Su Jia

Su Jia, Qian Xie, Nathan Kallus et al.

In many applications of online decision making, the environment is non-stationary and it is therefore crucial to use bandit algorithms that handle changes. Most existing approaches are designed to protect against non-smooth changes, constrained only by total variation or Lipschitzness over time. However, in practice, environments often change {\em smoothly}, so such algorithms may incur higher-than-necessary regret. We study a non-stationary bandits problem where each arm's mean reward sequence can be embedded into a $β$-Hölder function, i.e., a function that is $(β-1)$-times Lipschitz-continuously differentiable. The non-stationarity becomes more smooth as $β$ increases. When $β=1$, this corresponds to the non-smooth regime, where \cite{besbes2014stochastic} established a minimax regret of $\tilde Θ(T^{2/3})$. We show the first separation between the smooth (i.e., $β\ge 2$) and non-smooth (i.e., $β=1$) regimes by presenting a policy with $\tilde O(k^{4/5} T^{3/5})$ regret on any $k$-armed, $2$-Hölder instance. We complement this result by showing that the minimax regret on the $β$-Hölder family of instances is $Ω(T^{(β+1)/(2β+1)})$ for any integer $β\ge 1$. This matches our upper bound for $β=2$ up to logarithmic factors. Furthermore, we validated the effectiveness of our policy through a comprehensive numerical study using real-world click-through rate data.

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, Peter Frazier, Nathan Kallus

Experimentation with interference poses a significant challenge in contemporary online platforms. Prior research on experimentation with interference has concentrated on the final output of a policy. The cumulative performance, while equally crucial, is less well understood. To address this gap, we introduce the problem of {\em Multi-armed Bandits with Interference} (MABI), where the learner assigns an arm to each of $N$ experimental units over a time horizon of $T$ rounds. The reward of each unit in each round depends on the treatments of {\em all} units, where the influence of a unit decays in the spatial distance between units. Furthermore, we employ a general setup wherein the reward functions are chosen by an adversary and may vary arbitrarily across rounds and units. We first show that switchback policies achieve an optimal {\em expected} regret $\tilde O(\sqrt T)$ against the best fixed-arm policy. Nonetheless, the regret (as a random variable) for any switchback policy suffers a high variance, as it does not account for $N$. We propose a cluster randomization policy whose regret (i) is optimal in {\em expectation} and (ii) admits a high probability bound that vanishes in $N$.

Su Jia, Nathan Kallus, Christina Lee Yu

We consider experimentation in the presence of non-stationarity, inter-unit (spatial) interference, and carry-over effects (temporal interference), where we wish to estimate the global average treatment effect (GATE), the difference between average outcomes having exposed all units at all times to treatment or to control. We suppose spatial interference is described by a graph, where a unit's outcome depends on its neighborhood's treatments, and that temporal interference is described by an MDP, where the transition kernel under either treatment (action) satisfies a rapid mixing condition. We propose a clustered switchback design, where units are grouped into clusters and time steps are grouped into blocks, and each whole cluster-block combination is assigned a single random treatment. Under this design, we show that for graphs that admit good clustering, a truncated Horvitz-Thompson estimator achieves a $\tilde O(1/NT)$ mean squared error (MSE), matching the lower bound up to logarithmic terms for sparse graphs. Our results simultaneously generalize the results from \citet{hu2022switchback,ugander2013graph} and \citet{leung2022rate}. Simulation studies validate the favorable performance of our approach.

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.

Su Jia, Andrew Li, R. Ravi et al.

Modern platforms leverage randomized experiments to make informed decisions from a given set of items (``treatments''). As a particularly challenging scenario, these items may (i) arrive in high volume, with thousands of new items being released per hour, and (ii) have short lifetime, say, due to the item's transient nature or underlying non-stationarity that impels the platform to perceive the same item as distinct copies over time. Thus motivated, we study a Bayesian multiple-play bandit problem that encapsulates the key features of the multivariate testing (or ``multi-A/B testing'') problem with a high volume of short-lived arms. In each round, a set of $k$ arms arrive, each available for $w$ rounds. Without knowing the mean reward for each arm, the learner selects a multiset of $n$ arms and immediately observes their realized rewards. We aim to minimize the loss due to not knowing the mean rewards, averaged over instances generated from a given prior distribution. We show that when $k = O(n^ρ)$ for some constant $ρ>0$, our proposed policy has $\tilde O(n^{-\min \{ρ, \frac 12 (1+\frac 1w)^{-1}\}})$ loss on a sufficiently large class of prior distributions. We complement this result by showing that every policy suffers $Ω(n^{-\min \{ρ, \frac 12\}})$ loss on the same class of distributions. We further validate the effectiveness of our policy through a large-scale field experiment on {\em Glance}, a content-card-serving platform that faces exactly the above challenge. A simple variant of our policy outperforms the platform's current recommender by 4.32\% in total duration and 7.48\% in total number of click-throughs.

Su Jia, Andrew Li, R. Ravi

Consider a single-product revenue-maximization problem where the seller monotonically decreases the price in $n$ rounds with an unknown demand model coming from a given family. Without monotonicity, the minimax regret is $\tilde O(n^{2/3})$ for the Lipschitz demand family and $\tilde O(n^{1/2})$ for a general class of parametric demand models. With monotonicity, the minimax regret is $\tilde O(n^{3/4})$ if the revenue function is Lipschitz and unimodal. However, the minimax regret for parametric families remained open. In this work, we provide a complete settlement for this fundamental problem. We introduce the crossing number to measure the complexity of a family of demand functions. In particular, the family of degree-$k$ polynomials has a crossing number $k$. Based on conservatism under uncertainty, we present (i) a policy with an optimal $Θ(\log^2 n)$ regret for families with crossing number $k=0$, and (ii) another policy with an optimal $\tilde Θ(n^{k/(k+1)})$ regret when $k\ge 1$. These bounds are asymptotically higher than the $\tilde O(\log n)$ and $\tilde Θ(\sqrt n)$ minimax regret for the same families without the monotonicity constraint.

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.

Zhen Dong, Su Jia, Chi Zhang et al.

Recently, deep neural network has shown promising performance in face image recognition. The inputs of most networks are face images, and there is hardly any work reported in literature on network with face videos as input. To sufficiently discover the useful information contained in face videos, we present a novel network architecture called input aggregated network which is able to learn fixed-length representations for variable-length face videos. To accomplish this goal, an aggregation unit is designed to model a face video with various frames as a point on a Riemannian manifold, and the mapping unit aims at mapping the point into high-dimensional space where face videos belonging to the same subject are close-by and others are distant. These two units together with the frame representation unit build an end-to-end learning system which can learn representations of face videos for the specific tasks. Experiments on two public face video datasets demonstrate the effectiveness of the proposed network.