Targeting Makes Sample Efficiency in Auction Design

Abstract

This paper introduces the targeted sampling model in optimal auction design. In this model, the seller may specify a quantile interval and sample from a buyer's prior restricted to the interval. This can be interpreted as allowing the seller to, for example, examine the top 40% bids from previous buyers with the same characteristics. The targeting power is quantified with a parameter ∆ ∈ [0, 1] which lower bounds how small the quantile intervals could be. When ∆ = 1, it degenerates to Cole and Roughgarden's model of i.i.d. samples; when it is the idealized case of ∆ = 0, it degenerates to the model studied by Chen et al. [7]. For instance, for n buyers with bounded values in [0, 1],Õ (ϵ −1 ) targeted samples suffice while it is known that at leastΩ(nϵ −2 ) i.i.d. samples are needed. In other words, targeted sampling with sufficient targeting power allows us to remove the linear dependence in n, and to improve the quadratic dependence in ϵ −1 to linear. In this work, we introduce new technical ingredients and show that the number of targeted samples sufficient for learning an ϵ-optimal auction is substantially smaller than the sample complexity of i.i.d. samples for the full spectrum of ∆ ∈ [0, 1). Even with only mild targeting power, i.e., whenever ∆ = o(1), our targeted sample complexity upper bounds are strictly smaller than the optimal sample complexity of i.i.d. samples. CCS Concepts: • Theory of computation → Algorithmic game theory; Algorithmic mechanism design; Convergence and learning in games; Computational pricing and auctions.