Sponsored search positions are typically allocated through real-time auctions, where the outcomes depend on advertisers' quality-adjusted bids - the product of their bids and quality scores. Although quality scoring helps promote ads with higher conversion outcomes, setting these scores for new advertisers in any given market is challenging, leading to the cold-start problem. To address this, platforms incorporate multi-armed bandit algorithms in auctions to balance exploration and exploitation. However, little is known about the optimal exploration strategies in such auction environments. We utilize data from a leading Asian mobile app store that places sponsored ads for keywords. The platform employs a Thompson Sampling algorithm within a second-price auction to learn quality scores and allocate a single sponsored position for each keyword. We empirically quantify the gains from optimizing exploration under this combined auction-bandit model and show that this problem differs substantially from the canonical bandit problem. Drawing on these empirical insights, we propose a customized exploration strategy in which the platform adjusts the exploration levels for each keyword according to its characteristics. We derive the Pareto frontier for revenue and efficiency and provide actionable policies, demonstrating substantial gains for the platform on both metrics when using a tailored exploration approach.

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