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Acceleration and momentum are the de facto standard in modern applications of machine learning and optimization, yet the bulk of the work on implicit regularization focuses instead on unaccelerated methods. In this paper, we study the statistical risk of the iterates generated by Nesterov's accelerated gradient method and Polyak's heavy ball method, when applied to least squares regression, drawing several connections to explicit penalization. We carry out our analyses in continuous-time, allowing us to make sharper statements than in prior work, and revealing complex interactions between early stopping, stability, and the curvature of the loss function.

Deep neural networks (DNNs) are widely applied to artificial intelligence applications, achieving promising performance at the cost of massive computation, large power consumption, and high latency. Diverse solutions have been proposed to cope with the challenge of latency and power consumption, including light-weight neural networks and efficient hardware accelerators. Moreover, research on quantization reduces the cost of computation and shows the error resiliency of DNNs. To improve the latency and power efficiency of hardware accelerators by exploiting the error resiliency, we propose an application-specific optimization method for the automatic design of approximate multipliers for DNNs. The proposed method optimizes an approximate multiplier by minimizing the error according to the probability distributions extracted from DNNs. By applying the optimized approximate multiplier to a DNN, we obtain 1.60%, 15.32%, and 20.19% higher accuracies than the best reproduced approximate multiplier on the widely used MNIST, FashionMNIST, and CIFAR-10 datasets, respectively, with 12.17% smaller area, 23.38% less power consumption, and 16.53% lower latency. Compared with an exact multiplier, the optimized multiplier reduces the area, power consumption, and latency by 36.88%, 52.45%, and 26.63%, respectively. Applied to FPGA-based and ASIC-based DNN accelerator modules, our approximate multiplier obtains low LUT utilization and small area respectively with competitive max frequency and power consumption, which shows the effectiveness of the proposed method in reducing the hardware cost of DNN accelerators.

Evolutionary Algorithms (EAs) and Deep Reinforcement Learning (DRL) have recently been combined to integrate the advantages of the two solutions for better policy learning. However, in existing hybrid methods, EA is used to directly train the policy network, which will lead to sample inefficiency and unpredictable impact on the policy performance. To better integrate these two approaches and avoid the drawbacks caused by the introduction of EA, we devote ourselves to devising a more efficient and reasonable method of combining EA and DRL. In this paper, we propose Evolutionary Action Selection-Twin Delayed Deep Deterministic Policy Gradient (EAS-TD3), a novel combination of EA and DRL. In EAS, we focus on optimizing the action chosen by the policy network and attempt to obtain high-quality actions to guide policy learning through an evolutionary algorithm. We conduct several experiments on challenging continuous control tasks. The result shows that EAS-TD3 shows superior performance over other state-of-art methods.

As the scale of distributed training grows, communication becomes a bottleneck. To accelerate the communication, recent works introduce In-Network Aggregation (INA), which moves the gradients summation into network middle-boxes, e.g., programmable switches to reduce the traffic volume. However, switch memory is scarce compared to the volume of gradients transmitted in distributed training. Although literature applies methods like pool-based streaming or dynamic sharing to tackle the mismatch, switch memory is still a potential performance bottleneck. Furthermore, we observe the under-utilization of switch memory due to the synchronization requirement for aggregator deallocation in recent works. To improve the switch memory utilization, we propose ESA, an $\underline{E}$fficient Switch Memory $\underline{S}$cheduler for In-Network $\underline{A}$ggregation. At its cores, ESA enforces the preemptive aggregator allocation primitive and introduces priority scheduling at the data-plane, which improves the switch memory utilization and average job completion time (JCT). Experiments show that ESA can improve the average JCT by up to $1.35\times$.

Connected and automated vehicles have shown great potential in improving traffic mobility and reducing emissions, especially at unsignalized intersections. Previous research has shown that vehicle passing order is the key influencing factor in improving intersection traffic mobility. In this paper, we propose a graph-based cooperation method to formalize the conflict-free scheduling problem at an unsignalized intersection. Based on graphical analysis, a vehicle's trajectory conflict relationship is modeled as a conflict directed graph and a coexisting undirected graph. Then, two graph-based methods are proposed to find the vehicle passing order. The first is an improved depth-first spanning tree algorithm, which aims to find the local optimal passing order vehicle by vehicle. The other novel method is a minimum clique cover algorithm, which identifies the global optimal solution. Finally, a distributed control framework and communication topology are presented to realize the conflict-free cooperation of vehicles. Extensive numerical simulations are conducted for various numbers of vehicles and traffic volumes, and the simulation results prove the effectiveness of the proposed algorithms.

