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Physarum Powered Differentiable Linear Programming Layers and Applications [article]

Zihang Meng, Sathya N. Ravi, Vikas Singh
2021 arXiv   pre-print
Our proposal is easy to implement and can easily serve as layers whenever a learning procedure needs a fast approximate solution to a LP, within a larger network.  ...  We describe our development and show the use of our solver in a video segmentation task and meta-learning for few-shot learning.  ...  We thank Damian Straszak and Nisheeth Vishnoi for helpful clarifications regarding the convergence of continuous time physarum dynamics, and Yingxin Jia for interfacing our solver with a feature matching  ... 
arXiv:2004.14539v2 fatcat:3nghuh53grdelbxe4f7vdwucau

Optimization over Nonnegative and Convex Polynomials With and Without Semidefinite Programming [article]

Georgina Hall
2018 arXiv   pre-print
(See manuscript for the rest of the abstract.)  ...  In the first part of this thesis, we present two methods for approximately solving large-scale sum of squares programs that dispense altogether with semidefinite programming and only involve solving a  ...  These are regression trees and isotonic regression. In the first, the feature domain is recursively partitioned into smaller subdomains, where interactions between features are more manageable.  ... 
arXiv:1806.06996v1 fatcat:ywvkxguvobh43jvdaedk2tf3ju

On Nonparametric Ordinal Classification with Monotonicity Constraints

Wojciech Kotlowski, Roman Slowinski
2013 IEEE Transactions on Knowledge and Data Engineering  
Numerous people contributed to my research in different ways. I would  ...  heuristic algorithms for isotonic regression, working in O(n 2 ).  ...  In the isotonic regression problem, we minimize L 2 -norm (sum of squares) between vectors y = (y 1 , . . . , y n ) and p = (p 1 , . . . , p n ), while in (3.16) we minimize L 1 -norm (sum of absolute  ... 
doi:10.1109/tkde.2012.204 fatcat:q52dnmmmqbf6znbvt7rzb5igv4

Implicit regularization and momentum algorithms in nonlinear adaptive control and prediction [article]

Nicholas M. Boffi, Jean-Jacques E. Slotine
2020 arXiv   pre-print
in algorithm development for both adaptive nonlinear control and adaptive dynamics prediction.  ...  Despite being an established field with many practical applications and a rich theory, much of the development in adaptive control for nonlinear systems revolves around a few key algorithms.  ...  We take γ = 50 for the l 1 norm and γ = .5 for the l 10 norm 12 . In all cases, β = 1 and µ = 3γ 2ηβ .  ... 
arXiv:1912.13154v6 fatcat:7bs5d63sfbh7dbkxbqzcujhdde

Simulation-based optimization over discrete sets with noisy constraints

Yao Luo, Eunji Lim
2011 Proceedings of the 2011 Winter Simulation Conference (WSC)  
Furthermore, our LP formulation has a dual problem that exhibits a block-angular form in its constraints.  ...  Such an elaborated method can be further used to devise an algorithm to compute better estimators for steady-state performance measures by utilizing simulation output after the initial transient phase.  ...  a provably convergent algorithm to a local optimal solution.  ... 
doi:10.1109/wsc.2011.6148091 dblp:conf/wsc/LuoL11 fatcat:6pp3izsxqngw3nnx6gncxzbf74

Cost-to-Go Function Approximation [chapter]

2017 Encyclopedia of Machine Learning and Data Mining  
Mitchell's, (1982; candidate-elimination algorithm performs a bidirectional search in the hypothesis space.  ...  If there are any positive examples in the training set, it calls the subroutine FINDBESTRULE for learning a single rule that Nilsson NJ (1995) Reacting, planning and learning in an autonomous agent.  ...  Acknowledgements Sanjay Jain was supported in part by NUS grant numbers C252-000-087-001, R146-000- Synonyms Separate-and-conquer learning Method Most covering algorithms operate in a concept learning  ... 
doi:10.1007/978-1-4899-7687-1_100093 fatcat:vse7ncdqs5atlosjhz7fhlj3im

How to Certify Machine Learning Based Safety-critical Systems? A Systematic Literature Review [article]

Florian Tambon, Gabriel Laberge, Le An, Amin Nikanjam, Paulina Stevia Nouwou Mindom, Yann Pequignot, Foutse Khomh, Giulio Antoniol, Ettore Merlo, François Laviolette
2021 arXiv   pre-print
Results: The SLR results highlighted the enthusiasm of the community for this subject, as well as the lack of diversity in terms of datasets and type of models.  ...  Finally, it also illustrated the necessity to build connections between the above mention main pillars that are for now mainly studied separately.  ...  They all contributed to improving this SLR.  ... 
arXiv:2107.12045v3 fatcat:43vqxywawbeflhs6ehzovvsevm

OASIcs, Volume 69, SOSA'19, Complete Volume [article]

Jeremy T. Fineman, Michael Mitzenmacher
Acknowledgements We thank Dipen Rughwani, Kostas Tsioutsiouliklis, and Yunhong Zhou for telling us about [18], for extensive discussions about the problem and our algorithms, and for insightful comments  ...  Acknowledgements We thank Manfred Scheucher for implementing the algorithm and helping with the figures.  ...  while the Scaling PAV Algorithm is still busy in its sorting phase. 1:12 Isotonic Regression by Dynamic Programming A Weighted Isotonic L 2 Regression We state without proof the properties of the  ... 
doi:10.4230/oasics.sosa.2019 fatcat:qjz3tl5ccfe3nprcrv6msbfwbq

Computational and Statistical Advances in Testing and Learning

Aaditya Kumar Ramdas
Lastly, we develop fast state-of-the-art numerically stable algorithms for an important univariate regression problem called trend filtering with a wide variety of practical extensions.  ...  We also develop a unified proof for convergence rates of randomized algorithms for the ordinary least squares and ridge regression problems in a variety of settings, with the purpose of investigating which  ...  Acknowledgments Acknowledgements We thank Rui Castro for detailed conversations about our model and results. This work is supported in part by NSF Big Data grant IIS-1247658. Acknowledgments  ... 
doi:10.1184/r1/6715238 fatcat:6asjrtoczbeqxp3ydooy5aywlu

Modern Computational Approaches to Nonlinear Discrete Optimization and Applications in Process Systems Engineering

David Bernal Neira
In Chapter 2 we provide a review on the different solution algorithms and existing software to deterministically solve a subclass of MINLP problems called convex MINLP.  ...  The objective of this Thesis is to propose new solutions and modeling methods for nonlinear discrete optimization problems, which lead to improvements with respect to the existing solution approaches.  ...  description of the Outer-approximation method [25, 30] , in Algorithm 10, and the LP/NLP Branch & Bound method [90, 129] , in Algorithm 11. 7.B Reformulation of Norms 1 and ∞ using Linear Programming  ... 
doi:10.1184/r1/19146305.v1 fatcat:dvqfoztozjes7ejmoldd2smrha

Minimum Cost Disjoint Paths under Arc Dependences. Algorithms for Practice [article]

Martin Oellrich, Technische Universität Berlin, Technische Universität Berlin, Rolf H. Möhring
In this thesis, we develop a unified algorithmic framework for Minimum Cost Disjoint Paths Problems.  ...  A feasible solution is a set of connecting paths, one for each node pair, such that two conditions are satisfied: 1. all paths are pairwise nonintersecting in a given sense, 2. the total cost of the solution  ...  We then would need one separate call of Algorithm DijkPlain for each demand, but could save on label computations, as they are shared.  ... 
doi:10.14279/depositonce-1857 fatcat:6aofruxyjzfgdblqzvuuizvdm4