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Learning to optimize (L2O) is an emerging approach that leverages machine learning to develop optimization methods, aiming at reducing the laborious iterations of hand engineering. It automates the design of an optimization method based on its performance on a set of training problems. This data-driven procedure generates methods that can efficiently solve problems similar to those in training. In sharp contrast, the typical and traditional designs of optimization methods are theory-driven, so they obtain performance guarantees over the classes of problems specified by the theory. The difference makes L2O suitable for repeatedly solving a particular optimization problem over a specific distribution of data, while it typically fails on out-of-distribution problems. The practicality of L2O depends on the type of target optimization, the chosen architecture of the method to learn, and the training procedure. This new paradigm has motivated a community of researchers to explore L2O and report their findings. This article is poised to be the first comprehensive survey and benchmark of L2O for continuous optimization. We set up taxonomies, categorize existing works and research directions, present insights, and identify open challenges. We benchmarked many existing L2O approaches on a few representative optimization problems. For reproducible research and fair benchmarking purposes, we released our software implementation and data in the package Open-L2O at https://github.com/VITA-Group/Open-L2O. 

The record-breaking performance of deep neural networks (DNNs) comes with heavy parameter budgets, which leads to external dynamic random access memory (DRAM) for storage. The prohibitive energy of DRAM accesses makes it nontrivial for DNN deployment on resource-constrained devices, calling for minimizing the movements of weights and data in order to improve the energy efficiency. Driven by this critical bottleneck, we present SmartDeal, a hardware-friendly algorithm framework to trade higher-cost memory storage/access for lower-cost computation, in order to aggressively boost the storage and energy efficiency, for both DNN inference and training. The core technique of SmartDeal is a novel DNN weight matrix decomposition framework with respective structural constraints on each matrix factor, carefully crafted to unleash the hardware-aware efficiency potential. Specifically, we decompose each weight tensor as the product of a small basis matrix and a large structurally sparse coefficient matrix whose nonzero elements are readily quantized to the power-of-2. The resulting sparse and readily quantized DNNs enjoy greatly reduced energy consumption in data movement as well as weight storage, while incurring minimal overhead to recover the original weights thanks to the required sparse bit-operations and cost-favorable computations. Beyond inference, we take another leap to embrace energy-efficient training, by introducing several customized techniques to address the unique roadblocks arising in training while preserving the SmartDeal structures. We also design a dedicated hardware accelerator to fully utilize the new weight structure to improve the real energy efficiency and latency performance. We conduct experiments on both vision and language tasks, with nine models, four datasets, and three settings (inference-only, adaptation, and fine-tuning). Our extensive results show that 1) being applied to inference, SmartDeal achieves up to 2.44x improvement in energy efficiency as evaluated using real hardware implementations and 2) being applied to training, SmartDeal can lead to 10.56x and 4.48x reduction in the storage and the training energy cost, respectively, with usually negligible accuracy loss, compared to state-of-the-art training baselines. Our source codes are available at: https://github.com/VITA-Group/SmartDeal. 

(Frankle & Carbin, 2019) shows that there exist winning tickets (small but critical subnetworks) for dense, randomly initialized networks, that can be trained alone to achieve comparable accuracies to the latter in a similar number of iterations. However, the identification of these winning tickets still requires the costly train-prune-retrain process, limiting their practical benefits. In this paper, we discover for the first time that the winning tickets can be identified at the very early training stage, which we term as Early-Bird (EB) tickets, via low-cost training schemes (e.g., early stopping and low-precision training) at large learning rates. Our finding of EB tickets is consistent with recently reported observations that the key connectivity patterns of neural networks emerge early. Furthermore, we propose a mask distance metric that can be used to identify EB tickets with low computational overhead, without needing to know the true winning tickets that emerge after the full training. Finally, we leverage the existence of EB tickets and the proposed mask distance to develop efficient training methods, which are achieved by first identifying EB tickets via low-cost schemes, and then continuing to train merely the EB tickets towards the target accuracy. Experiments based on various deep networks and datasets validate: 1) the existence of EB tickets and the effectiveness of mask distance in efficiently identifying them; and 2) that the proposed efficient training via EB tickets can achieve up to 5.8x ~ 10.7x energy savings while maintaining comparable or even better accuracy as compared to the most competitive state-of-the-art training methods, demonstrating a promising and easily adopted method for tackling cost-prohibitive deep network training.