Quality diversity (QD) is a growing branch of stochastic optimization research that studies the problem of generating an archive of solutions that maximize a given objective function but are also diverse with respect to a set of specified measure functions. However, even when these functions are differentiable, QD algorithms treat them as "black boxes", ignoring gradient information. We present the differentiable quality diversity (DQD) problem, a special case of QD, where both the objective and measure functions are first order differentiable. We then present MAP-Elites via a Gradient Arborescence (MEGA), a DQD algorithm that leverages gradient information to efficiently explore the joint range of the objective and measure functions. Results in two QD benchmark domains and in searching the latent space of a StyleGAN show that MEGA significantly outperforms state-ofthe-art QD algorithms, highlighting DQD's promise for efficient quality diversity optimization when gradient information is available. Source code is available at https://github.com/icaros-usc/dqd.

Quality diversity (QD) is a growing branch of stochastic optimization research that studies the problem of generating an archive of solutions that maximize a given objective function but are also diverse with respect to a set of specified measure functions. However, even when these functions are differentiable, QD algorithms treat them as black boxes, ignoring gradient information. We present the differentiable quality diversity (DQD) problem, a special case of QD, where both the objective and measure functions are first order differentiable. We then present MAP-Elites via a Gradient Arborescence (MEGA), a DQD algorithm that leverages gradient information to efficiently explore the joint range of the objective and measure functions. Results in two QD benchmark domains and in searching the latent space of a StyleGAN show that MEGA significantly outperforms state-of-the-art QD algorithms, highlighting DQD's promise for efficient quality diversity optimization when gradient information is available. Source code is available at https://github.com/icaros-usc/dqd.

Machine Learning surrogates have been developed to accelerate solving systems dynamics of complex processes in different science and engineering applications. To faithfully capture governing systems dynamics, these methods rely on large training datasets, hence restricting their applicability in real-world problems. In this work, we propose BayPOD-AL, an active learning framework based on an uncertainty-aware Bayesian proper orthogonal decomposition (POD) approach, which aims to effectively learn reduced-order models from high-fidelity full-order models representing complex systems. Experimental results on predicting the temperature evolution over a rod demonstrate BayPOD-AL's effectiveness in suggesting the informative data and reducing computational cost related to constructing a training dataset compared to other uncertainty-guided active learning strategies. Furthermore, we demonstrate BayPOD-AL's generalizability and efficiency by evaluating its performance on a dataset of higher temporal resolution than the training dataset.

Imitation learning (IL) (Pomerleau, 1991; Ng et al., 2000; Syed and Schapire, 2007; Ho and Ermon, 2016), a realm distinct from standard reinforcement learning (RL) (Puterman, 2014; Sutton and Barto, 2018), is independent on rewards provided by the environment. This characteristic makes IL particularly suited for numerous real-world applications (Bhattacharyya et al., 2018; Shi et al., 2019; Jabri, 2021). The general IL paradigm leverages the guidance from expert demonstrations with information of both states and actions to mimic an outstanding policy (Abbeel and Ng, 2004; Ho and Ermon, 2016; Kostrikov et al., 2020). According to the strategy of policy training, IL is divided into two main schemes based on policy training strategy: on-policy and off-policy training. The on-policy scheme (Ho and Ermon, 2016; Chen et al., 2020) is noted for its stability but requires a significant volume of samples.

Quality diversity (QD) is a growing branch of stochastic optimization research that studies the problem of generating an archive of solutions that maximize a given objective function but are also diverse with respect to a set of specified measure functions. However, even when these functions are differentiable, QD algorithms treat them as "black boxes", ignoring gradient information. We present the differentiable quality diversity (DQD) problem, a special case of QD, where both the objective and measure functions are first order differentiable. We then present MAP-Elites via a Gradient Arborescence (MEGA), a DQD algorithm that leverages gradient information to efficiently explore the joint range of the objective and measure functions. Results in two QD benchmark domains and in searching the latent space of a StyleGAN show that MEGA significantly outperforms state-of-the-art QD algorithms, highlighting DQD's promise for efficient quality diversity optimization when gradient information is available. Source code is available at https://github.com/icaros-usc/dqd.

Training generally capable agents that perform well in unseen dynamic environments is a long-term goal of robot learning. Quality Diversity Reinforcement Learning (QD-RL) is an emerging class of reinforcement learning (RL) algorithms that blend insights from Quality Diversity (QD) and RL to produce a collection of high performing and behaviorally diverse policies with respect to a behavioral embedding. Existing QD-RL approaches have thus far taken advantage of sample-efficient off-policy RL algorithms. However, recent advances in high-throughput, massively parallelized robotic simulators have opened the door for algorithms that can take advantage of such parallelism, and it is unclear how to scale existing off-policy QD-RL methods to these new data-rich regimes. In this work, we take the first steps to combine on-policy RL methods, specifically Proximal Policy Optimization (PPO), that can leverage massive parallelism, with QD, and propose a new QD-RL method with these high-throughput simulators and on-policy training in mind. Our proposed Proximal Policy Gradient Arborescence (PPGA) algorithm yields a 4x improvement over baselines on the challenging humanoid domain.

Quality diversity (QD) is a growing branch of stochastic optimization research that studies the problem of generating an archive of solutions that maximize a given objective function but are also diverse with respect to a set of specified measure functions. However, even when these functions are differentiable, QD algorithms treat them as "black boxes", ignoring gradient information. We present the differentiable quality diversity (DQD) problem, a special case of QD, where both the objective and measure functions are first order differentiable. We then present MAP-Elites via Gradient Arborescence (MEGA), a DQD algorithm that leverages gradient information to efficiently explore the joint range of the objective and measure functions. Results in two QD benchmark domains and in searching the latent space of a StyleGAN show that MEGA significantly outperforms state-of-the-art QD algorithms, highlighting DQD's promise for efficient quality diversity optimization when gradient information is available. Source code is available at https://github.com/icaros-usc/dqd.

Modern data sets in many applications no longer comprise samples of real vectors in a real vector space but samples of much more complex structures which may be represented as points in a space with certain underlying geometric structure, namely a manifold. Manifold learning is an emerging field for learning the underlying structure. The study of manifold learning can be split into two main branches, namely dimension reduction and manifold fitting. With the aim of interacting statistics and geometry, we tackle the problem of manifold fitting in the ambient space. Inspired by the relation between the eigenvalues of the Laplace-Beltrami operator and the geometry of a manifold, we aim to find a small set of points that preserve the geometry of the underlying manifold. Based on this relationship, we extend the idea of subsampling to noisy datasets in high dimensional space and utilize the Moving Least Squares (MLS) approach to approximate the underlying manifold. We analyze the two core steps in our proposed method theoretically and also provide the bounds for the MLS approach. Our simulation results and real data analysis demonstrate the superiority of our method in estimating the underlying manifold from noisy data.

Advanced engineering materials design involves the exploration of massive multidimensional feature spaces, the correlation of materials properties and the processing parameters derived from disparate sources. The search for alternative materials or processing property strategies, whether through analytical, experimental or simulation approaches, has been a slow and arduous task, punctuated by infrequent and often expected discoveries. A few systematic efforts have been made to analyze the trends in data as a basis for classifications and predictions. This is particularly due to the lack of large amounts of organized data and more importantly the challenging of shifting through them in a timely and efficient manner. The application of recent advances in Data Mining on materials informatics is the state of art of computational and experimental approaches for materials discovery. In this paper similarity based engineering materials selection model is proposed and implemented to select engineering materials based on the composite materials constraints. The result reviewed from this model is sustainable for effective decision making in advanced engineering materials design applications.