Conformal prediction has emerged as an effective strategy for uncertainty quantification by modifying a model to output sets of labels instead of a single label. These prediction sets come with the guarantee that they contain the true label with high probability. However, conformal prediction typically requires a large calibration dataset of i.i.d. examples. We consider the online learning setting, where examples arrive over time, and the goal is to construct prediction sets dynamically. Departing from existing work, we assume semi-bandit feedback, where we *only observe the true label if it is contained in the prediction set*. For instance, consider calibrating a document retrieval model to a new domain; in this setting, a user would only be able to provide the true label if the target document is in the prediction set of retrieved documents. We propose a novel conformal prediction algorithm targeted at this setting, and prove that it obtains sublinear regret compared to the optimal conformal predictor. We evaluate our algorithm on a retrieval task, an image classification task, and an auction price-setting task, and demonstrate that it empirically achieves good performance compared to several baselines.

We study the stochastic bandit problem with ReLU neural network structure. We show that a $\tilde{O}(\sqrt{T})$ regret guarantee is achievable by considering bandits with one-layer ReLU neural networks; to the best of our knowledge, our work is the first to achieve such a guarantee. In this specific setting, we propose an OFU-ReLU algorithm that can achieve this upper bound. The algorithm first explores randomly until it reaches a linear regime, and then implements a UCB-type linear bandit algorithm to balance exploration and exploitation. Our key insight is that we can exploit the piecewise linear structure of ReLU activations and convert the problem into a linear bandit in a transformed feature space, once we learn the parameters of ReLU relatively accurately during the exploration stage. To remove dependence on model parameters, we design an OFU-ReLU+ algorithm based on a batching strategy, which can provide the same theoretical guarantee.

Existing approaches to algorithmic fairness aim to ensure equitable outcomes if human decision-makers comply perfectly with algorithmic decisions. However, perfect compliance with the algorithm is rarely a reality or even a desirable outcome in human-AI collaboration. Yet, recent studies have shown that selective compliance with fair algorithms can amplify discrimination relative to the prior human policy. As a consequence, ensuring equitable outcomes requires fundamentally different algorithmic design principles that ensure robustness to the decision-maker's (a priori unknown) compliance pattern. We define the notion of compliance-robustly fair algorithmic recommendations that are guaranteed to (weakly) improve fairness in decisions, regardless of the human's compliance pattern. We propose a simple optimization strategy to identify the best performance-improving compliance-robustly fair policy. However, we show that it may be infeasible to design algorithmic recommendations that are simultaneously fair in isolation, compliance-robustly fair, and more accurate than the human policy; thus, if our goal is to improve the equity and accuracy of human-AI collaboration, it may not be desirable to enforce traditional algorithmic fairness constraints. We illustrate the value of our approach on criminal sentencing data before and after the introduction of an algorithmic risk assessment tool in Virginia.

Offline model-based optimization seeks to optimize against a learned surrogate model without querying the true oracle objective function during optimization. Such tasks are commonly encountered in protein design, robotics, and clinical medicine where evaluating the oracle function is prohibitively expensive. However, inaccurate surrogate model predictions are frequently encountered along offline optimization trajectories. To address this limitation, we propose *generative adversarial model-based optimization* using **adaptive source critic regularization (aSCR)**—a task- and optimizer- agnostic framework for constraining the optimization trajectory to regions of the design space where the surrogate function is reliable. We propose a computationally tractable algorithm to dynamically adjust the strength of this constraint, and show how leveraging aSCR with standard Bayesian optimization outperforms existing methods on a suite of offline generative design tasks. Our code is available at https://github.com/michael-s-yao/gabo.

A key challenge to deploying reinforcement learning in practice is avoiding excessive (harmful) exploration in individual episodes. We propose a natural constraint on exploration—uniformly outperforming a conservative policy (adaptively estimated from all data observed thus far), up to a per-episode exploration budget. We design a novel algorithm that uses a UCB reinforcement learning policy for exploration, but overrides it as needed to satisfy our exploration constraint with high probability. Importantly, to ensure unbiased exploration across the state space, our algorithm adaptively determines when to explore. We prove that our approach remains conservative while minimizing regret in the tabular setting. We experimentally validate our results on a sepsis treatment task and an HIV treatment task, demonstrating that our algorithm can learn while ensuring good performance compared to the baseline policy for every patient; the latter task also demonstrates that our approach extends to continuous state spaces via deep reinforcement learning.

Sparse regression has recently been applied to enable transfer learning from very limited data. We study an extension of this approach to unsupervised learning—in particular, learning word embeddings from unstructured text corpora using low-rank matrix factorization. Intuitively, when transferring word embeddings to a new domain, we expect that the embeddings change for only a small number of words—e.g., the ones with novel meanings in that domain. We propose a novel group-sparse penalty that exploits this sparsity to perform transfer learning when there is very little text data available in the target domain—e.g., a single article of text. We prove generalization bounds for our algorithm. Furthermore, we empirically evaluate its effectiveness, both in terms of prediction accuracy in downstream tasks as well as in terms of interpretability of the results.