A Decision-Language Model (DLM) for Dynamic Restless Multi-Armed Bandit Tasks in Public Health

Efforts to reduce maternal mortality rate, a key UN Sustainable Development target (SDG Target 3.1), rely largely on preventative care programs to spread critical health information to high-risk populations. These programs face two important challenges: efficiently allocating limited health resources to large beneficiary populations, and adapting to evolving policy priorities. While prior works in restless multi-armed bandit (RMAB) demonstrated success in public health allocation tasks, they lack flexibility to adapt to evolving policy priorities. Concurrently, Large Language Models (LLMs) have emerged as adept, automated planners in various domains, including robotic control and navigation. In this paper, we propose DLM: a Decision Language Model for RMABs. To enable dynamic fine-tuning of RMAB policies for challenging public health settings using human-language commands, we propose using LLMs as automated planners to (1) interpret human policy preference prompts, (2) propose code reward functions for a multi-agent RL environment for RMABs, and (3) iterate on the generated reward using feedback from RMAB simulations to effectively adapt policy outcomes. In collaboration with ARMMAN, an India-based public health organization promoting preventative care for pregnant mothers, we conduct a simulation study, showing DLM can dynamically shape policy outcomes using only human language commands as input.

Towards Zero Shot Learning in Restless Multi-armed Bandits

Restless multi-arm bandits (RMABs), a class of resource allocation problems with broad application in areas such as healthcare, online advertising, and anti-poaching, have recently been studied from a multi-agent reinforcement learning perspective. Prior RMAB research suffers from several limitations, e.g., it fails to adequately address continuous states, and requires retraining from scratch when arms opt-in and opt-out over time, a common challenge in many real world applications. We address these limitations by developing a neural network-based pre-trained model (PreFeRMAB) that has general zero-shot ability on a wide range of previously unseen RMABs, and which can be fine-tuned on specific instances in a more sample-efficient way than retraining from scratch. Our model also accommodates general multi-action settings and discrete or continuous state spaces. To enable fast generalization, we learn a novel single policy network model that utilizes feature information and employs a training procedure in which arms opt-in and out over time. We derive a new update rule for a crucial $\lambda$-network with theoretical convergence guarantees and empirically demonstrate the advantages of our approach on several challenging, real-world inspired problems.

Scalable Neural Network Kernels

We introduce the concept of scalable neural network kernels (SNNKs), the replacements of regular feedforward layers (FFLs), capable of approximating the latter, but with favorable computational properties. SNNKs effectively disentangle the inputs from the parameters of the neural network in the FFL, only to connect them in the final computation via the dot-product kernel. They are also strictly more expressive, as allowing to model complicated relationships beyond the functions of the dot-products of parameter-input vectors. We also introduce the neural network bundling process that applies SNNKs to compactify deep neural network architectures, resulting in additional compression gains. In its extreme version, it leads to the fully bundled network whose optimal parameters can be expressed via explicit formulae for several loss functions (e.g. mean squared error), opening a possibility to bypass backpropagation. As a by-product of our analysis, we introduce the mechanism of the universal random features (or URFs), applied to instantiate several SNNK variants, and interesting on its own in the context of scalable kernel methods. We provide rigorous theoretical analysis of all these concepts as well as an extensive empirical evaluation, ranging from point-wise kernel estimation to Transformers' fine-tuning with novel adapter layers inspired by SNNKs. Our mechanism provides up to 5x reduction in the number of trainable parameters, while maintaining competitive accuracy.

Estimate-Then-Optimize Versus Integrated-Estimation-Optimization: A Stochastic Dominance Perspective

In data-driven stochastic optimization, model parameters of the underlying distribution need to be estimated from data in addition to the optimization task. Recent literature suggests the integration of the estimation and optimization processes, by selecting model parameters that lead to the best empirical objective performance. Such an integrated approach can be readily shown to outperform simple ``estimate then optimize" when the model is misspecified. In this paper, we argue that when the model class is rich enough to cover the ground truth, the performance ordering between the two approaches is reversed for nonlinear problems in a strong sense. Simple ``estimate then optimize" outperforms the integrated approach in terms of stochastic dominance of the asymptotic optimality gap, i,e, the mean, all other moments, and the entire asymptotic distribution of the optimality gap is always better. Analogous results also hold under constrained settings and when contextual features are available. We also provide experimental findings to support our theory.

Balanced Off-Policy Evaluation for Personalized Pricing

We consider a personalized pricing problem in which we have data consisting of feature information, historical pricing decisions, and binary realized demand. The goal is to perform off-policy evaluation for a new personalized pricing policy that maps features to prices. Methods based on inverse propensity weighting (including doubly robust methods) for off-policy evaluation may perform poorly when the logging policy has little exploration or is deterministic, which is common in pricing applications. Building on the balanced policy evaluation framework of Kallus (2018), we propose a new approach tailored to pricing applications. The key idea is to compute an estimate that minimizes the worst-case mean squared error or maximizes a worst-case lower bound on policy performance, where in both cases the worst-case is taken with respect to a set of possible revenue functions. We establish theoretical convergence guarantees and empirically demonstrate the advantage of our approach using a real-world pricing dataset.

Efficient Graph Field Integrators Meet Point Clouds

We present two new classes of algorithms for efficient field integration on graphs encoding point clouds. The first class, SeparatorFactorization(SF), leverages the bounded genus of point cloud mesh graphs, while the second class, RFDiffusion(RFD), uses popular epsilon-nearest-neighbor graph representations for point clouds. Both can be viewed as providing the functionality of Fast Multipole Methods (FMMs), which have had a tremendous impact on efficient integration, but for non-Euclidean spaces. We focus on geometries induced by distributions of walk lengths between points (e.g., shortest-path distance). We provide an extensive theoretical analysis of our algorithms, obtaining new results in structural graph theory as a byproduct. We also perform exhaustive empirical evaluation, including on-surface interpolation for rigid and deformable objects (particularly for mesh-dynamics modeling), Wasserstein distance computations for point clouds, and the Gromov-Wasserstein variant.

Implicit Two-Tower Policies

We present a new class of structured reinforcement learning policy-architectures, Implicit Two-Tower (ITT) policies, where the actions are chosen based on the attention scores of their learnable latent representations with those of the input states. By explicitly disentangling action from state processing in the policy stack, we achieve two main goals: substantial computational gains and better performance. Our architectures are compatible with both: discrete and continuous action spaces. By conducting tests on 15 environments from OpenAI Gym and DeepMind Control Suite, we show that ITT-architectures are particularly suited for blackbox/evolutionary optimization and the corresponding policy training algorithms outperform their vanilla unstructured implicit counterparts as well as commonly used explicit policies. We complement our analysis by showing how techniques such as hashing and lazy tower updates, critically relying on the two-tower structure of ITTs, can be applied to obtain additional computational improvements.

Nuances in Margin Conditions Determine Gains in Active Learning

We consider nonparametric classification with smooth regression functions, where it is well known that notions of margin in $E[Y|X]$ determine fast or slow rates in both active and passive learning. Here we elucidate a striking distinction between the two settings. Namely, we show that some seemingly benign nuances in notions of margin -- involving the uniqueness of the Bayes classifier, and which have no apparent effect on rates in passive learning -- determine whether or not any active learner can outperform passive learning rates. In particular, for Audibert-Tsybakov's margin condition (allowing general situations with non-unique Bayes classifiers), no active learner can gain over passive learning in commonly studied settings where the marginal on $X$ is near uniform. Our results thus negate the usual intuition from past literature that active rates should improve over passive rates in nonparametric settings.