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Online Local Learning via Semidefinite Programming [article]

Paul Christiano
2014 arXiv   pre-print
We show that a simple algorithm based on semidefinite programming can obtain asymptotically optimal regret in the case where the number of possible labels is O(1), resolving an open problem posed by Hazan  ...  In many online learning problems we are interested in predicting local information about some universe of items.  ...  This regularizer is perhaps most common as a barrier function in semidefinite programming; there is an analogy between our approach and a path-following algorithm for semidefinite programming, though again  ... 
arXiv:1403.5287v1 fatcat:rkzmc5vvpvf6pfyhnybostise4

Competitive online algorithms for resource allocation over the positive semidefinite cone

Reza Eghbali, James Saunderson, Maryam Fazel
2018 Mathematical programming  
We consider a new and general online resource allocation problem, where the goal is to maximize a function of a positive semidefinite (PSD) matrix with a scalar budget constraint.  ...  The problem data arrives online, and the algorithm needs to make an irrevocable decision at each step.  ...  Online SDP problem of [EKN16] . To the best of our knowledge, [EKN16] is the only existing work that studies an online semidefinite program.  ... 
doi:10.1007/s10107-018-1305-1 fatcat:zgf2ghqgnfdkddgqqck3ouhwp4

Online Semidefinite Programming *

Noa Elad, Satyen Kale, Joseph Seffi, Naor
In what way does it make sense for a semidefinite program to be revealed? We answer these questions by defining a model for online semidefinite programming.  ...  We design an online algorithm for semidefinite programming, utilizing the online primal-dual method, achieving a competitive ratio of O (log n), where n is the number of matrices in the primal semidefinite  ...  For box constraints, we define the sparsity of an online semidefinite program, a measure capturing the potential to overshoot when solving a sub-problem of a semidefinite program.  ... 

Measurement-driven reconstruction of many-particle quantum processes by semidefinite programming with application to photosynthetic light harvesting

Jonathan J. Foley, David A. Mazziotti
2012 Physical Review A. Atomic, Molecular, and Optical Physics  
We develop a general approach based on semidefinite programming [D. A. Mazziotti, Phys. Rev.  ...  We discuss the use of this methodology for reconstructing p-particle reduced density matrices (p-RDMs) of N -particle systems where additional semidefinite constraints, known as N -representability conditions  ...  an energy functional for many-electron systems are naturally formulated as semidefinite programs, solvable by semidefinite programming.  ... 
doi:10.1103/physreva.86.012512 fatcat:v5qh5acsvzfu7aix52nqrikd6m

Low-Rank Semidefinite Programming: Theory and Applications

Alex Lemon, Anthony Man-Cho So, Yinyu Ye
2016 Foundations and Trends® in Optimization  
ISSN online version 2167-3918. Also available as a combined paper and online subscription. Abstract Finding low-rank solutions of semidefinite programs is important in many applications.  ...  For example, semidefinite programs that arise as relaxations of polynomial optimization problems are exact relaxations when the semidefinite program has a rank-1 solution.  ... 
doi:10.1561/2400000009 fatcat:pkdri5xlnnfnnfs2dlstphtvim

Approximate Dynamic Programming via Sum of Squares Programming [article]

Tyler H. Summers, Konstantin Kunz, Nikolaos Kariotoglou, Maryam Kamgarpour, Sean Summers, John Lygeros
2012 arXiv   pre-print
An approximate value function can then be computed offline by solving a semidefinite program, without having to sample the infinite constraint.  ...  The policy is evaluated online by solving a polynomial optimization problem, which also turns out to be convex in some cases.  ...  be expressed as a semidefinite program.  ... 
arXiv:1212.1269v1 fatcat:3pd5gcd5k5dmdfb4anhupaacne

Erratum to: On second-order duality of minimax fractional programming with square root term involving generalized $${\varvec{B}}$$ B - $${\varvec{(p,\,r)}}$$ ( p , r ) -invex functions

Sonali, N. Kailey, V. Sharma
2017 Annals of Operations Research  
On second-order duality of minimax fractional programming with square root term involving generalized B-(p, r)-invex functions. Annals of Operations Research, 244, 603-617].  ...  instead of positive semidefinite.  ...  The online version of the original article can be found under doi:10.1007/s10479-016-2147-y. Mathematics, Thapar University, Patiala 147 004, India  ... 
doi:10.1007/s10479-017-2502-7 fatcat:mc7vngt77feqzphmrkphzxo77m

