Quan Dong Nguyen

Quan Nguyen, Emma Lejeune

From biological organs to soft robotics, highly deformable materials are essential components of natural and engineered systems. These highly deformable materials can have heterogeneous material properties, and can experience heterogeneous deformations with or without underlying material heterogeneity. Many recent works have established that computational modeling approaches are well suited for understanding and predicting the consequences of material heterogeneity and for interpreting observed heterogeneous strain fields. In particular, there has been significant work towards developing inverse analysis approaches that can convert observed kinematic quantities (e.g., displacement, strain) to material properties and mechanical state. Despite the success of these approaches, they are not necessarily generalizable and often rely on tight control and knowledge of boundary conditions. Here, we will build on the recent advances (and ubiquity) of machine learning approaches to explore alternative approaches to detect patterns in heterogeneous material properties and mechanical behavior. Specifically, we will explore unsupervised learning approaches to clustering and ensemble clutering to identify heterogeneous regions. Overall, we find that these approaches are effective, yet limited in their abilities. Through this initial exploration (where all data and code is published alongside this manuscript), we set the stage for future studies that more specifically adapt these methods to mechanical data.

Quan Nguyen, Adji Bousso Dieng

Experimental design techniques such as active search and Bayesian optimization are widely used in the natural sciences for data collection and discovery. However, existing techniques tend to favor exploitation over exploration of the search space, which causes them to get stuck in local optima. This ``collapse" problem prevents experimental design algorithms from yielding diverse high-quality data. In this paper, we extend the Vendi scores -- a family of interpretable similarity-based diversity metrics -- to account for quality. We then leverage these quality-weighted Vendi scores to tackle experimental design problems across various applications, including drug discovery, materials discovery, and reinforcement learning. We found that quality-weighted Vendi scores allow us to construct policies for experimental design that flexibly balance quality and diversity, and ultimately assemble rich and diverse sets of high-performing data points. Our algorithms led to a 70%-170% increase in the number of effective discoveries compared to baselines.

Quan Nguyen, Shinji Ito, Junpei Komiyama et al.

Existing data-dependent and best-of-both-worlds regret bounds for multi-armed bandits problems have limited adaptivity as they are either data-dependent but not best-of-both-worlds (BOBW), BOBW but not data-dependent or have sub-optimal $O(\sqrt{T\ln{T}})$ worst-case guarantee in the adversarial regime. To overcome these limitations, we propose real-time stability-penalty matching (SPM), a new method for obtaining regret bounds that are simultaneously data-dependent, best-of-both-worlds and $T$-optimal for multi-armed bandits problems. In particular, we show that real-time SPM obtains bounds with worst-case guarantees of order $O(\sqrt{T})$ in the adversarial regime and $O(\ln{T})$ in the stochastic regime while simultaneously being adaptive to data-dependent quantities such as sparsity, variations, and small losses. Our results are obtained by extending the SPM technique for tuning the learning rates in the follow-the-regularized-leader (FTRL) framework, which further indicates that the combination of SPM and FTRL is a promising approach for proving new adaptive bounds in online learning problems.

Quan Nguyen, Roman Garnett

Active search is a setting in adaptive experimental design where we aim to uncover members of rare, valuable class(es) subject to a budget constraint. An important consideration in this problem is diversity among the discovered targets -- in many applications, diverse discoveries offer more insight and may be preferable in downstream tasks. However, most existing active search policies either assume that all targets belong to a common positive class or encourage diversity via simple heuristics. We present a novel formulation of active search with multiple target classes, characterized by a utility function chosen from a flexible family whose members encourage diversity via a diminishing returns mechanism. We then study this problem under the Bayesian lens and prove a hardness result for approximating the optimal policy for arbitrary positive, increasing, and concave utility functions. Finally, we design an efficient, nonmyopic approximation to the optimal policy for this class of utilities and demonstrate its superior empirical performance in a variety of settings, including drug discovery.