting to unknown corruption and delivering strong empirical results.

Abstract

Online learning to rank (OLTR) studies how to recommend a short ranked list of items from a large pool and improves future rankings based on user clicks. This setting is commonly modeled as cascading bandits, where the objective is to maximize the likelihood that the user clicks on at least one of the presented items across as many timesteps as possible. However, such systems are vulnerable to click fraud and other manipulations (i.e., corruption), where bots or paid click farms inject corrupted feedback that misleads the learning process and degrades user experience. In this paper, we propose MSUCB, a robust algorithm that incorporates a novel mean-of-medians estimator, which to our knowledge is applied to bandits with corruption setting for the first time. This estimator behaves like a standard mean in the absence of corruption, so no cost is paid for robustness. Under corruption, the median step filters out outliers and corrupted samples, keeping the estimate close to its true value. Updating this estimate at every round further accelerates empirical convergence in experiments. Hence, MSUCB achieves optimal logarithmic regret in the absence of corruption and degrades gracefully under corruptions, with regret increasing only by an additive term tied to the total corruption. Comprehensive and extensive experiments on real-world datasets further demonstrate that our approach consistently outperforms prior methods while maintaining strong robustness. In particular, it achieves a \(97.35\%\) and a \(91.60\%\) regret improvement over two state-of-the-art methods.

Online Learning to Rank under Corruption: A Robust Cascading Bandits Approach

TL;DR

This work tackles online learning to rank under corrupted feedback by developing M2UCB-V, a corruption-robust cascading bandit algorithm. It fuses a calibrated mean-of-medians estimator with a variance-aware UCB and a model-selection wrapper to adapt automatically to unknown corruption levels, achieving near-optimal regret in the corruption-free setting and additive regret under corruption. Theoretical guarantees are complemented by extensive experiments on Yelp, MovieLens, and LastFM, where M2UCB-V consistently outperforms strong baselines across diverse corruption levels. The practical impact is a robust OLTR method capable of maintaining performance in real-world, fraud-prone environments without prior knowledge of the corruption budget. The paper also extends CBARBAR to the cascading setting as CascadeCBARBAR for comparison. Overall, M2UCB-V represents the first corruption-robust cascading bandit method that attains stochastic-optimal performance while adapting to unknown corruption and delivering strong empirical results.

Abstract

Online learning to rank (OLTR) studies how to recommend a short ranked list of items from a large pool and improves future rankings based on user clicks. This setting is commonly modeled as cascading bandits, where the objective is to maximize the likelihood that the user clicks on at least one of the presented items across as many timesteps as possible. However, such systems are vulnerable to click fraud and other manipulations (i.e., corruption), where bots or paid click farms inject corrupted feedback that misleads the learning process and degrades user experience. In this paper, we propose MSUCB, a robust algorithm that incorporates a novel mean-of-medians estimator, which to our knowledge is applied to bandits with corruption setting for the first time. This estimator behaves like a standard mean in the absence of corruption, so no cost is paid for robustness. Under corruption, the median step filters out outliers and corrupted samples, keeping the estimate close to its true value. Updating this estimate at every round further accelerates empirical convergence in experiments. Hence, MSUCB achieves optimal logarithmic regret in the absence of corruption and degrades gracefully under corruptions, with regret increasing only by an additive term tied to the total corruption. Comprehensive and extensive experiments on real-world datasets further demonstrate that our approach consistently outperforms prior methods while maintaining strong robustness. In particular, it achieves a and a regret improvement over two state-of-the-art methods.

Paper Structure

This paper contains 31 sections, 9 theorems, 39 equations, 4 figures, 1 table, 5 algorithms.

Table of Contents

  1. Introduction
  2. Algorithm design
  3. Theoretical guarantees.
  4. Empirical evaluation.
  5. Related Work
  6. Cascading Bandits
  7. Bandits with Adversarial Corruption
  8. Problem Setting
  9. Cascading Bandits
  10. Adversarial Corruption Model
  11. The M2UCB-V Algorithm
  12. The Mean-of-Medians Estimator
  13. MUCB-V
  14. Integration into Model Selection Framework.
  15. Theoretical Analysis
  16. ...and 16 more sections

Key Result

Theorem 1

The expected regret of the MUCB-V in a cascading bandits setting with corruption of level at most $C$ is bounded by:

Figures (4)

  • Figure 1: Comparing final cumulative regret of the algorithms after 40K rounds with list size $d=10$.
  • Figure 2: Growth of cumulative regret as a function of rounds for the Yelp dataset, with list size $d=10$.
  • Figure 3: Growth of cumulative regret as a function of rounds for the MovieLens dataset, with list size $d=10$.
  • Figure 4: Growth of cumulative regret as a function of rounds for the LastFM dataset, with list size $d=10$.

Theorems & Definitions (9)

  • Theorem 1
  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Theorem 2: Regret of M2UCB-V
  • Lemma 3
  • Lemma 3
  • Lemma 3
  • Proposition 1