Bayesian Collaborative Bandits with Thompson Sampling for Improved Outreach in Maternal Health Program

Mobile health (mHealth) programs face a critical challenge in optimizing the timing of automated health information calls to beneficiaries. This challenge has been formulated as a collaborative multi-armed bandit problem, requiring online learning of a low-rank reward matrix. Existing solutions often rely on heuristic combinations of offline matrix completion and exploration strategies. In this work, we propose a principled Bayesian approach using Thompson Sampling for this collaborative bandit problem. Our method leverages prior information through efficient Gibbs sampling for posterior inference over the low-rank matrix factors, enabling faster convergence. We demonstrate significant improvements over state-of-the-art baselines on a real-world dataset from the world's largest maternal mHealth program. Our approach achieves a $16\%$ reduction in the number of calls compared to existing methods and a $47$\% reduction compared to the deployed random policy. This efficiency gain translates to a potential increase in program capacity by $0.5-1.4$ million beneficiaries, granting them access to vital ante-natal and post-natal care information. Furthermore, we observe a $7\%$ and $29\%$ improvement in beneficiary retention (an extremely hard metric to impact) compared to state-of-the-art and deployed baselines, respectively. Synthetic simulations further demonstrate the superiority of our approach, particularly in low-data regimes and in effectively utilizing prior information. We also provide a theoretical analysis of our algorithm in a special setting using Eluder dimension.

Near-Optimal Streaming Heavy-Tailed Statistical Estimation with Clipped SGD

We consider the problem of high-dimensional heavy-tailed statistical estimation in the streaming setting, which is much harder than the traditional batch setting due to memory constraints. We cast this problem as stochastic convex optimization with heavy tailed stochastic gradients, and prove that the widely used Clipped-SGD algorithm attains near-optimal sub-Gaussian statistical rates whenever the second moment of the stochastic gradient noise is finite. More precisely, with $T$ samples, we show that Clipped-SGD, for smooth and strongly convex objectives, achieves an error of $\sqrt{\frac{\mathsf{Tr}(\Sigma)+\sqrt{\mathsf{Tr}(\Sigma)\|\Sigma\|_2}\log(\frac{\log(T)}{\delta})}{T}}$ with probability $1-\delta$, where $\Sigma$ is the covariance of the clipped gradient. Note that the fluctuations (depending on $\frac{1}{\delta}$) are of lower order than the term $\mathsf{Tr}(\Sigma)$. This improves upon the current best rate of $\sqrt{\frac{\mathsf{Tr}(\Sigma)\log(\frac{1}{\delta})}{T}}$ for Clipped-SGD, known only for smooth and strongly convex objectives. Our results also extend to smooth convex and lipschitz convex objectives. Key to our result is a novel iterative refinement strategy for martingale concentration, improving upon the PAC-Bayes approach of Catoni and Giulini.

Efficient Public Health Intervention Planning Using Decomposition-Based Decision-Focused Learning

The declining participation of beneficiaries over time is a key concern in public health programs. A popular strategy for improving retention is to have health workers `intervene' on beneficiaries at risk of dropping out. However, the availability and time of these health workers are limited resources. As a result, there has been a line of research on optimizing these limited intervention resources using Restless Multi-Armed Bandits (RMABs). The key technical barrier to using this framework in practice lies in the need to estimate the beneficiaries' RMAB parameters from historical data. Recent research has shown that Decision-Focused Learning (DFL), which focuses on maximizing the beneficiaries' adherence rather than predictive accuracy, improves the performance of intervention targeting using RMABs. Unfortunately, these gains come at a high computational cost because of the need to solve and evaluate the RMAB in each DFL training step. In this paper, we provide a principled way to exploit the structure of RMABs to speed up intervention planning by cleverly decoupling the planning for different beneficiaries. We use real-world data from an Indian NGO, ARMMAN, to show that our approach is up to two orders of magnitude faster than the state-of-the-art approach while also yielding superior model performance. This would enable the NGO to scale up deployments using DFL to potentially millions of mothers, ultimately advancing progress toward UNSDG 3.1.

Second Order Methods for Bandit Optimization and Control

Bandit convex optimization (BCO) is a general framework for online decision making under uncertainty. While tight regret bounds for general convex losses have been established, existing algorithms achieving these bounds have prohibitive computational costs for high dimensional data. In this paper, we propose a simple and practical BCO algorithm inspired by the online Newton step algorithm. We show that our algorithm achieves optimal (in terms of horizon) regret bounds for a large class of convex functions that we call $\kappa$-convex. This class contains a wide range of practically relevant loss functions including linear, quadratic, and generalized linear models. In addition to optimal regret, this method is the most efficient known algorithm for several well-studied applications including bandit logistic regression. Furthermore, we investigate the adaptation of our second-order bandit algorithm to online convex optimization with memory. We show that for loss functions with a certain affine structure, the extended algorithm attains optimal regret. This leads to an algorithm with optimal regret for bandit LQR/LQG problems under a fully adversarial noise model, thereby resolving an open question posed in \citep{gradu2020non} and \citep{sun2023optimal}. Finally, we show that the more general problem of BCO with (non-affine) memory is harder. We derive a $\tilde{\Omega}(T^{2/3})$ regret lower bound, even under the assumption of smooth and quadratic losses.

Responsible AI (RAI) Games and Ensembles

Several recent works have studied the societal effects of AI; these include issues such as fairness, robustness, and safety. In many of these objectives, a learner seeks to minimize its worst-case loss over a set of predefined distributions (known as uncertainty sets), with usual examples being perturbed versions of the empirical distribution. In other words, aforementioned problems can be written as min-max problems over these uncertainty sets. In this work, we provide a general framework for studying these problems, which we refer to as Responsible AI (RAI) games. We provide two classes of algorithms for solving these games: (a) game-play based algorithms, and (b) greedy stagewise estimation algorithms. The former class is motivated by online learning and game theory, whereas the latter class is motivated by the classical statistical literature on boosting, and regression. We empirically demonstrate the applicability and competitive performance of our techniques for solving several RAI problems, particularly around subpopulation shift.