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Second-Order Information in Non-Convex Stochastic Optimization: Power and Limitations [article]

Yossi Arjevani, Yair Carmon, John C. Duchi, Dylan J. Foster, Ayush Sekhari, Karthik Sridharan
2020 arXiv   pre-print
Together, these results characterize the complexity of non-convex stochastic optimization with second-order methods and beyond.  ...  Expanding our scope to the oracle complexity of finding (ϵ,γ)-approximate second-order stationary points, we establish nearly matching upper and lower bounds for stochastic second-order methods.  ...  Second-Order Information in Non-Convex Stochastic Optimization: Power and Limitations  ... 
arXiv:2006.13476v1 fatcat:ayf2gykjpfeldogyxjgmstraam

Optimal and Near-Optimal Policies for Wireless Power Transfer in Energy-Limited and Power-Limited Scenarios [article]

Roohollah Rezaei, Mohammad Movahednasab, Naeimeh Omidvar, Mohammad Reza Pakravan
2018 arXiv   pre-print
The formulated problems are non-convex stochastic optimization problems that are very challenging to solve.  ...  do not require such information and perform well in practice.  ...  The optimization problem (5) is highly non-trivial and includes some challenges that need to be addressed properly. First, due to constraint (5b), the problem is non-convex.  ... 
arXiv:1804.05569v1 fatcat:dujiyqhxyrhh5da63mjvxcnrs4

Online Power Optimization in Feedback-Limited, Dynamic and Unpredictable IoT Networks

Alexandre Marcastel, Elena Veronica Belmega, Panayotis Mertikopoulos, Inbar Fijalkow
2019 IEEE Transactions on Signal Processing  
algorithms) are no longer relevant; and b) the lack of sufficient information at the device end.  ...  One of the key challenges in Internet of Things (IoT) networks is to connect many different types of autonomous devices while reducing their individual power consumption.  ...  This means that only a single scalar worth of information is needed at the transmitting device -a major advantage in feedback-limited and dynamic networks, where the acquisition of non-causal and complete  ... 
doi:10.1109/tsp.2019.2910479 fatcat:znaoxfiqurbtrahypq56unmfzu

Distributionally Robust Co-Optimization of Power Dispatch and Do-Not-Exceed Limits [article]

Hongyan Ma, Ruiwei Jiang, Zheng Yan
2018 arXiv   pre-print
In this paper, we propose a two-stage distributionally robust optimization model that co-optimizes the power dispatch and the DNE limits, by adopting an affinely adjustable power re-dispatch and an adjustable  ...  Notably, this model admits a second-order conic reformulation that can be efficiently solved by the commercial solvers (e.g., MOSEK).  ...  In Fig. 1 , we display the minimum power dispatch cost and the optimal DNE limits under various δ values.  ... 
arXiv:1808.02007v1 fatcat:z36c52n6o5bp7lb6jgvhxyioci

On the Power and Limitations of Random Features for Understanding Neural Networks [article]

Gilad Yehudai, Ohad Shamir
2022 arXiv   pre-print
In this paper, we first review these techniques, providing a simple and self-contained analysis for one-hidden-layer networks.  ...  We then argue that despite the impressive positive results, random feature approaches are also inherently limited in what they can explain.  ...  We thank Yuanzhi Li for some helpful comments on a previous version of this paper and for Pritish Kamath for spotting a bug in a previous version of the paper.  ... 
arXiv:1904.00687v4 fatcat:yan3loce7ve6di2q26b35krhtu

Executive Discretion and Crisis Prevention: An Efficiency Rationale for Limitations on Executive Power

Tiberiu Dragu, Mattias K. Polborn
2012 Social Science Research Network  
Abstract What is the role of legal limits on executive action, if any, in times of crises when citizens demand more security and allowing executive officials legal flexibility appears necessary to achieve  ...  In contrast, when the executive faces increased electoral incentives to provide security and there is an explicit limit on executive antiterrorism actions, security from terrorism always increases.  ...  To this end, the government needs to collect information in order to identify individuals or groups that might be planning attacks in order to detect threats before they matured into terrorist attacks.  ... 
doi:10.2139/ssrn.2138331 fatcat:iljwz5jtxjg2vfppmmzjbdgwqq

AC OPF in radial distribution networks – Part I: On the limits of the branch flow convexification and the alternating direction method of multipliers

Konstantina Christakou, Dan-Cristian Tomozei, Jean-Yves Le Boudec, Mario Paolone
2017 Electric power systems research  
The optimal power-flow problem (OPF) has always played a key role in the planning and operation of power systems.  ...  To overcome the aforementioned limitations, we propose a specific algorithm for the solution of a non-approximated, non-convex OPF problem in radial distribution systems.  ...  To overcome the aforementioned limitations, here in this second part, we propose an algorithm for the solution of the non-approximated non-convex AC OPF problem in radial networks.  ... 
doi:10.1016/j.epsr.2016.07.030 fatcat:3rtxrqsoczdodehyggoo5basvq

Stochastic Non-convex Optimization with Strong High Probability Second-order Convergence [article]

