Optimization
Mathematical Optimization and Machine Learning - Gurobi Optimization
Dr. Rothberg has served in senior leadership positions in optimization software companies for more than twenty years. Prior to his role as Gurobi CEO, Dr. Rothberg held the Gurobi COO position since co-founding Gurobi in 2008, and prior to that he led the ILOG CPLEX team. Dr. Edward Rothberg has a BS in Mathematical and Computational Science from Stanford University, and an MS and PhD in Computer Science, also from Stanford University. Dr. Rothberg has published numerous papers in the fields of linear algebra, parallel computing, and mathematical programming. He is one of the world's leading experts in sparse Cholesky factorization and computational linear, integer, and quadratic programming.
A Survey on Influence Maximization: From an ML-Based Combinatorial Optimization
Li, Yandi, Gao, Haobo, Gao, Yunxuan, Guo, Jianxiong, Wu, Weili
Influence Maximization (IM) is a classical combinatorial optimization problem, which can be widely used in mobile networks, social computing, and recommendation systems. It aims at selecting a small number of users such that maximizing the influence spread across the online social network. Because of its potential commercial and academic value, there are a lot of researchers focusing on studying the IM problem from different perspectives. The main challenge comes from the NP-hardness of the IM problem and \#P-hardness of estimating the influence spread, thus traditional algorithms for overcoming them can be categorized into two classes: heuristic algorithms and approximation algorithms. However, there is no theoretical guarantee for heuristic algorithms, and the theoretical design is close to the limit. Therefore, it is almost impossible to further optimize and improve their performance. With the rapid development of artificial intelligence, the technology based on Machine Learning (ML) has achieved remarkable achievements in many fields. In view of this, in recent years, a number of new methods have emerged to solve combinatorial optimization problems by using ML-based techniques. These methods have the advantages of fast solving speed and strong generalization ability to unknown graphs, which provide a brand-new direction for solving combinatorial optimization problems. Therefore, we abandon the traditional algorithms based on iterative search and review the recent development of ML-based methods, especially Deep Reinforcement Learning, to solve the IM problem and other variants in social networks. We focus on summarizing the relevant background knowledge, basic principles, common methods, and applied research. Finally, the challenges that need to be solved urgently in future IM research are pointed out.
SLOPT: Bandit Optimization Framework for Mutation-Based Fuzzing
Koike, Yuki, Katsura, Hiroyuki, Yakura, Hiromu, Kurogome, Yuma
Mutation-based fuzzing has become one of the most common vulnerability discovery solutions over the last decade. Fuzzing can be optimized when targeting specific programs, and given that, some studies have employed online optimization methods to do it automatically, i.e., tuning fuzzers for any given program in a program-agnostic manner. However, previous studies have neither fully explored mutation schemes suitable for online optimization methods, nor online optimization methods suitable for mutation schemes. In this study, we propose an optimization framework called SLOPT that encompasses both a bandit-friendly mutation scheme and mutation-scheme-friendly bandit algorithms. The advantage of SLOPT is that it can generally be incorporated into existing fuzzers, such as AFL and Honggfuzz. As a proof of concept, we implemented SLOPT-AFL++ by integrating SLOPT into AFL++ and showed that the program-agnostic optimization delivered by SLOPT enabled SLOPT-AFL++ to achieve higher code coverage than AFL++ in all of ten real-world FuzzBench programs. Moreover, we ran SLOPT-AFL++ against several real-world programs from OSS-Fuzz and successfully identified three previously unknown vulnerabilities, even though these programs have been fuzzed by AFL++ for a considerable number of CPU days on OSS-Fuzz.
Off-Policy Evaluation with Policy-Dependent Optimization Response
Guo, Wenshuo, Jordan, Michael I., Zhou, Angela
The intersection of causal inference and machine learning for decision-making is rapidly expanding, but the default decision criterion remains an \textit{average} of individual causal outcomes across a population. In practice, various operational restrictions ensure that a decision-maker's utility is not realized as an \textit{average} but rather as an \textit{output} of a downstream decision-making problem (such as matching, assignment, network flow, minimizing predictive risk). In this work, we develop a new framework for off-policy evaluation with \textit{policy-dependent} linear optimization responses: causal outcomes introduce stochasticity in objective function coefficients. Under this framework, a decision-maker's utility depends on the policy-dependent optimization, which introduces a fundamental challenge of \textit{optimization} bias even for the case of policy evaluation. We construct unbiased estimators for the policy-dependent estimand by a perturbation method, and discuss asymptotic variance properties for a set of adjusted plug-in estimators. Lastly, attaining unbiased policy evaluation allows for policy optimization: we provide a general algorithm for optimizing causal interventions. We corroborate our theoretical results with numerical simulations.
Batch Active Learning from the Perspective of Sparse Approximation
Shen, Maohao, Jiang, Bowen, Zhang, Jacky Yibo, Koyejo, Oluwasanmi
Active learning enables efficient model training by leveraging interactions between machine learning agents and human annotators. We study and propose a novel framework that formulates batch active learning from the sparse approximation's perspective. Our active learning method aims to find an informative subset from the unlabeled data pool such that the corresponding training loss function approximates its full data pool counterpart. We realize the framework as sparsity-constrained discontinuous optimization problems, which explicitly balance uncertainty and representation for large-scale applications and could be solved by greedy or proximal iterative hard thresholding algorithms. The proposed method can adapt to various settings, including both Bayesian and non-Bayesian neural networks. Numerical experiments show that our work achieves competitive performance across different settings with lower computational complexity.
