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Qi Deng

Publications and source records attributed to Qi Deng.

At least 37 records · Page 2Linked to original sources
arXiv2024

Faster Accelerated First-order Methods for Convex Optimization with Strongly Convex Function Constraints

In this paper, we introduce faster accelerated primal-dual algorithms for minimizing a convex function subject to strongly convex function constraints. Prior to our work, the best complexity bound was $\mathcal{O}(1/{\varepsilon})$, regardless of the strong convexity of the constraint function. It is unclear whether the strong convexity assumption can enable even better convergence results. To address this issue, we have developed novel techniques to progressively estimate the strong convexity of the Lagrangian function. Our approach, for the first time, effectively leverages the constraint strong convexity, obtaining an improved complexity of $\mathcal{O}(1/\sqrt{\varepsilon})$. This rate matches the complexity lower bound for strongly-convex-concave saddle point optimization and is therefore order-optimal. We show the superior performance of our methods in sparsity-inducing constrained optimization, notably Google's personalized PageRank problem. Furthermore, we show that a restarted version of the proposed methods can effectively identify the optimal solution's sparsity pattern within a finite number of steps, a result that appears to have independent significance.

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arXiv2024

Spatio-temporal Causal Learning for Streamflow Forecasting

Streamflow plays an essential role in the sustainable planning and management of national water resources. Traditional hydrologic modeling approaches simulate streamflow by establishing connections across multiple physical processes, such as rainfall and runoff. These data, inherently connected both spatially and temporally, possess intrinsic causal relations that can be leveraged for robust and accurate forecasting. Recently, spatio-temporal graph neural networks (STGNNs) have been adopted, excelling in various domains, such as urban traffic management, weather forecasting, and pandemic control, and they also promise advances in streamflow management. However, learning causal relationships directly from vast observational data is theoretically and computationally challenging. In this study, we employ a river flow graph as prior knowledge to facilitate the learning of the causal structure and then use the learned causal graph to predict streamflow at targeted sites. The proposed model, Causal Streamflow Forecasting (CSF) is tested in a real-world study in the Brazos River basin in Texas. Our results demonstrate that our method outperforms regular spatio-temporal graph neural networks and achieves higher computational efficiency compared to traditional simulation methods. By effectively integrating river flow graphs with STGNNs, this research offers a novel approach to streamflow prediction, showcasing the potential of combining advanced neural network techniques with domain-specific knowledge for enhanced performance in hydrologic modeling.

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arXiv2024

Stochastic Weakly Convex Optimization Beyond Lipschitz Continuity

This paper considers stochastic weakly convex optimization without the standard Lipschitz continuity assumption. Based on new adaptive regularization (stepsize) strategies, we show that a wide class of stochastic algorithms, including the stochastic subgradient method, preserve the $\mathcal{O} ( 1 / \sqrt{K})$ convergence rate with constant failure rate. Our analyses rest on rather weak assumptions: the Lipschitz parameter can be either bounded by a general growth function of $\|x\|$ or locally estimated through independent random samples.

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arXiv2024

First Place Solution to the ECCV 2024 ROAD++ Challenge @ ROAD++ Spatiotemporal Agent Detection 2024

This report presents our team's solutions for the Track 1 of the 2024 ECCV ROAD++ Challenge. The task of Track 1 is spatiotemporal agent detection, which aims to construct an "agent tube" for road agents in consecutive video frames. Our solutions focus on the challenges in this task, including extreme-size objects, low-light scenarios, class imbalance, and fine-grained classification. Firstly, the extreme-size object detection heads are introduced to improve the detection performance of large and small objects. Secondly, we design a dual-stream detection model with a low-light enhancement stream to improve the performance of spatiotemporal agent detection in low-light scenes, and the feature fusion module to integrate features from different branches. Subsequently, we develop a multi-branch detection framework to mitigate the issues of class imbalance and fine-grained classification, and we design a pre-training and fine-tuning approach to optimize the above multi-branch framework. Besides, we employ some common data augmentation techniques, and improve the loss function and upsampling operation. We rank first in the test set of Track 1 for the ROAD++ Challenge 2024, and achieve 30.82% average video-mAP.

cs.CV↗
arXiv2024

Accelerating Low-Rank Factorization-Based Semidefinite Programming Algorithms on GPU

