Su Jia

Titing Cui, Su Jia, Thomas Lavastida · cmu

Dynamic pricing models often posit that a $\textbf{stream}$ of customer interactions occur sequentially, where customers' valuations are drawn independently. However, this model is not entirely reflective of the real world, as it overlooks a critical aspect, the law of diminishing marginal utility, which states that a customer's marginal utility from each additional unit declines. This causes the valuation distribution to shift towards the lower end, which is not captured by the stream model. This motivates us to study a pool-based model, where a $\textbf{pool}$ of customers repeatedly interacts with a monopolist seller, each of whose valuation diminishes in the number of purchases made according to a discount function. In particular, when the discount function is constant, our pool model recovers the stream model. We focus on the most fundamental special case, where a customer's valuation becomes zero once a purchase is made. Given $k$ prices, we present a non-adaptive, detail-free (i.e., does not "know" the valuations) policy that achieves a $1/k$ competitive ratio, which is optimal among non-adaptive policies. Furthermore, based on a novel debiasing technique, we propose an adaptive learn-then-earn policy with a $\tilde O(k^{2/3} n^{2/3})$ regret.

Su Jia, Fatemeh Navidi, Viswanath Nagarajan et al.

In pool-based active learning, the learner is given an unlabeled data set and aims to efficiently learn the unknown hypothesis by querying the labels of the data points. This can be formulated as the classical Optimal Decision Tree (ODT) problem: Given a set of tests, a set of hypotheses, and an outcome for each pair of test and hypothesis, our objective is to find a low-cost testing procedure (i.e., decision tree) that identifies the true hypothesis. This optimization problem has been extensively studied under the assumption that each test generates a deterministic outcome. However, in numerous applications, for example, clinical trials, the outcomes may be uncertain, which renders the ideas from the deterministic setting invalid. In this work, we study a fundamental variant of the ODT problem in which some test outcomes are noisy, even in the more general case where the noise is persistent, i.e., repeating a test gives the same noisy output. Our approximation algorithms provide guarantees that are nearly best possible and hold for the general case of a large number of noisy outcomes per test or per hypothesis where the performance degrades continuously with this number. We numerically evaluated our algorithms for identifying toxic chemicals and learning linear classifiers, and observed that our algorithms have costs very close to the information-theoretic minimum.

Kyra Gan, Su Jia, Andrew Li

In the problem of active sequential hypothesis testing (ASHT), a learner seeks to identify the true hypothesis from among a known set of hypotheses. The learner is given a set of actions and knows the random distribution of the outcome of any action under any true hypothesis. Given a target error $δ>0$, the goal is to sequentially select the fewest number of actions so as to identify the true hypothesis with probability at least $1 - δ$. Motivated by applications in which the number of hypotheses or actions is massive (e.g., genomics-based cancer detection), we propose efficient (greedy, in fact) algorithms and provide the first approximation guarantees for ASHT, under two types of adaptivity. Both of our guarantees are independent of the number of actions and logarithmic in the number of hypotheses. We numerically evaluate the performance of our algorithms using both synthetic and real-world DNA mutation data, demonstrating that our algorithms outperform previously proposed heuristic policies by large margins.