Convex Loss Functions for Contextual Pricing with Observational
Posted-Price Data
- URL: http://arxiv.org/abs/2202.10944v1
- Date: Wed, 16 Feb 2022 22:35:39 GMT
- Title: Convex Loss Functions for Contextual Pricing with Observational
Posted-Price Data
- Authors: Max Biggs
- Abstract summary: We study an off-policy contextual pricing problem where the seller has access to samples of prices which customers were previously offered.
This is in contrast to the well-studied setting in which samples of the customer's valuation (willingness to pay) are observed.
In our setting, the observed data is influenced by the historic pricing policy, and we do not know how customers would have responded to alternative prices.
- Score: 2.538209532048867
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We study an off-policy contextual pricing problem where the seller has access
to samples of prices which customers were previously offered, whether they
purchased at that price, and auxiliary features describing the customer and/or
item being sold. This is in contrast to the well-studied setting in which
samples of the customer's valuation (willingness to pay) are observed. In our
setting, the observed data is influenced by the historic pricing policy, and we
do not know how customers would have responded to alternative prices. We
introduce suitable loss functions for this pricing setting which can be
directly optimized to find an effective pricing policy with expected revenue
guarantees without the need for estimation of an intermediate demand function.
We focus on convex loss functions. This is particularly relevant when linear
pricing policies are desired for interpretability reasons, resulting in a
tractable convex revenue optimization problem. We further propose generalized
hinge and quantile pricing loss functions, which price at a multiplicative
factor of the conditional expected value or a particular quantile of the
valuation distribution when optimized, despite the valuation data not being
observed. We prove expected revenue bounds for these pricing policies
respectively when the valuation distribution is log-concave, and provide
generalization bounds for the finite sample case. Finally, we conduct
simulations on both synthetic and real-world data to demonstrate that this
approach is competitive with, and in some settings outperforms,
state-of-the-art methods in contextual pricing.
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