Leveraging Offline Data in Linear Latent Bandits

Sequential decision-making domains such as recommender systems, healthcare and education often have unobserved heterogeneity in the population that can be modeled using latent bandits $-$ a framework where an unobserved latent state determines the model for a trajectory. While the latent bandit framework is compelling, the extent of its generality is unclear. We first address this by establishing a de Finetti theorem for decision processes, and show that $\textit{every}$ exchangeable and coherent stateless decision process is a latent bandit. The latent bandit framework lends itself particularly well to online learning with offline datasets, a problem of growing interest in sequential decision-making. One can leverage offline latent bandit data to learn a complex model for each latent state, so that an agent can simply learn the latent state online to act optimally. We focus on a linear model for a latent bandit with $d_A$-dimensional actions, where the latent states lie in an unknown $d_K$-dimensional subspace for $d_K \ll d_A$. We present SOLD, a novel principled method to learn this subspace from short offline trajectories with guarantees. We then provide two methods to leverage this subspace online: LOCAL-UCB and ProBALL-UCB. We demonstrate that LOCAL-UCB enjoys $\tilde O(\min(d_A\sqrt{T}, d_K\sqrt{T}(1+\sqrt{d_AT/d_KN})))$ regret guarantees, where the effective dimension is lower when the size $N$ of the offline dataset is larger. ProBALL-UCB enjoys a slightly weaker guarantee, but is more practical and computationally efficient. Finally, we establish the efficacy of our methods using experiments on both synthetic data and real-life movie recommendation data from MovieLens.

Conformalized Late Fusion Multi-View Learning

Uncertainty quantification for multi-view learning is motivated by the increasing use of multi-view data in scientific problems. A common variant of multi-view learning is late fusion: train separate predictors on individual views and combine them after single-view predictions are available. Existing methods for uncertainty quantification for late fusion often rely on undesirable distributional assumptions for validity. Conformal prediction is one approach that avoids such distributional assumptions. However, naively applying conformal prediction to late-stage fusion pipelines often produces overly conservative and uninformative prediction regions, limiting its downstream utility. We propose a novel methodology, Multi-View Conformal Prediction (MVCP), where conformal prediction is instead performed separately on the single-view predictors and only fused subsequently. Our framework extends the standard scalar formulation of a score function to a multivariate score that produces more efficient downstream prediction regions in both classification and regression settings. We then demonstrate that such improvements can be realized in methods built atop conformalized regressors, specifically in robust predict-then-optimize pipelines.

Smoothed Online Classification can be Harder than Batch Classification

We study online classification under smoothed adversaries. In this setting, at each time point, the adversary draws an example from a distribution that has a bounded density with respect to a fixed base measure, which is known apriori to the learner. For binary classification and scalar-valued regression, previous works \citep{haghtalab2020smoothed, block2022smoothed} have shown that smoothed online learning is as easy as learning in the iid batch setting under PAC model. However, we show that smoothed online classification can be harder than the iid batch classification when the label space is unbounded. In particular, we construct a hypothesis class that is learnable in the iid batch setting under the PAC model but is not learnable under the smoothed online model. Finally, we identify a condition that ensures that the PAC learnability of a hypothesis class is sufficient for its smoothed online learnability.

Online Classification with Predictions

We study online classification when the learner has access to predictions about future examples. We design an online learner whose expected regret is never worse than the worst-case regret, gracefully improves with the quality of the predictions, and can be significantly better than the worst-case regret when the predictions of future examples are accurate. As a corollary, we show that if the learner is always guaranteed to observe data where future examples are easily predictable, then online learning can be as easy as transductive online learning. Our results complement recent work in online algorithms with predictions and smoothed online classification, which go beyond a worse-case analysis by using machine-learned predictions and distributional assumptions respectively.

