Causal Inference with Differentially Private (Clustered) Outcomes

Estimating causal effects from randomized experiments is only feasible if participants agree to reveal their potentially sensitive responses. Of the many ways of ensuring privacy, label differential privacy is a widely used measure of an algorithm's privacy guarantee, which might encourage participants to share responses without running the risk of de-anonymization. Many differentially private mechanisms inject noise into the original data-set to achieve this privacy guarantee, which increases the variance of most statistical estimators and makes the precise measurement of causal effects difficult: there exists a fundamental privacy-variance trade-off to performing causal analyses from differentially private data. With the aim of achieving lower variance for stronger privacy guarantees, we suggest a new differential privacy mechanism, "Cluster-DP", which leverages any given cluster structure of the data while still allowing for the estimation of causal effects. We show that, depending on an intuitive measure of cluster quality, we can improve the variance loss while maintaining our privacy guarantees. We compare its performance, theoretically and empirically, to that of its unclustered version and a more extreme uniform-prior version which does not use any of the original response distribution, both of which are special cases of the "Cluster-DP" algorithm.

Causal Estimation of User Learning in Personalized Systems

In online platforms, the impact of a treatment on an observed outcome may change over time as 1) users learn about the intervention, and 2) the system personalization, such as individualized recommendations, change over time. We introduce a non-parametric causal model of user actions in a personalized system. We show that the Cookie-Cookie-Day (CCD) experiment, designed for the measurement of the user learning effect, is biased when there is personalization. We derive new experimental designs that intervene in the personalization system to generate the variation necessary to separately identify the causal effect mediated through user learning and personalization. Making parametric assumptions allows for the estimation of long-term causal effects based on medium-term experiments. In simulations, we show that our new designs successfully recover the dynamic causal effects of interest.

Learning across Data Owners with Joint Differential Privacy

In this paper, we study the setting in which data owners train machine learning models collaboratively under a privacy notion called joint differential privacy [Kearns et al., 2018]. In this setting, the model trained for each data owner $j$ uses $j$'s data without privacy consideration and other owners' data with differential privacy guarantees. This setting was initiated in [Jain et al., 2021] with a focus on linear regressions. In this paper, we study this setting for stochastic convex optimization (SCO). We present an algorithm that is a variant of DP-SGD [Song et al., 2013; Abadi et al., 2016] and provides theoretical bounds on its population loss. We compare our algorithm to several baselines and discuss for what parameter setups our algorithm is more preferred. We also empirically study joint differential privacy in the multi-class classification problem over two public datasets. Our empirical findings are well-connected to the insights from our theoretical results.

Learning from Aggregated Data: Curated Bags versus Random Bags

Protecting user privacy is a major concern for many machine learning systems that are deployed at scale and collect from a diverse set of population. One way to address this concern is by collecting and releasing data labels in an aggregated manner so that the information about a single user is potentially combined with others. In this paper, we explore the possibility of training machine learning models with aggregated data labels, rather than individual labels. Specifically, we consider two natural aggregation procedures suggested by practitioners: curated bags where the data points are grouped based on common features and random bags where the data points are grouped randomly in bag of similar sizes. For the curated bag setting and for a broad range of loss functions, we show that we can perform gradient-based learning without any degradation in performance that may result from aggregating data. Our method is based on the observation that the sum of the gradients of the loss function on individual data examples in a curated bag can be computed from the aggregate label without the need for individual labels. For the random bag setting, we provide a generalization risk bound based on the Rademacher complexity of the hypothesis class and show how empirical risk minimization can be regularized to achieve the smallest risk bound. In fact, in the random bag setting, there is a trade-off between size of the bag and the achievable error rate as our bound indicates. Finally, we conduct a careful empirical study to confirm our theoretical findings. In particular, our results suggest that aggregate learning can be an effective method for preserving user privacy while maintaining model accuracy.

Robust and differentially private stochastic linear bandits

In this paper, we study the stochastic linear bandit problem under the additional requirements of differential privacy, robustness and batched observations. In particular, we assume an adversary randomly chooses a constant fraction of the observed rewards in each batch, replacing them with arbitrary numbers. We present differentially private and robust variants of the arm elimination algorithm using logarithmic batch queries under two privacy models and provide regret bounds in both settings. In the first model, every reward in each round is reported by a potentially different client, which reduces to standard local differential privacy (LDP). In the second model, every action is "owned" by a different client, who may aggregate the rewards over multiple queries and privatize the aggregate response instead. To the best of our knowledge, our algorithms are the first simultaneously providing differential privacy and adversarial robustness in the stochastic linear bandits problem.