In this paper, we address a long-standing challenge: how to achieve both efficiency and scalability in solving semidefinite programming problems. We propose breakthrough acceleration techniques for a wide range of low-rank factorization-based first-order methods using GPUs, making the computation much more efficient and scalable. To illustrate the idea and effectiveness of our approach, we use the low-rank factorization-based SDP solver, LoRADS, as an example, which involves both the classic Burer-Monterio method and a novel splitting scheme with a starting logarithmic rank. Our numerical results demonstrate that the accelerated GPU version of LoRADS, cuLoRADS, can solve huge-scale semidefinite programming problems with remarkable efficiency. By effectively leveraging GPU computational power, cuLoRADS exhibits outstanding performance. Specifically, it can solve a set of MaxCut problems with $10^7 \times 10^7$ matrix variables in 10 seconds to 1 minute each on an NVIDIA H100 GPU with 80GB memory, whereas previous solvers demonstrated the capability of handling problems of this scale, required at least dozens of hours per problem on CPUs. Additionally, cuLoRADS shows exceptional scalability by solving 1) a MaxCut problem with a $170 \text{ million} \times 170 \text{ million}$ matrix variable and 2) a Matrix Completion problem with a 20 million $\times$ 20 million matrix variable and approximately 200 million constraints, both in a matter of minutes.

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arXiv2024

A Low-Rank ADMM Splitting Approach for Semidefinite Programming

We introduce a new first-order method for solving general semidefinite programming problems, based on the alternating direction method of multipliers (ADMM) and a matrix-splitting technique. Our algorithm has an advantage over the Burer-Monteiro approach as it only involves much easier quadratically regularized subproblems in each iteration. For a linear objective, the subproblems are well-conditioned quadratic programs that can be efficiently solved by the standard conjugate gradient method. We show that the ADMM algorithm achieves sublinear or linear convergence rates to the KKT solutions under different conditions. Building on this theoretical development, we present LoRADS, a new solver for linear SDP based on the Low-Rank ADMM Splitting approach. LoRADS incorporates several strategies that significantly increase its efficiency. Firstly, it initiates with a warm-start phase that uses the Burer-Monteiro approach. Moreover, motivated by the SDP low-rank theory [So et al. 2008], LoRADS chooses an initial rank of logarithmic order and then employs a dynamic approach to increase the rank. Numerical experiments indicate that LoRADS exhibits promising performance on various SDP problems. A noteworthy achievement of LoRADS is its successful solving of a matrix completion problem with $15,694,167$ constraints and a matrix variable of size $40,000 \times 40,000$ in $351$ seconds.

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arXiv2024

A Single-Loop Robust Policy Gradient Method for Robust Markov Decision Processes

Robust Markov Decision Processes (RMDPs) have recently been recognized as a valuable and promising approach to discovering a policy with creditable performance, particularly in the presence of a dynamic environment and estimation errors in the transition matrix due to limited data. Despite extensive exploration of dynamic programming algorithms for solving RMDPs, there has been a notable upswing in interest in developing efficient algorithms using the policy gradient method. In this paper, we propose the first single-loop robust policy gradient (SRPG) method with the global optimality guarantee for solving RMDPs through its minimax formulation. Moreover, we complement the convergence analysis of the nonconvex-nonconcave min-max optimization problem with the objective function's gradient dominance property, which is not explored in the prior literature. Numerical experiments validate the efficacy of SRPG, demonstrating its faster and more robust convergence behavior compared to its nested-loop counterpart.

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arXiv2024

A Homogenization Approach for Gradient-Dominated Stochastic Optimization

Gradient dominance property is a condition weaker than strong convexity, yet sufficiently ensures global convergence even in non-convex optimization. This property finds wide applications in machine learning, reinforcement learning (RL), and operations management. In this paper, we propose the stochastic homogeneous second-order descent method (SHSODM) for stochastic functions enjoying gradient dominance property based on a recently proposed homogenization approach. Theoretically, we provide its sample complexity analysis, and further present an enhanced result by incorporating variance reduction techniques. Our findings show that SHSODM matches the best-known sample complexity achieved by other second-order methods for gradient-dominated stochastic optimization but without cubic regularization. Empirically, since the homogenization approach only relies on solving extremal eigenvector problem at each iteration instead of Newton-type system, our methods gain the advantage of cheaper computational cost and robustness in ill-conditioned problems. Numerical experiments on several RL tasks demonstrate the better performance of SHSODM compared to other off-the-shelf methods.