Sample Efficient Myopic Exploration Through Multitask Reinforcement Learning with Diverse Tasks

Multitask Reinforcement Learning (MTRL) approaches have gained increasing attention for its wide applications in many important Reinforcement Learning (RL) tasks. However, while recent advancements in MTRL theory have focused on the improved statistical efficiency by assuming a shared structure across tasks, exploration--a crucial aspect of RL--has been largely overlooked. This paper addresses this gap by showing that when an agent is trained on a sufficiently diverse set of tasks, a generic policy-sharing algorithm with myopic exploration design like $\epsilon$-greedy that are inefficient in general can be sample-efficient for MTRL. To the best of our knowledge, this is the first theoretical demonstration of the "exploration benefits" of MTRL. It may also shed light on the enigmatic success of the wide applications of myopic exploration in practice. To validate the role of diversity, we conduct experiments on synthetic robotic control environments, where the diverse task set aligns with the task selection by automatic curriculum learning, which is empirically shown to improve sample-efficiency.

Optimal Thresholding Linear Bandit

We study a novel pure exploration problem: the $\epsilon$-Thresholding Bandit Problem (TBP) with fixed confidence in stochastic linear bandits. We prove a lower bound for the sample complexity and extend an algorithm designed for Best Arm Identification in the linear case to TBP that is asymptotically optimal.

The Complexity of Sequential Prediction in Dynamical Systems

We study the problem of learning to predict the next state of a dynamical system when the underlying evolution function is unknown. Unlike previous work, we place no parametric assumptions on the dynamical system, and study the problem from a learning theory perspective. We define new combinatorial measures and dimensions and show that they quantify the optimal mistake and regret bounds in the realizable and agnostic setting respectively.

A Primal-Dual Algorithm for Offline Constrained Reinforcement Learning with Low-Rank MDPs

Offline reinforcement learning (RL) aims to learn a policy that maximizes the expected cumulative reward using a pre-collected dataset. Offline RL with low-rank MDPs or general function approximation has been widely studied recently, but existing algorithms with sample complexity $O(\epsilon^{-2})$ for finding an $\epsilon$-optimal policy either require a uniform data coverage assumptions or are computationally inefficient. In this paper, we propose a primal dual algorithm for offline RL with low-rank MDPs in the discounted infinite-horizon setting. Our algorithm is the first computationally efficient algorithm in this setting that achieves sample complexity of $O(\epsilon^{-2})$ with partial data coverage assumption. This improves upon a recent work that requires $O(\epsilon^{-4})$ samples. Moreover, our algorithm extends the previous work to the offline constrained RL setting by supporting constraints on additional reward signals.

A Framework for Partially Observed Reward-States in RLHF

The study of reinforcement learning from human feedback (RLHF) has gained prominence in recent years due to its role in the development of LLMs. Neuroscience research shows that human responses to stimuli are known to depend on partially-observed "internal states." Unfortunately current models of RLHF do not take take this into consideration. Moreover most RLHF models do not account for intermediate feedback, which is gaining importance in empirical work and can help improve both sample complexity and alignment. To address these limitations, we model RLHF as reinforcement learning with partially observed reward-states (PORRL). We show reductions from the the two dominant forms of human feedback in RLHF - cardinal and dueling feedback to PORRL. For cardinal feedback, we develop generic statistically efficient algorithms and instantiate them to present POR-UCRL and POR-UCBVI. For dueling feedback, we show that a naive reduction to cardinal feedback fails to achieve sublinear dueling regret. We then present the first explicit reduction that converts guarantees for cardinal regret to dueling regret. We show that our models and guarantees in both settings generalize and extend existing ones. Finally, we identify a recursive structure on our model that could improve the statistical and computational tractability of PORRL, giving examples from past work on RLHF as well as learning perfect reward machines, which PORRL subsumes.

Revisiting the Learnability of Apple Tasting

In online binary classification under \textit{apple tasting} feedback, the learner only observes the true label if it predicts "1". First studied by \cite{helmbold2000apple}, we revisit this classical partial-feedback setting and study online learnability from a combinatorial perspective. We show that the Littlestone dimension continues to prove a tight quantitative characterization of apple tasting in the agnostic setting, closing an open question posed by \cite{helmbold2000apple}. In addition, we give a new combinatorial parameter, called the Effective width, that tightly quantifies the minimax expected mistakes in the realizable setting. As a corollary, we use the Effective width to establish a \textit{trichotomy} of the minimax expected number of mistakes in the realizable setting. In particular, we show that in the realizable setting, the expected number of mistakes for any learner under apple tasting feedback can only be $\Theta(1), \Theta(\sqrt{T})$, or $\Theta(T)$.