Site Bai · 柏思特

Recent advances (Sherman, 2017; Sidford and Tian, 2018; Cohen et al., 2021) have overcome the fundamental barrier of dimension dependence in the iteration complexity of solving $\ell_\infty$ regression with first-order methods. Yet it remains unclear to what extent such acceleration can be achieved for general $\ell_p$ smooth functions. In this paper, we propose a new accelerated first-order method for convex optimization under non-Euclidean smoothness assumptions. In contrast to standard acceleration techniques, our approach uses primal-dual iterate sequences taken with respect to differing norms, which are then coupled using an implicitly determined interpolation parameter. For \(\ell_p\) norm smooth problems in \(d\) dimensions, our method provides an iteration complexity improvement of up to \(O(d^{1-\frac{2}{p}})\) in terms of calls to a first-order oracle, thereby allowing us to circumvent long-standing barriers in accelerated non-Euclidean steepest descent.

In this paper, we provide tight lower bounds for the oracle complexity of minimizing high-order Hölder smooth and uniformly convex functions. Specifically, for a function whose \(p^{th}\)-order derivatives are Hölder continuous with degree \(\nu\) and parameter \(H\), and that is uniformly convex with degree \(q\) and parameter \(\sigma\), we focus on two asymmetric cases: (1) \(q > p + \nu\), and (2) \(q < p+\nu\). Given up to \(p^{th}\)-order oracle access, we establish worst-case oracle complexities of \(\Omega\left( \left( \frac{H}{\sigma}\right)^\frac{2}{3(p+\nu)-2}\left( \frac{\sigma}{\epsilon}\right)^\frac{2(q-p-\nu)}{q(3(p+\nu)-2)}\right)\) in the first case and \(\Omega\left(\left(\frac{H}{\sigma}\right)^\frac{2}{3(p+\nu)-2}+ \log^2\left(\frac{\sigma^{p+\nu}}{H^q}\right)^\frac{1}{p+\nu-q}\right)\) in the second case for reaching an \(\epsilon\)-approximate solution, in terms of the optimality gap. Our analysis generalizes previous lower bounds for functions under first- and second-order smoothness as well as those for uniformly convex functions, and furthermore our results match the corresponding upper bounds in the general setting.

Distributed optimization (DO) approaches for saddle point problems (SPP) have recently gained in popularity due to the critical role they play in machine learning (ML). Existing works mostly target smooth unconstrained objectives in Euclidean space, whereas ML problems often involve constraints or non-smooth regularization, which results in a need for composite optimization. Moreover, although non-smooth regularization often serves to induce structure (e.g., sparsity), standard aggregation schemes in distributed optimization break this structure. Addressing these issues, we propose Federated Dual Extrapolation (FeDualEx), an extra-step primal-dual algorithm with local updates, which is the first of its kind to encompass both saddle point optimization and composite objectives under the distributed paradigm. Using a generalized notion of Bregman divergence, we analyze its convergence and communication complexity in the homogeneous setting. Furthermore, the empirical evaluation demonstrates the effectiveness of FeDualEx for inducing structure in these challenging settings.

We propose the framework of dual convexified convolutional neural networks (DCCNNs). In this framework, we first introduce a primal learning problem motivated from convexified convolutional neural networks (CCNNs), and then construct the dual convex training program through careful analysis of the Karush-Kuhn-Tucker (KKT) conditions and Fenchel conjugates. Our approach reduces the memory overhead of constructing a large kernel matrix and eliminates the ambiguity of factorizing the matrix. Due to the low-rank structure in CCNNs and the related subdifferential of nuclear norms, there is no closed-form expression to recover the primal solution from the dual solution. To overcome this, we propose a highly novel weight recovery algorithm, which takes the dual solution and the kernel information as the input, and recovers the linear and convolutional weights of a CCNN. Furthermore, our recovery algorithm exploits the low-rank structure and imposes a small number of filters indirectly, which reduces the parameter size. As a result, DCCNNs inherit all the statistical benefits of CCNNs, while enjoying a more formal and efficient workflow.

Reinforcement Learning(RL) with sparse rewards is a major challenge. We propose Hindsight Trust Region Policy Optimization(HTRPO), a new RL algorithm that extends the highly successful TRPO algorithm with hindsight to tackle the challenge of sparse rewards. Hindsight refers to the algorithm’s ability to learn from information across goals, including ones not intended for the current task. HTRPO leverages two main ideas. It introduces QKL, a quadratic approximation to the KL divergence constraint on the trust region, leading to reduced variance in KL divergence estimation and improved stability in policy update. It also presents Hindsight Goal Filtering(HGF) to select conductive hindsight goals. In experiments, we evaluate HTRPO in various sparse reward tasks, including simple benchmarks, image-based Atari games, and simulated robot control. Ablation studies indicate that QKL and HGF contribute greatly to learning stability and high performance. Comparison results show that in all tasks, HTRPO consistently outperforms both TRPO and HPG, a state-of-the-art algorithm for RL with sparse rewards.

Grasp detection considering the affiliations between grasps and their owner in object overlapping scenes is a necessary and challenging task for the practical use of the robotic grasping approach. In this paper, a robotic grasp detection algorithm named ROI-GD is proposed to provide a feasible solution to this problem based on Region of Interest (ROI), which is the region proposal for objects. ROI-GD uses features from ROIs to detect grasps instead of the whole scene. It has two stages: the first stage is to provide ROIs in the input image and the second-stage is the grasp detector based on ROI features. We also contribute a multi-object grasp dataset, which is much larger than Cornell Grasp Dataset, by labeling Visual Manipulation Relationship Dataset. Experimental results demonstrate that ROI-GD performs much better in object overlapping scenes and at the meantime, remains comparable with state-of-the-art grasp detection algorithms on Cornell Grasp Dataset and Jacquard Dataset. Robotic experiments demonstrate that ROI-GD can help robots grasp the target in single-object and multi-object scenes with the overall success rates of 92.5% and 83.8% respectively.

Autonomous robotic grasping plays an important role in intelligent robotics. However, how to help the robot grasp specific objects in object stacking scenes is still an open problem, because there are two main challenges for autonomous robots: (1)it is a comprehensive task to know what and how to grasp; (2)it is hard to deal with the situations in which the target is hidden or covered by other objects. In this paper, we propose a multi-task convolutional neural network for autonomous robotic grasping, which can help the robot find the target, make the plan for grasping and finally grasp the target step by step in object stacking scenes. We integrate vision-based robotic grasping detection and visual manipulation relationship reasoning in one single deep network and build the autonomous robotic grasping system. Experimental results demonstrate that with our model, Baxter robot can autonomously grasp the target with a success rate of 90.6%, 71.9% and 59.4% in object cluttered scenes, familiar stacking scenes and complex stacking scenes respectively.