We study an off-policy contextual pricing problem where the seller has access to samples of prices that customers were previously offered, whether they purchased at that price, and auxiliary features. This is in contrast to the well-studied setting in which samples of the customer's valuation are observed. We focus on convex loss functions for pricing in this setting, prove expected revenue bounds when the valuation distribution is log-concave, and provide generalization bounds.

We study the design of stochastic optimization methods with a focus on guaranteed out-of-sample performance when data is corrupted. We design a novel robust approach that offers protection against corruption while ensuring strong generalization. Our approach is based on distributionally robust optimization with a combination of Kullback-Leibler and Levy-Prokhorov ambiguity sets. Our method is applied to training neural networks, resulting in robust networks with state-of-the-art performance.

The paper presents dynamic pricing with demand learning in presence of covariates and develops safe UCB pricing algorithms. The pricing algorithm minimizes total regret where the expected regret of the pricing policy should be at least as good as a fraction of that of the baseline policy. We extend it to the case that the cumulative reward of the algorithm is at least as high as a fraction of the cumulative reward of the baseline policy with known and unknown baseline expected reward.