In this paper we consider a linearized variable-time-step two-step backward differentiation formula (BDF2) scheme for solving nonlinear parabolic equations. The scheme is constructed by using the variable time-step BDF2 for the linear term and a Newton linearized method for the nonlinear term in time combining with a Galerkin finite element method (FEM) in space. We prove the unconditionally optimal error estimate of the proposed scheme under mild restrictions on the ratio of adjacent time-steps, i.e. $0<r_k < r_{\max} \approx 4.8645$ and on the maximum time step. The proof involves the discrete orthogonal convolution (DOC) and discrete complementary convolution (DCC) kernels, and the error splitting approach. In addition, our analysis also shows that the first level solution $u^1$ obtained by BDF1 (i.e. backward Euler scheme) does not cause the loss of global accuracy of second order. Numerical examples are provided to demonstrate our theoretical results.

Zeroth-order optimization methods are developed to overcome the practical hurdle of having knowledge of explicit derivatives. Instead, these schemes work with merely access to noisy functions evaluations. The predominant approach is to mimic first-order methods by means of some gradient estimator. The theoretical limitations are well-understood, yet, as most of these methods rely on finite-differencing for shrinking differences, numerical cancellation can be catastrophic. The numerical community developed an efficient method to overcome this by passing to the complex domain. This approach has been recently adopted by the optimization community and in this work we analyze the practically relevant setting of dealing with computational noise. To exemplify the possibilities we focus on the strongly-convex optimization setting and provide a variety of non-asymptotic results, corroborated by numerical experiments, and end with local non-convex optimization.

It has been shown that deep neural networks are prone to overfitting on biased training data. Towards addressing this issue, meta-learning employs a meta model for correcting the training bias. Despite the promising performances, super slow training is currently the bottleneck in the meta learning approaches. In this paper, we introduce a novel Faster Meta Update Strategy (FaMUS) to replace the most expensive step in the meta gradient computation with a faster layer-wise approximation. We empirically find that FaMUS yields not only a reasonably accurate but also a low-variance approximation of the meta gradient. We conduct extensive experiments to verify the proposed method on two tasks. We show our method is able to save two-thirds of the training time while still maintaining the comparable or achieving even better generalization performance. In particular, our method achieves the state-of-the-art performance on both synthetic and realistic noisy labels, and obtains promising performance on long-tailed recognition on standard benchmarks.

Interpretation of Deep Neural Networks (DNNs) training as an optimal control problem with nonlinear dynamical systems has received considerable attention recently, yet the algorithmic development remains relatively limited. In this work, we make an attempt along this line by reformulating the training procedure from the trajectory optimization perspective. We first show that most widely-used algorithms for training DNNs can be linked to the Differential Dynamic Programming (DDP), a celebrated second-order trajectory optimization algorithm rooted in the Approximate Dynamic Programming. In this vein, we propose a new variant of DDP that can accept batch optimization for training feedforward networks, while integrating naturally with the recent progress in curvature approximation. The resulting algorithm features layer-wise feedback policies which improve convergence rate and reduce sensitivity to hyper-parameter over existing methods. We show that the algorithm is competitive against state-ofthe-art first and second order methods. Our work opens up new avenues for principled algorithmic design built upon the optimal control theory.

Policy gradient methods are widely used in reinforcement learning algorithms to search for better policies in the parameterized policy space. They do gradient search in the policy space and are known to converge very slowly. Nesterov developed an accelerated gradient search algorithm for convex optimization problems. This has been recently extended for non-convex and also stochastic optimization. We use Nesterov's acceleration for policy gradient search in the well-known actor-critic algorithm and show the convergence using ODE method. We tested this algorithm on a scheduling problem. Here an incoming job is scheduled into one of the four queues based on the queue lengths. We see from experimental results that algorithm using Nesterov's acceleration has significantly better performance compared to algorithm which do not use acceleration. To the best of our knowledge this is the first time Nesterov's acceleration has been used with actor-critic algorithm.