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arXiv2024

First-order methods for Stochastic Variational Inequality problems with Function Constraints

The monotone Variational Inequality (VI) is a general model with important applications in various engineering and scientific domains. In numerous instances, the VI problems are accompanied by function constraints that can be data-driven, making the usual projection operator challenging to compute. This paper presents novel first-order methods for the function-constrained Variational Inequality (FCVI) problem in smooth or nonsmooth settings with possibly stochastic operators and constraints. We introduce the AdOpEx method, which employs an operator extrapolation on the KKT operator of the FCVI in a smooth deterministic setting. Since this operator is not uniformly Lipschitz continuous in the Lagrange multipliers, we employ an adaptive two-timescale algorithm leading to bounded multipliers and achieving the optimal $O(1/T)$ convergence rate. For the nonsmooth and stochastic VIs, we introduce design changes to the AdOpEx method and propose a novel P-OpEx method that takes partial extrapolation. It converges at the rate of $O(1/\sqrt{T})$ when both the operator and constraints are stochastic or nonsmooth. This method has suboptimal dependence on the noise and Lipschitz constants of function constraints. We propose a constraint extrapolation approach leading to the OpConEx method that improves this dependence by an order of magnitude. All our algorithms easily extend to saddle point problems with function constraints that couple the primal and dual variables while maintaining the same complexity results. To the best of our knowledge, all our complexity results are new in the literature

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arXiv2024

Liquidity Jump, Liquidity Diffusion, and Treatment on Wash Trading of Crypto Assets

We propose that the liquidity of an asset includes two components: liquidity jump and liquidity diffusion. We show that liquidity diffusion has a higher correlation with crypto wash trading than liquidity jump and demonstrate that treatment on wash trading significantly reduces the level of liquidity diffusion, but only marginally reduces that of liquidity jump. We confirm that the autoregressive models are highly effective in modeling the liquidity-adjusted return with and without the treatment on wash trading. We argue that treatment on wash trading is unnecessary in modeling established crypto assets that trade in unregulated but mainstream exchanges.

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arXiv2024

Solving the Food-Energy-Water Nexus Problem via Intelligent Optimization Algorithms

The application of evolutionary algorithms (EAs) to multi-objective optimization problems has been widespread. However, the EA research community has not paid much attention to large-scale multi-objective optimization problems arising from real-world applications. Especially, Food-Energy-Water systems are intricately linked among food, energy and water that impact each other. They usually involve a huge number of decision variables and many conflicting objectives to be optimized. Solving their related optimization problems is essentially important to sustain the high-quality life of human beings. Their solution space size expands exponentially with the number of decision variables. Searching in such a vast space is challenging because of such large numbers of decision variables and objective functions. In recent years, a number of large-scale many-objectives optimization evolutionary algorithms have been proposed. In this paper, we solve a Food-Energy-Water optimization problem by using the state-of-art intelligent optimization methods and compare their performance. Our results conclude that the algorithm based on an inverse model outperforms the others. This work should be highly useful for practitioners to select the most suitable method for their particular large-scale engineering optimization problems.

cs.NE↗
arXiv2024

An Enhanced ADMM-based Interior Point Method for Linear and Conic Optimization

The ADMM-based interior point (ABIP, Lin et al. 2021) method is a hybrid algorithm that effectively combines interior point method (IPM) and first-order methods to achieve a performance boost in large-scale linear optimization. Different from traditional IPM that relies on computationally intensive Newton steps, the ABIP method applies the alternating direction method of multipliers (ADMM) to approximately solve the barrier penalized problem. However, similar to other first-order methods, this technique remains sensitive to condition number and inverse precision. In this paper, we provide an enhanced ABIP method with multiple improvements. Firstly, we develop an ABIP method to solve the general linear conic optimization and establish the associated iteration complexity. Secondly, inspired by some existing methods, we develop different implementation strategies for ABIP method, which substantially improve its performance in linear optimization. Finally, we conduct extensive numerical experiments in both synthetic and real-world datasets to demonstrate the empirical advantage of our developments. In particular, the enhanced ABIP method achieves a 5.8x reduction in the geometric mean of run time on $105$ selected LP instances from Netlib, and it exhibits advantages in certain structured problems such as SVM and PageRank. However, the enhanced ABIP method still falls behind commercial solvers in many benchmarks, especially when high accuracy is desired. We posit that it can serve as a complementary tool alongside well-established solvers.

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arXiv2024

Liquidity Premium, Liquidity-Adjusted Return and Volatility, and Extreme Liquidity

We establish innovative liquidity premium measures, and construct liquidity-adjusted return and volatility to model assets with extreme liquidity, represented by a portfolio of selected crypto assets, and upon which we develop a set of liquidity-adjusted ARMA-GARCH/EGARCH models. We demonstrate that these models produce superior predictability at extreme liquidity to their traditional counterparts. We provide empirical support by comparing the performances of a series of Mean Variance portfolios.

