Bandits Meet Mechanism Design to Combat Clickbait in Online Recommendation

TL;DR

This paper introduces the strategic click-bandit model for online recommendations, addressing strategic behavior of arms and proposing an incentive-aware algorithm that balances learning and strategic incentives, achieving low regret.

Contribution

It develops UCB-S, the first incentive-aware algorithm for strategic bandits, and characterizes equilibrium behavior with provable regret bounds.

Findings

UCB-S incentivizes desirable arm behavior under uncertainty.

Achieves $ ilde{O}( oot{K}{T})$ regret uniformly across equilibria.

Incentive-unaware algorithms perform poorly in strategic settings.

Abstract

We study a strategic variant of the multi-armed bandit problem, which we coin the strategic click-bandit. This model is motivated by applications in online recommendation where the choice of recommended items depends on both the click-through rates and the post-click rewards. Like in classical bandits, rewards follow a fixed unknown distribution. However, we assume that the click-rate of each arm is chosen strategically by the arm (e.g., a host on Airbnb) in order to maximize the number of times it gets clicked. The algorithm designer does not know the post-click rewards nor the arms' actions (i.e., strategically chosen click-rates) in advance, and must learn both values over time. To solve this problem, we design an incentive-aware learning algorithm, UCB-S, which achieves two goals simultaneously: (a) incentivizing desirable arm behavior under uncertainty; (b) minimizing regret by learning unknown parameters. We characterize all approximate Nash equilibria among arms under UCB-S and show a $\tilde{\mathcal{O}} (\sqrt{KT})$ regret bound uniformly in every equilibrium. We also show that incentive-unaware algorithms generally fail to achieve low regret in the strategic click-bandit. Finally, we support our theoretical results by simulations of strategic arm behavior which confirm the effectiveness and robustness of our proposed incentive design.