Sunil Gupta

Thanh Nguyen-Tang, Sunil Gupta, A. Tuan Nguyen et al.

Offline policy learning (OPL) leverages existing data collected a priori for policy optimization without any active exploration. Despite the prevalence and recent interest in this problem, its theoretical and algorithmic foundations in function approximation settings remain under-developed. In this paper, we consider this problem on the axes of distributional shift, optimization, and generalization in offline contextual bandits with neural networks. In particular, we propose a provably efficient offline contextual bandit with neural network function approximation that does not require any functional assumption on the reward. We show that our method provably generalizes over unseen contexts under a milder condition for distributional shift than the existing OPL works. Notably, unlike any other OPL method, our method learns from the offline data in an online manner using stochastic gradient descent, allowing us to leverage the benefits of online learning into an offline setting. Moreover, we show that our method is more computationally efficient and has a better dependence on the effective dimension of the neural network than an online counterpart. Finally, we demonstrate the empirical effectiveness of our method in a range of synthetic and real-world OPL problems.

Anusua Trivedi, Jocelyn Desbiens, Ron Gross et al.

Purpose: To demonstrate that retinal microvasculature per se is a reliable biomarker for Diabetic Retinopathy (DR) and, by extension, cardiovascular diseases. Methods: Deep Learning Convolutional Neural Networks (CNN) applied to color fundus images for semantic segmentation of the blood vessels and severity classification on both vascular and full images. Vessel reconstruction through harmonic descriptors is also used as a smoothing and de-noising tool. The mathematical background of the theory is also outlined. Results: For diabetic patients, at least 93.8% of DR No-Refer vs. Refer classification can be related to vasculature defects. As for the Non-Sight Threatening vs. Sight Threatening case, the ratio is as high as 96.7%. Conclusion: In the case of DR, most of the disease biomarkers are related topologically to the vasculature. Translational Relevance: Experiments conducted on eye blood vasculature reconstruction as a biomarker shows a strong correlation between vasculature shape and later stages of DR.

Hung Tran-The, Sunil Gupta, Thanh Nguyen-Tang et al.

We address policy learning with logged data in contextual bandits. Current offline-policy learning algorithms are mostly based on inverse propensity score (IPS) weighting requiring the logging policy to have \emph{full support} i.e. a non-zero probability for any context/action of the evaluation policy. However, many real-world systems do not guarantee such logging policies, especially when the action space is large and many actions have poor or missing rewards. With such \emph{support deficiency}, the offline learning fails to find optimal policies. We propose a novel approach that uses a hybrid of offline learning with online exploration. The online exploration is used to explore unsupported actions in the logged data whilst offline learning is used to exploit supported actions from the logged data avoiding unnecessary explorations. Our approach determines an optimal policy with theoretical guarantees using the minimal number of online explorations. We demonstrate our algorithms' effectiveness empirically on a diverse collection of datasets.

Thanh Nguyen-Tang, Sunil Gupta, Hung Tran-The et al.

Offline reinforcement learning (RL) leverages previously collected data for policy optimization without any further active exploration. Despite the recent interest in this problem, its theoretical results in neural network function approximation settings remain elusive. In this paper, we study the statistical theory of offline RL with deep ReLU network function approximation. In particular, we establish the sample complexity of $n = \tilde{\mathcal{O}}( H^{4 + 4 \frac{d}α} κ_μ^{1 + \frac{d}α} ε^{-2 - 2\frac{d}α} )$ for offline RL with deep ReLU networks, where $κ_μ$ is a measure of distributional shift, {$H = (1-γ)^{-1}$ is the effective horizon length}, $d$ is the dimension of the state-action space, $α$ is a (possibly fractional) smoothness parameter of the underlying Markov decision process (MDP), and $ε$ is a user-specified error. Notably, our sample complexity holds under two novel considerations: the Besov dynamic closure and the correlated structure. While the Besov dynamic closure subsumes the dynamic conditions for offline RL in the prior works, the correlated structure renders the prior works of offline RL with general/neural network function approximation improper or inefficient {in long (effective) horizon problems}. To the best of our knowledge, this is the first theoretical characterization of the sample complexity of offline RL with deep neural network function approximation under the general Besov regularity condition that goes beyond {the linearity regime} in the traditional Reproducing Hilbert kernel spaces and Neural Tangent Kernels.