Mingrui Liu, Tianbao Yang
2017 arXiv   pre-print
However, existing results on stochastic non-convex optimization are limited, especially with a high probability second-order convergence.  ...  In this paper, we study stochastic non-convex optimization with non-convex random functions.  ...  non-convex optimization are still limited.  ... 
arXiv:1710.09447v2 fatcat:2756sh6h4jc2lam2ts2mucedsi

Convex Optimal Uncertainty Quantification [article]

Shuo Han, Molei Tao, Ufuk Topcu, Houman Owhadi, Richard M. Murray
2015 arXiv   pre-print
The sufficient conditions include that the objective function is piecewise concave and the constraints are piecewise convex.  ...  In particular, we show that piecewise concave objective functions may appear in applications where the objective is defined by the optimal value of a parameterized linear program.  ...  Acknowledgment This work was supported in part by NSF grant CNS-0931746 and AFOSR grant FA9550-12-1-0389.  ... 
arXiv:1311.7130v2 fatcat:blr3jmusq5bozmgn5ymb35ohui

NEON+: Accelerated Gradient Methods for Extracting Negative Curvature for Non-Convex Optimization [article]

Yi Xu, Rong Jin, Tianbao Yang
2018 arXiv   pre-print
However, the analysis of AG methods for non-convex optimization is still limited.  ...  proposed in a recent manuscript AGNON, which directly analyzed the Nesterov's AG method for non-convex optimization and appeared online on November 29, 2017.  ...  Non-Convex Optimization As a byproduct, we can also use Neon + in stochastic non-convex optimization for extracging negative curvature to strengthen first-order stochastic methods for enjoying convergence  ... 
arXiv:1712.01033v2 fatcat:jzs5l2uzefcmjnja426ubzdgeq

Two-stage stochastic optimization for optimal power flow under renewable generation uncertainty

Dzung Phan, Soumyadip Ghosh
2014 ACM Transactions on Modeling and Computer Simulation  
Any supply-demand mis-match in the second stage must be alleviated using high marginal-cost power sources that can be tapped in short order.  ...  We propose a two-stage stochastic version of the classical economic dispatch problem with alternating current (AC) power flow constraints, a nonconvex optimization formulation that is central to power  ...  Moreover, the second-stage optimal solutions yield sub-gradient information for this convex recourse function (Theorem 3.1 in Section 3).  ... 
doi:10.1145/2553084 fatcat:fjtuly4phnfmhhuhbjb6mt23ta

Stochastic Successive Convex Approximation for Non-Convex Constrained Stochastic Optimization [article]

An Liu and Vincent Lau and Borna Kananian
2019 arXiv   pre-print
The proposed CSSCA algorithm can also handle stochastic non-convex constraints in optimization problems, and it opens the way to solving more challenging optimization problems that occur in many applications  ...  Most existing methods for non-convex stochastic optimization, such as the stochastic (average) gradient and stochastic majorization-minimization, only consider minimizing a stochastic non-convex objective  ...  In [22] , a stochastic parallel SCA method is proposed for non-convex stochastic sum-utility optimization problems in multi-agent networks.  ... 
arXiv:1801.08266v2 fatcat:br2c2zdmf5h4bgjelnkcv76fr4

Sinkhorn Distributionally Robust Optimization [article]

Jie Wang, Rui Gao, Yao Xie
2021 arXiv   pre-print
We derive convex programming dual reformulations when the nominal distribution is an empirical distribution and a general distribution, respectively.  ...  We study distributionally robust optimization with Sinkorn distance -- a variant of Wasserstein distance based on entropic regularization.  ...  The set Θ is closed, convex, and contains a non-empty interior.  ... 
arXiv:2109.11926v1 fatcat:lcwrltfisjbyznk3743vxhcsme

Large-Scale Convex Optimization for Ultra-Dense Cloud-RAN [article]

Yuanming Shi and Jun Zhang and Khaled B. Letaief and Bo Bai and Wei Chen
2015 arXiv   pre-print
Network power minimization and channel state information acquisition will be used as two typical examples to demonstrate the effectiveness of convex optimization methods.  ...  , while convex optimization will serve as a powerful tool for such purposes.  ...  (e.g., second-order cones and positive semidefinite cones).  ... 
arXiv:1506.04243v1 fatcat:h45a7e4hmrfwteln76umylowaq

Sub-sampled Cubic Regularization for Non-convex Optimization [article]

Jonas Moritz Kohler, Aurelien Lucchi
2017 arXiv   pre-print
This approach is particularly attractive because it escapes strict saddle points and it provides stronger convergence guarantees than first- and second-order as well as classical trust region methods.  ...  We consider the minimization of non-convex functions that typically arise in machine learning. Specifically, we focus our attention on a variant of trust region methods known as cubic regularization.  ...  results demonstrating significant speed-ups compared to standard first and second-order optimization methods for various convex and non-convex objectives.  ... 
arXiv:1705.05933v3 fatcat:zx2rrkfgsfhfhd2vhjipljquvi
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