Active Cost-aware Labeling of Streaming Data

We study actively labeling streaming data, where an active learner is faced with a stream of data points and must carefully choose which of these points to label via an expensive experiment. Such problems frequently arise in applications such as healthcare and astronomy. We first study a setting when the data's inputs belong to one of $K$ discrete distributions and formalize this problem via a loss that captures the labeling cost and the prediction error. When the labeling cost is $B$, our algorithm, which chooses to label a point if the uncertainty is larger than a time and cost dependent threshold, achieves a worst-case upper bound of $O(B^{\frac{1}{3}} K^{\frac{1}{3}} T^{\frac{2}{3}})$ on the loss after $T$ rounds. We also provide a more nuanced upper bound which demonstrates that the algorithm can adapt to the arrival pattern, and achieves better performance when the arrival pattern is more favorable. We complement both upper bounds with matching lower bounds. We next study this problem when the inputs belong to a continuous domain and the output of the experiment is a smooth function with bounded RKHS norm. After $T$ rounds in $d$ dimensions, we show that the loss is bounded by $O(B^{\frac{1}{d+3}} T^{\frac{d+2}{d+3}})$ in an RKHS with a squared exponential kernel and by $O(B^{\frac{1}{2d+3}} T^{\frac{2d+2}{2d+3}})$ in an RKHS with a Mat\'ern kernel. Our empirical evaluation demonstrates that our method outperforms other baselines in several synthetic experiments and two real experiments in medicine and astronomy

Leveraging Reviews: Learning to Price with Buyer and Seller Uncertainty

In online marketplaces, customers have access to hundreds of reviews for a single product. Buyers often use reviews from other customers that share their type -- such as height for clothing, skin type for skincare products, and location for outdoor furniture -- to estimate their values, which they may not know a priori. Customers with few relevant reviews may hesitate to make a purchase except at a low price, so for the seller, there is a tension between setting high prices and ensuring that there are enough reviews so that buyers can confidently estimate their values. Simultaneously, sellers may use reviews to gauge the demand for items they wish to sell. In this work, we study this pricing problem in an online setting where the seller interacts with a set of buyers of finitely many types, one by one, over a series of $T$ rounds. At each round, the seller first sets a price. Then a buyer arrives and examines the reviews of the previous buyers with the same type, which reveal those buyers' ex-post values. Based on the reviews, the buyer decides to purchase if they have good reason to believe that their ex-ante utility is positive. Crucially, the seller does not know the buyer's type when setting the price, nor even the distribution over types. We provide a no-regret algorithm that the seller can use to obtain high revenue. When there are $d$ types, after $T$ rounds, our algorithm achieves a problem-independent $\tilde O(T^{2/3}d^{1/3})$ regret bound. However, when the smallest probability $q_{\text{min}}$ that any given type appears is large, specifically when $q_{\text{min}} \in \Omega(d^{-2/3}T^{-1/3})$, then the same algorithm achieves a $\tilde O(T^{1/2}q_{\text{min}}^{-1/2})$ regret bound. We complement these upper bounds with matching lower bounds in both regimes, showing that our algorithm is minimax optimal up to lower-order terms