Simin Liu

Yi Li, Honghao Lin, Simin Liu et al.

We consider sketching algorithms which first compress data by multiplication with a random sketch matrix, and then apply the sketch to quickly solve an optimization problem, e.g., low-rank approximation and regression. In the learning-based sketching paradigm proposed by~\cite{indyk2019learning}, the sketch matrix is found by choosing a random sparse matrix, e.g., CountSketch, and then the values of its non-zero entries are updated by running gradient descent on a training data set. Despite the growing body of work on this paradigm, a noticeable omission is that the locations of the non-zero entries of previous algorithms were fixed, and only their values were learned. In this work, we propose the first learning-based algorithms that also optimize the locations of the non-zero entries. Our first proposed algorithm is based on a greedy algorithm. However, one drawback of the greedy algorithm is its slower training time. We fix this issue and propose approaches for learning a sketching matrix for both low-rank approximation and Hessian approximation for second order optimization. The latter is helpful for a range of constrained optimization problems, such as LASSO and matrix estimation with a nuclear norm constraint. Both approaches achieve good accuracy with a fast running time. Moreover, our experiments suggest that our algorithm can still reduce the error significantly even if we only have a very limited number of training matrices.

Simin Liu, Tianrui Liu, Ali Vakilian et al.

We consider sketching algorithms which first quickly compress data by multiplication with a random sketch matrix, and then apply the sketch to quickly solve an optimization problem, e.g., low rank approximation. In the learning-based sketching paradigm proposed by Indyk et al. [2019], the sketch matrix is found by choosing a random sparse matrix, e.g., the CountSketch, and then updating the values of the non-zero entries by running gradient descent on a training data set. Despite the growing body of work on this paradigm, a noticeable omission is that the locations of the non-zero entries of previous algorithms were fixed, and only their values were learned. In this work we propose the first learning algorithm that also optimizes the locations of the non-zero entries. We show this algorithm gives better accuracy for low rank approximation than previous work, and apply it to other problems such as $k$-means clustering for the first time. We show that our algorithm is provably better in the spiked covariance model and for Zipfian matrices. We also show the importance of the sketch monotonicity property for combining learned sketches. Our empirical results show the importance of optimizing not only the values of the non-zero entries but also their positions.

Anusha Nagabandi, Ignasi Clavera, Simin Liu et al.

Although reinforcement learning methods can achieve impressive results in simulation, the real world presents two major challenges: generating samples is exceedingly expensive, and unexpected perturbations or unseen situations cause proficient but specialized policies to fail at test time. Given that it is impractical to train separate policies to accommodate all situations the agent may see in the real world, this work proposes to learn how to quickly and effectively adapt online to new tasks. To enable sample-efficient learning, we consider learning online adaptation in the context of model-based reinforcement learning. Our approach uses meta-learning to train a dynamics model prior such that, when combined with recent data, this prior can be rapidly adapted to the local context. Our experiments demonstrate online adaptation for continuous control tasks on both simulated and real-world agents. We first show simulated agents adapting their behavior online to novel terrains, crippled body parts, and highly-dynamic environments. We also illustrate the importance of incorporating online adaptation into autonomous agents that operate in the real world by applying our method to a real dynamic legged millirobot. We demonstrate the agent's learned ability to quickly adapt online to a missing leg, adjust to novel terrains and slopes, account for miscalibration or errors in pose estimation, and compensate for pulling payloads.