Near-Optimal Regret for the Safe Learning-based Control of the Constrained Linear Quadratic Regulator

We study the problem of adaptive control of the stochastic linear quadratic regulator (LQR) with constraints that must be satisfied at every time step. Prior work on the multidimensional problem has shown $\tilde{O}(T^{2/3})$ regret and satisfaction of robust constraints, leaving open the question of whether $\tilde{O}(\sqrt{T})$ regret can be attained in the constrained LQR setting. We contribute to this problem by showing $\tilde{O}(\sqrt{T})$ regret and satisfaction of chance constraints. This type of constraints allow us to handle unbounded noise and also enable analytical techniques not directly applicable to robust constraints. Our proposed algorithm for this problem uses an SDP to select an optimistic policy, and then "scales back" this policy until it is verifiably-safe. Our theoretical analysis establishes regret and constraint guarantees via a key lemma that bounds the system covariance in terms of the chosen policy. This covariance-based analysis is in contrast with the cost-to-go based analysis that is typically used in adaptive LQR.

Stochastic Gradient Descent with Strategic Querying

This paper considers a finite-sum optimization problem under first-order queries and investigates the benefits of strategic querying on stochastic gradient-based methods compared to uniform querying strategy. We first introduce Oracle Gradient Querying (OGQ), an idealized algorithm that selects one user's gradient yielding the largest possible expected improvement (EI) at each step. However, OGQ assumes oracle access to the gradients of all users to make such a selection, which is impractical in real-world scenarios. To address this limitation, we propose Strategic Gradient Querying (SGQ), a practical algorithm that has better transient-state performance than SGD while making only one query per iteration. For smooth objective functions satisfying the Polyak-Lojasiewicz condition, we show that under the assumption of EI heterogeneity, OGQ enhances transient-state performance and reduces steady-state variance, while SGQ improves transient-state performance over SGD. Our numerical experiments validate our theoretical findings.

Pruning-aware Sparse Regularization for Network Pruning

Structural neural network pruning aims to remove the redundant channels in the deep convolutional neural networks (CNNs) by pruning the filters of less importance to the final output accuracy. To reduce the degradation of performance after pruning, many methods utilize the loss with sparse regularization to produce structured sparsity. In this paper, we analyze these sparsity-training-based methods and find that the regularization of unpruned channels is unnecessary. Moreover, it restricts the network's capacity, which leads to under-fitting. To solve this problem, we propose a novel pruning method, named MaskSparsity, with pruning-aware sparse regularization. MaskSparsity imposes the fine-grained sparse regularization on the specific filters selected by a pruning mask, rather than all the filters of the model. Before the fine-grained sparse regularization of MaskSparity, we can use many methods to get the pruning mask, such as running the global sparse regularization. MaskSparsity achieves 63.03%-FLOPs reduction on ResNet-110 by removing 60.34% of the parameters, with no top-1 accuracy loss on CIFAR-10. On ILSVRC-2012, MaskSparsity reduces more than 51.07% FLOPs on ResNet-50, with only a loss of 0.76% in the top-1 accuracy. The code is released at https://github.com/CASIA-IVA-Lab/MaskSparsity. Moreover, we have integrated the code of MaskSparity into a PyTorch pruning toolkit, EasyPruner, at https://gitee.com/casia_iva_engineer/easypruner.