q-fin.PM↗
arXiv2024

Level Constrained First Order Methods for Function Constrained Optimization

We present a new feasible proximal gradient method for constrained optimization where both the objective and constraint functions are given by the summation of a smooth, possibly nonconvex function and a convex simple function. The algorithm converts the original problem into a sequence of convex subproblems. Formulating those subproblems requires the evaluation of at most one gradient value of the original objective and constraint functions. Either exact or approximate subproblem solutions can be computed efficiently in many cases. An important feature of the algorithm is the constraint level parameter. By carefully increasing this level for each subproblem, we provide a simple solution to overcome the challenge of bounding the Lagrangian multipliers and show that the algorithm follows a strictly feasible solution path till convergence to the stationary point. We develop a simple, proximal gradient descent type analysis, showing that the complexity bound of this new algorithm is comparable to gradient descent for the unconstrained setting, which is new in the literature. Exploiting this new design and analysis technique, we extend our algorithms to some more challenging constrained optimization problems where 1) the objective is a stochastic or finite-sum function, and 2) structured nonsmooth functions replace smooth components of both objective and constraint functions. Complexity results for these problems also seem to be new in the literature. Finally, our method can also be applied to convex function-constrained problems where we show complexities similar to the proximal gradient method.

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arXiv2023

Cryogenic quasi-static embedded DRAM for energy-efficient compute-in-memory applications

Compute-in-memory (CIM) presents an attractive approach for energy-efficient computing in data-intensive applications. However, the development of suitable memory designs to achieve high-performance CIM remains a challenging task. Here, we propose a cryogenic quasi-static embedded DRAM to address the logic-memory mismatch of CIM. Guided by the re-calibrated cryogenic device model, the designed four-transistor bit-cell achieves full-swing data storage, low power consumption, and extended retention time at cryogenic temperatures. Combined with the adoption of cryogenic write bitline biasing technique and readout circuitry optimization, our 4Kb cryogenic eDRAM chip demonstrates a 1.37$\times$10$^6$ times improvement in retention time, while achieving a 75 times improvement in retention variability, compared to room-temperature operation. Moreover, it also achieves outstanding power performance with a retention power of 112 fW and a dynamic power of 108 $μ$W at 4.2 K, which can be further decreased by 7.1% and 13.6% using the dynamic voltage scaling technique. This work reveals the great potential of cryogenic CMOS for high-density data storage and lays a solid foundation for energy-efficient CIM implementations.

cs.ET↗
arXiv2023

Delayed Stochastic Algorithms for Distributed Weakly Convex Optimization

This paper studies delayed stochastic algorithms for weakly convex optimization in a distributed network with workers connected to a master node. Recently, Xu et al. 2022 showed that an inertial stochastic subgradient method converges at a rate of $\mathcal{O}(τ_{\text{max}}/\sqrt{K})$ which depends on the maximum information delay $τ_{\text{max}}$. In this work, we show that the delayed stochastic subgradient method ($\texttt{DSGD}$) obtains a tighter convergence rate which depends on the expected delay $\barτ$. Furthermore, for an important class of composition weakly convex problems, we develop a new delayed stochastic prox-linear ($\texttt{DSPL}$) method in which the delays only affect the high-order term in the complexity rate and hence, are negligible after a certain number of $\texttt{DSPL}$ iterations. In addition, we demonstrate the robustness of our proposed algorithms against arbitrary delays. By incorporating a simple safeguarding step in both methods, we achieve convergence rates that depend solely on the number of workers, eliminating the effect of the delay. Our numerical experiments further confirm the empirical superiority of our proposed methods.

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arXiv2023

GBM-based Bregman Proximal Algorithms for Constrained Learning

As the complexity of learning tasks surges, modern machine learning encounters a new constrained learning paradigm characterized by more intricate and data-driven function constraints. Prominent applications include Neyman-Pearson classification (NPC) and fairness classification, which entail specific risk constraints that render standard projection-based training algorithms unsuitable. Gradient boosting machines (GBMs) are among the most popular algorithms for supervised learning; however, they are generally limited to unconstrained settings. In this paper, we adapt the GBM for constrained learning tasks within the framework of Bregman proximal algorithms. We introduce a new Bregman primal-dual method with a global optimality guarantee when the learning objective and constraint functions are convex. In cases of nonconvex functions, we demonstrate how our algorithm remains effective under a Bregman proximal point framework. Distinct from existing constrained learning algorithms, ours possess a unique advantage in their ability to seamlessly integrate with publicly available GBM implementations such as XGBoost (Chen and Guestrin, 2016) and LightGBM (Ke et al., 2017), exclusively relying on their public interfaces. We provide substantial experimental evidence to showcase the effectiveness of the Bregman algorithm framework. While our primary focus is on NPC and fairness ML, our framework holds significant potential for a broader range of constrained learning applications. The source code is currently freely available at https://github.com/zhenweilin/ConstrainedGBM}{https://github.com/zhenweilin/ConstrainedGBM.

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