On Constraints in First-Order Optimization: A View from Non-Smooth Dynamical Systems
Muehlebach, Michael, Jordan, Michael I.
We introduce a class of first-order methods for smooth constrained optimization that are based on an analogy to non-smooth dynamical systems. Two distinctive features of our approach are that (i) projections or optimizations over the entire feasible set are avoided, in stark contrast to projected gradient methods or the Frank-Wolfe method, and (ii) iterates are allowed to become infeasible, which differs from active set or feasible direction methods, where the descent motion stops as soon as a new constraint is encountered. The resulting algorithmic procedure is simple to implement even when constraints are nonlinear, and is suitable for large-scale constrained optimization problems in which the feasible set fails to have a simple structure. The key underlying idea is that constraints are expressed in terms of velocities instead of positions, which has the algorithmic consequence that optimizations over feasible sets at each iteration are replaced with optimizations over local, sparse convex approximations. In particular, this means that at each iteration only constraints that are violated are taken into account. The result is a simplified suite of algorithms and an expanded range of possible applications in machine learning.
ON-DEMAND-FL: A Dynamic and Efficient Multi-Criteria Federated Learning Client Deployment Scheme
Chahoud, Mario, Sami, Hani, Mourad, Azzam, Otoum, Safa, Otrok, Hadi, Bentahar, Jamal, Guizani, Mohsen
In this paper, we increase the availability and integration of devices in the learning process to enhance the convergence of federated learning (FL) models. To address the issue of having all the data in one location, federated learning, which maintains the ability to learn over decentralized data sets, combines privacy and technology. Until the model converges, the server combines the updated weights obtained from each dataset over a number of rounds. The majority of the literature suggested client selection techniques to accelerate convergence and boost accuracy. However, none of the existing proposals have focused on the flexibility to deploy and select clients as needed, wherever and whenever that may be. Due to the extremely dynamic surroundings, some devices are actually not available to serve as clients in FL, which affects the availability of data for learning and the applicability of the existing solution for client selection. In this paper, we address the aforementioned limitations by introducing an On-Demand-FL, a client deployment approach for FL, offering more volume and heterogeneity of data in the learning process. We make use of the containerization technology such as Docker to build efficient environments using IoT and mobile devices serving as volunteers. Furthermore, Kubernetes is used for orchestration. The Genetic algorithm (GA) is used to solve the multi-objective optimization problem due to its evolutionary strategy. The performed experiments using the Mobile Data Challenge (MDC) dataset and the Localfed framework illustrate the relevance of the proposed approach and the efficiency of the on-the-fly deployment of clients whenever and wherever needed with less discarded rounds and more available data.
Learning Product Graphs from Spectral Templates
Einizade, Aref, Sardouie, Sepideh Hajipour
Graph Learning (GL) is at the core of inference and analysis of connections in data mining and machine learning (ML). By observing a dataset of graph signals, and considering specific assumptions, Graph Signal Processing (GSP) tools can provide practical constraints in the GL approach. One applicable constraint can infer a graph with desired frequency signatures, i.e., spectral templates. However, a severe computational burden is a challenging barrier, especially for inference from high-dimensional graph signals. To address this issue and in the case of the underlying graph having graph product structure, we propose learning product (high dimensional) graphs from product spectral templates with significantly reduced complexity rather than learning them directly from high-dimensional graph signals, which, to the best of our knowledge, has not been addressed in the related areas. In contrast to the rare current approaches, our approach can learn all types of product graphs (with more than two graphs) without knowing the type of graph products and has fewer parameters. Experimental results on both the synthetic and real-world data, i.e., brain signal analysis and multi-view object images, illustrate explainable and meaningful factor graphs supported by expert-related research, as well as outperforming the rare current restricted approaches.
Robust Lottery Tickets for Pre-trained Language Models
Zheng, Rui, Bao, Rong, Zhou, Yuhao, Liang, Di, Wang, Sirui, Wu, Wei, Gui, Tao, Zhang, Qi, Huang, Xuanjing
Recent works on Lottery Ticket Hypothesis have shown that pre-trained language models (PLMs) contain smaller matching subnetworks(winning tickets) which are capable of reaching accuracy comparable to the original models. However, these tickets are proved to be notrobust to adversarial examples, and even worse than their PLM counterparts. To address this problem, we propose a novel method based on learning binary weight masks to identify robust tickets hidden in the original PLMs. Since the loss is not differentiable for the binary mask, we assign the hard concrete distribution to the masks and encourage their sparsity using a smoothing approximation of L0 regularization.Furthermore, we design an adversarial loss objective to guide the search for robust tickets and ensure that the tickets perform well bothin accuracy and robustness. Experimental results show the significant improvement of the proposed method over previous work on adversarial robustness evaluation.
A Multi-Criteria Metaheuristic Algorithm for Distributed Optimization of Electric Energy Storage
Schrage, Rico, Tiemann, Paul Hendrik, Nieße, Astrid
The distributed schedule optimization of energy storage constitutes a challenge. Such algorithms often expect an input set containing all feasible schedules or respectively require to efficiently search the schedule space. It is hardly possible to accomplish this with energy storage due to its high flexibility. In this paper, the problem is introduced in detail and addressed by a metaheuristic algorithm, which generates a preselection of schedules. Three contributions are presented to achieve this goal: First, an extension for a distributed schedule optimization allowing a simultaneous optimization is developed. Second, an evolutionary algorithm is designed to generate optimized schedules. Third, the algorithm is extended to include an arbitrary local criterion. It is shown that the presented approach is suitable to schedule electric energy storage in real households and industries with different generator and storage types.