Chordal Graphs and Semidefinite Optimization

Lieven Vandenberghe, Martin S. Andersen
2015 Foundations and Trends® in Optimization  
ISSN online version 2167-3918. Also available as a combined paper and online subscription.  ...  Examples include the solution of sparse linear equations (Gauss elimination), dynamic programming (eliminating optimization variables by optimizing over them), and marginalization of probability distributions  ... 
doi:10.1561/2400000006 fatcat:jarefwxrsjdodpyistl2225mte

On the Minimax Design of Passband Linear-Phase Variable Digital Filters Using Semidefinite Programming

K.M. Tsui, K.S. Yeung, S.C. Chan, K.W. Tse
2004 IEEE Signal Processing Letters  
Index Terms-Variable digital filter (VDF) design, low-delay, minimax, semidefinite programming (SDP), variable cutoff frequency, variable fractional delay.  ...  Variable digital filters (VDFs) are useful to the implementation of digital receivers because its frequency characteristics such as fractional delays and cutoff frequencies can be varied online.  ...  On the Minimax Design of Passband Linear-Phase Variable Digital Filters Using Semidefinite Programming K. M. Tsui, K. S. Yeung, S. C. Chan, and K. W.  ... 
doi:10.1109/lsp.2004.833585 fatcat:4r22ueubifae5gtnnndb5xgpsu

A Semidefinite Programming Approach to Source Localization in Wireless Sensor Networks

Chen Meng, Zhi Ding, S. Dasgupta
2008 IEEE Signal Processing Letters  
Index Terms-Maximum likelihood estimation, semidefinite programming, source localization, wireless sensor network. I.  ...  Based on the problem transformation, we develop a fast low-complexity semidefinite programming (SDP) algorithm for two different source localization models.  ... 
doi:10.1109/lsp.2008.916731 fatcat:xwm6rhr47rcojljlhmja5rnu44

A successive constraint approach to solving parameter-dependent linear matrix inequalities

Robert O'Connor
2017 Comptes rendus. Mathematique  
We also extend the method to approximate solutions to semidefinite programming problems.  ...  The efficiency of our method is made possible by an offline/online decomposition of the workload.  ...  The semidefinite programming problem In this section we will show how our methods can be used to approximate solutions to the semidefinite program (S).  ... 
doi:10.1016/j.crma.2017.05.001 fatcat:vndxkorfn5dwfleut3beriwph4

Erratum: Numerical estimation of the relative entropy of entanglement [Phys. Rev. A82, 052336 (2010)]

Mark W. Girard, Yuriy Zinchenko, Shmuel Friedland, Gilad Gour
2015 Physical Review A. Atomic, Molecular, and Optical Physics  
The original code relies on SEDUMI [1] as its internal solver for semidefinite programming.  ...  In particular, CVX allows one to more easily define the positive partial transpose (PPT) constraint when setting up a semidefinite program.  ... 
doi:10.1103/physreva.91.029901 fatcat:xltfgqeucvbqxpzcsr23o6utla

On reduced semidefinite programs for second order moment bounds with applications

Karthik Natarajan, Chung-Piaw Teo
2016 Mathematical programming  
In fact, we can replace the completely positive programming formulation for the moment bound on X , with an associated semidefinite program, provided we have a linear or a semidefinite representation of  ...  For X described explicitly by a finite set of points, our formulation leads to a reduction in the size of the semidefinite program.  ...  When m is large, the size of the semidefinite program (14) is much smaller than the size of the semidefinite program (7) .  ... 
doi:10.1007/s10107-016-1019-1 fatcat:hck37c3gqfazjb2qxb3yc74oma

Time-reversal of rank-one quantum strategy functions [article]

Yuan Su, John Watrous
2018 arXiv   pre-print
We prove a time-reversal property for a class of linear functions, defined on quantum strategy representations within this framework, that corresponds to the set of rank-one positive semidefinite operators  ...  Figure 3 : 3 The semidefinite program representing a maximization of a linear function of an n-turn strategy.  ...  program maximize: ρ, X subject to: X ∈ S n (X 1 , . . . , X n ; Y 1 , . . . , Y n ) that concerns an online variant of entanglement manipulation, as is explained shortly.  ... 
arXiv:1801.08491v1 fatcat:bm5kllumybcnzpxltzkv63rnly

Min-Max Design of FIR Digital Filters by Semidefinite Programming [chapter]

Masaaki Nagahara
2011 Applications of Digital Signal Processing  
,α N of the optimal FIR filter by semidefinite programming as mentioned in Section 4. MATLAB codes for the semidefinite programming are shown in Section 7.  ...  For MATLAB codes of the semidefinite programming above, see Section 7.  ...  MATLAB codes for semidefinite programming In this section, we give MATLAB codes for the semidefinite programming derived in previous sections.  ... 
doi:10.5772/25413 fatcat:bxc2gc37crdszejcczxwgeauay
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