We consider the contextual bandit problem where at each time, the agent only has access to a noisy version of the context and the error variance (or an estimator of this variance). This setting is motivated by a wide range of applications where the true context for decision-making is unobserved, and only a prediction of the context by a potentially complex machine learning algorithm is available. When the context error is non-vanishing, classical bandit algorithms fail to achieve sublinear regret. We propose the first online algorithm in this setting with sublinear regret guarantees under mild conditions. The key idea is to extend the measurement error model in classical statistics to the online decision-making setting, which is nontrivial due to the policy being dependent on the noisy context observations. We further demonstrate the benefits of the proposed approach in simulation environments based on synthetic and real digital intervention datasets.

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.

Single-particle cryo-electron microscopy (cryo-EM) has become one of the mainstream structural biology techniques because of its ability to determine high-resolution structures of dynamic bio-molecules. However, cryo-EM data acquisition remains expensive and labor-intensive, requiring substantial expertise. Structural biologists need a more efficient and objective method to collect the best data in a limited time frame. We formulate the cryo-EM data collection task as an optimization problem in this work. The goal is to maximize the total number of good images taken within a specified period. We show that reinforcement learning offers an effective way to plan cryo-EM data collection, successfully navigating heterogenous cryo-EM grids. The approach we developed, cryoRL, demonstrates better performance than average users for data collection under similar settings.

Curriculum learning (CL) is a commonly used machine learning training strategy. However, we still lack a clear theoretical understanding of CL’s benefits. In this paper, we study the benefits of CL in the multitask linear regression problem under both structured and unstructured settings. For both settings, we derive the minimax rates for CL with the oracle that provides the optimal curriculum and without the oracle, where the agent has to adaptively learn a good curriculum. Our results reveal that adaptive learning can be fundamentally harder than the oracle learning in the unstructured setting, but it merely introduces a small extra term in the structured setting. To connect theory with practice, we provide justification for a popular empirical method that selects tasks with highest local prediction gain by comparing its guarantees with the minimax rates mentioned above.

In this paper, we study a sequential decision-making problem, called Adaptive Sampling for Discovery (ASD). Starting with a large unlabeled dataset, algorithms for ASD adaptively label the points with the goal to maximize the sum of responses.This problem has wide applications to real-world discovery problems, for example drug discovery with the help of machine learning models. ASD algorithms face the well-known exploration-exploitation dilemma. The algorithm needs to choose points that yield information to improve model estimates but it also needs to exploit the model. We rigorously formulate the problem and propose a general information-directed sampling (IDS) algorithm. We provide theoretical guarantees for the performance of IDS in linear, graph and low-rank models. The benefits of IDS are shown in both simulation experiments and real-data experiments for discovering chemical reaction conditions.

This paper studies the decision making problem with Funnel Structure. Funnel structure, a well-known concept in the marketing field, occurs in those systems where the decision maker interacts with the environment in a layered manner receiving far fewer observations from deep layers than shallow ones. For example, in the email marketing campaign application, the layers correspond to Open, Click and Purchase events. Conversions from Click to Purchase happen very infrequently because a purchase cannot be made unless the link in an email is clicked on. We formulate this challenging decision making problem as a contextual bandit with funnel structure and develop a multi-task learning algorithm that mitigates the lack of sufficient observations from deeper layers. We analyze both the prediction error and the regret of our algorithms. We verify our theory on prediction errors through a simple simulation. Experiments on both a simulated environment and an environment based on real-world data from a major email marketing company show that our algorithms offer significant improvement over previous methods.

Recent papers on the theory of representation learning has shown the importance of a quantity called diversity when generalizing from a set of source tasks to a target task. Most of these papers assume that the function mapping shared representations to predictions is linear, for both source and target tasks. In practice, researchers in deep learning use different numbers of extra layers following the pretrained model based on the difficulty of the new task. This motivates us to ask whether diversity can be achieved when source tasks and the target task use different prediction function spaces beyond linear functions. We show that diversity holds even if the target task uses a neural network with multiple layers, as long as source tasks use linear functions. If source tasks use nonlinear prediction functions, we provide a negative result by showing that depth-1 neural networks with ReLu activation function need exponentially many source tasks to achieve diversity. For a general function class, we find that eluder dimension gives a lower bound on the number of tasks required for diversity. Our theoretical results imply that simpler tasks generalize better. Though our theoretical results are shown for the global minimizer of empirical risks, their qualitative predictions still hold true for gradient-based optimization algorithms as verified by our simulations on deep neural networks.

Molecular geometry prediction of flexible molecules, or conformer search, is a long-standing challenge in computational chemistry. This task is of great importance for predicting structure-activity relationships for a wide variety of substances ranging from biomolecules to ubiquitous materials. Substantial computational resources are invested in Monte Carlo and Molecular Dynamics methods to generate diverse and representative conformer sets for medium to large molecules, which are yet intractable to chemoinformatic conformer search methods. We present TorsionNet, an efficient sequential conformer search technique based on reinforcement learning under the rigid rotor approximation. The model is trained via curriculum learning, whose theoretical benefit is explored in detail, to maximize a novel metric grounded in thermodynamics called the Gibbs Score. Our experimental results show that TorsionNet outperforms the highest-scoring chemoinformatics method by 4x on large branched alkanes, and by several orders of magnitude on the previously unexplored biopolymer lignin, with applications in renewable energy. TorsionNet also outperforms the far more exhaustive but computationally intensive Self-Guided Molecular Dynamics sampling method.

We study reinforcement learning in non-episodic factored Markov decision processes (FMDPs). We propose two near-optimal and oracle-efficient algorithms for FMDPs. Assuming oracle access to an FMDP planner, they enjoy a Bayesian and a frequentist regret bound respectively, both of which reduce to the near-optimal bound $O(DS\sqrt{AT})$ for standard non-factored MDPs. We propose a tighter connectivity measure, factored span, for FMDPs and prove a lower bound that depends on the factored span rather than the diameter $D$. In order to decrease the gap between lower and upper bounds, we propose an adaptation of the REGAL.C algorithm whose regret bound depends on the factored span. Our oracle-efficient algorithms outperform previously proposed near-optimal algorithms on computer network administration simulations.