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COBRA: Contextual Bandit Algorithm for Ensuring Truthful Strategic Agents

Arun Verma, Indrajit Saha, Makoto Yokoo, Bryan Kian Hsiang Low

TL;DR

The paper addresses contextual bandits with multiple strategic agents who may misreport arm features to gain more selections. It introduces LOOM, a VCG-inspired Leave-One-Out mechanism, to detect misreporting using cross-agent data, and COBRA, an incentive-compatible contextual bandit algorithm that leverages LOOM to disincentivize strategic manipulation without payments. In the linear case, COBRA achieves an $ ilde{O}(d\sqrt{T})$-NE and sub-linear regret $\tilde{O}(d\sqrt{T})$ when agents report truthfully, with a broader bound $\tilde{O}(d\sqrt{T}+\sqrt{NT})$ under any Nash equilibrium; the approach extends to non-linear rewards via LOOM-compatible bandits. Empirical results corroborate the theory, showing COBRA outperforms baselines and that TS-based variants typically perform best, validating the practicality of non-monetary incentive design in strategic contextual bandits.

Abstract

This paper considers a contextual bandit problem involving multiple agents, where a learner sequentially observes the contexts and the agent's reported arms, and then selects the arm that maximizes the system's overall reward. Existing work in contextual bandits assumes that agents truthfully report their arms, which is unrealistic in many real-life applications. For instance, consider an online platform with multiple sellers; some sellers may misrepresent product quality to gain an advantage, such as having the platform preferentially recommend their products to online users. To address this challenge, we propose an algorithm, COBRA, for contextual bandit problems involving strategic agents that disincentivize their strategic behavior without using any monetary incentives, while having incentive compatibility and a sub-linear regret guarantee. Our experimental results also validate the different performance aspects of our proposed algorithm.

COBRA: Contextual Bandit Algorithm for Ensuring Truthful Strategic Agents

TL;DR

The paper addresses contextual bandits with multiple strategic agents who may misreport arm features to gain more selections. It introduces LOOM, a VCG-inspired Leave-One-Out mechanism, to detect misreporting using cross-agent data, and COBRA, an incentive-compatible contextual bandit algorithm that leverages LOOM to disincentivize strategic manipulation without payments. In the linear case, COBRA achieves an -NE and sub-linear regret when agents report truthfully, with a broader bound under any Nash equilibrium; the approach extends to non-linear rewards via LOOM-compatible bandits. Empirical results corroborate the theory, showing COBRA outperforms baselines and that TS-based variants typically perform best, validating the practicality of non-monetary incentive design in strategic contextual bandits.

Abstract

This paper considers a contextual bandit problem involving multiple agents, where a learner sequentially observes the contexts and the agent's reported arms, and then selects the arm that maximizes the system's overall reward. Existing work in contextual bandits assumes that agents truthfully report their arms, which is unrealistic in many real-life applications. For instance, consider an online platform with multiple sellers; some sellers may misrepresent product quality to gain an advantage, such as having the platform preferentially recommend their products to online users. To address this challenge, we propose an algorithm, COBRA, for contextual bandit problems involving strategic agents that disincentivize their strategic behavior without using any monetary incentives, while having incentive compatibility and a sub-linear regret guarantee. Our experimental results also validate the different performance aspects of our proposed algorithm.

Paper Structure

This paper contains 17 sections, 16 theorems, 89 equations, 5 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Contextual Bandits with Strategic Agents
  4. Leave-One-Out-based Mechanism (LOOM)
  5. Incentive-Compatible Contextual Bandit Algorithm: COBRA
  6. NE and Regret Analysis
  7. Experiments
  8. Conclusion
  9. Leftover Proofs
  10. Leftover proofs from Section 3
  11. Leftover proofs from Section 4
  12. Proof of Theorem 2
  13. Proof of Theorem 3
  14. Non-linear Reward Function
  15. Theoretical Results
  16. ...and 2 more sections

Key Result

Lemma 1

Let $S_t(a)$ be the number of times that agent $a$ is selected until round $t$, and $\varepsilon_s$ be $R$-sub-Gaussian in the observed reward $y_s$, where $1 \le s \le t$. Then, with probability at least $1-\delta_{t,a}^y$

Figures (5)

  • Figure 1: Example of a contextual bandit problem with strategic agents: Consider an online platform recommending service providers (agents) to users (context) who arrive sequentially. Since service providers can misreport their private information to receive more recommendations, the platform must implement a mechanism incentivizing truthful reporting. With accurate private information, the platform can recommend the best service provider, thereby improving the overall user experience.
  • Figure 2: Comparing cumulative regret of COBRA with different baselines.
  • Figure 3: Cumulative regret of COBRA vs. different types of strategic manipulations.
  • Figure 4: Cumulative regret of COBRA vs. different values of $N$ and $d$.
  • Figure 5: Comparing the cumulative regret of COBRA with different baselines for problem instances with non-linear reward functions.

Theorems & Definitions (33)

  • Definition 1: Truthful
  • Definition 2: $\varepsilon$-Nash Equilibrium
  • Definition 3: Incentive Compatible
  • Lemma 1
  • Theorem 1
  • Remark 1: Agent under-reporting.
  • Theorem 2
  • Theorem 3
  • Lemma 1
  • proof
  • ...and 23 more