Measuring Re-identification Risk

Compact user representations (such as embeddings) form the backbone of personalization services. In this work, we present a new theoretical framework to measure re-identification risk in such user representations. Our framework, based on hypothesis testing, formally bounds the probability that an attacker may be able to obtain the identity of a user from their representation. As an application, we show how our framework is general enough to model important real-world applications such as the Chrome's Topics API for interest-based advertising. We complement our theoretical bounds by showing provably good attack algorithms for re-identification that we use to estimate the re-identification risk in the Topics API. We believe this work provides a rigorous and interpretable notion of re-identification risk and a framework to measure it that can be used to inform real-world applications.

Learning Rate Schedules in the Presence of Distribution Shift

We design learning rate schedules that minimize regret for SGD-based online learning in the presence of a changing data distribution. We fully characterize the optimal learning rate schedule for online linear regression via a novel analysis with stochastic differential equations. For general convex loss functions, we propose new learning rate schedules that are robust to distribution shift, and we give upper and lower bounds for the regret that only differ by constants. For non-convex loss functions, we define a notion of regret based on the gradient norm of the estimated models and propose a learning schedule that minimizes an upper bound on the total expected regret. Intuitively, one expects changing loss landscapes to require more exploration, and we confirm that optimal learning rate schedules typically increase in the presence of distribution shift. Finally, we provide experiments for high-dimensional regression models and neural networks to illustrate these learning rate schedules and their cumulative regret.

Replicable Clustering

In this paper, we design replicable algorithms in the context of statistical clustering under the recently introduced notion of replicability. A clustering algorithm is replicable if, with high probability, it outputs the exact same clusters after two executions with datasets drawn from the same distribution when its internal randomness is shared across the executions. We propose such algorithms for the statistical $k$-medians, statistical $k$-means, and statistical $k$-centers problems by utilizing approximation routines for their combinatorial counterparts in a black-box manner. In particular, we demonstrate a replicable $O(1)$-approximation algorithm for statistical Euclidean $k$-medians ($k$-means) with $\operatorname{poly}(d)$ sample complexity. We also describe a $O(1)$-approximation algorithm with an additional $O(1)$-additive error for statistical Euclidean $k$-centers, albeit with $\exp(d)$ sample complexity.

Multi-channel Autobidding with Budget and ROI Constraints

In digital online advertising, advertisers procure ad impressions simultaneously on multiple platforms, or so-called channels, such as Google Ads, Meta Ads Manager, etc., each of which consists of numerous ad auctions. We study how an advertiser maximizes total conversion (e.g. ad clicks) while satisfying aggregate return-on-investment (ROI) and budget constraints across all channels. In practice, an advertiser does not have control over, and thus cannot globally optimize, which individual ad auctions she participates in for each channel, and instead authorizes a channel to procure impressions on her behalf: the advertiser can only utilize two levers on each channel, namely setting a per-channel budget and per-channel target ROI. In this work, we first analyze the effectiveness of each of these levers for solving the advertiser's global multi-channel problem. We show that when an advertiser only optimizes over per-channel ROIs, her total conversion can be arbitrarily worse than what she could have obtained in the global problem. Further, we show that the advertiser can achieve the global optimal conversion when she only optimizes over per-channel budgets. In light of this finding, under a bandit feedback setting that mimics real-world scenarios where advertisers have limited information on ad auctions in each channels and how channels procure ads, we present an efficient learning algorithm that produces per-channel budgets whose resulting conversion approximates that of the global optimal problem. Finally, we argue that all our results hold for both single-item and multi-item auctions from which channels procure impressions on advertisers' behalf.

Approximately Optimal Core Shapes for Tensor Decompositions

This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its reconstruction error via connections to higher-order singular values. Specifically, we introduce a novel Tucker packing problem, which we prove is NP-hard, and give a polynomial-time approximation scheme based on a reduction to the 2-dimensional knapsack problem with a matroid constraint. We also generalize our techniques to tree tensor network decompositions. We implement our algorithm using an integer programming solver, and show that its solution quality is competitive with (and sometimes better than) the greedy algorithm that uses the true Tucker decomposition loss at each step, while also running up to 1000x faster.