scholarly journals Kernel-based Methods for Bandit Convex Optimization

2021 ◽  
Vol 68 (4) ◽  
pp. 1-35
Author(s):  
Sébastien Bubeck ◽  
Ronen Eldan ◽  
Yin Tat Lee
Keyword(s):  
Convex Optimization ◽  
Time Algorithm ◽  
Linear Functions ◽  
Query Complexity ◽  
Time Result ◽  
Derivative Free Optimization ◽  
Bernoulli Convolutions ◽  
New Ideas ◽  
Simple Variant ◽  
The Cost

We consider the adversarial convex bandit problem and we build the first poly( T )-time algorithm with poly( n ) √ T -regret for this problem. To do so, we introduce three new ideas in the derivative-free optimization literature: (i) kernel methods, (ii) a generalization of Bernoulli convolutions, and (iii) a new annealing schedule for exponential weights (with increasing learning rate). The basic version of our algorithm achieves Õ( n 9.5 √ T )-regret, and we show that a simple variant of this algorithm can be run in poly( n log ( T ))-time per step (for polytopes with polynomially many constraints) at the cost of an additional poly( n ) T o(1) factor in the regret. These results improve upon the Õ( n 11 √ T -regret and exp (poly( T ))-time result of the first two authors and the log ( T ) poly( n ) √ T -regret and log( T ) poly( n ) -time result of Hazan and Li. Furthermore, we conjecture that another variant of the algorithm could achieve Õ( n 1.5 √ T )-regret, and moreover that this regret is unimprovable (the current best lower bound being Ω ( n √ T ) and it is achieved with linear functions). For the simpler situation of zeroth order stochastic convex optimization this corresponds to the conjecture that the optimal query complexity is of order n 3 / ɛ 2 .

Subsea Production Layout: Design and Cost

2017 ◽  
Author(s):  
Cheng Hong ◽  
Yuxi Wang ◽  
Jiankun Yang ◽  
Yuri M. Berbert ◽  
Marcelo I. Lourenço ◽  
...  
Keyword(s):  
Design Procedure ◽  
Layout Design ◽  
Harsh Environment ◽  
Deep Waters ◽  
Complex Design ◽  
Hybrid Solution ◽  
New Ideas ◽  
Water Field ◽  
The Cost ◽  
Very High

The development of a subsea field implies a complex design procedure with very high costs involved. The combination of low oil price, harsh environment, very deep waters and high drilling costs has emphasized the need for new ideas to reduce both CAPEX and OPEX. The paper considers different subsea layout scenarios of a typical deep water field. Each scenario is optimized considering pipeline length, equipment cost and flow assurance. The software QUE$TOR is then applied to estimate the cost of each optimized scenario. Two of them are selected for further studies, FPSO connected to six slots subsea manifolds, and subsea separator connected to eight slots cluster manifolds with tie-back to an existing platform. The latter representing a hybrid solution based on the subsea-to-shore concept. Cost and technical feasibility are considered in order to evaluate the two scenarios.

scholarly journals On the Hausdorff Dimension of Bernoulli Convolutions

2018 ◽  
Vol 2020 (19) ◽  
pp. 6569-6595 ◽  
Author(s):  
Shigeki Akiyama ◽  
De-Jun Feng ◽  
Tom Kempton ◽  
Tomas Persson
Keyword(s):  
Hausdorff Dimension ◽  
Rate Of Convergence ◽  
Finite Time ◽  
Time Algorithm ◽  
Bernoulli Convolution ◽  
Bernoulli Convolutions ◽  
Explicit Rate ◽  
Products Of Matrices

Abstract We give an expression for the Garsia entropy of Bernoulli convolutions in terms of products of matrices. This gives an explicit rate of convergence of the Garsia entropy and shows that one can calculate the Hausdorff dimension of the Bernoulli convolution $\nu _{\beta }$ to arbitrary given accuracy whenever $\beta $ is algebraic. In particular, if the Garsia entropy $H(\beta )$ is not equal to $\log (\beta )$ then we have a finite time algorithm to determine whether or not $\operatorname{dim_H} (\nu _{\beta })=1$.

THE STRANGULATION OF EXPLORATION GEOPHYSICS

Geophysics ◽  
1973 ◽  
Vol 38 (2) ◽  
pp. 406-407
Author(s):  
Carl H. Savit
Keyword(s):  
Solid Earth ◽  
Common Property ◽  
Professional Activity ◽  
General Level ◽  
Beneficial Effects ◽  
The Earth ◽  
New Ideas ◽  
Level Of Knowledge ◽  
The Common ◽  
The Cost

Exploration geophysics is a profession whose sole activity is to explore the solid earth by physical means. The aim or purpose of exploration geophysical activity is to obtain information about the earth which may be economically or scientifically useful. During the first few decades of the application of geophysics, constraints on geophysical professional activity were of a type we can call “natural”; that is, our profession was limited in its accomplishments by our own level of knowledge, by the general level of associated sciences and technologies, and by the cost and perceived value of the information we produced. All of these natural constraints have the common property that they can be modified by improvements within our profession. Each time we tried something new we observed the results and adopted those new ideas and techniques which produced beneficial effects. Variations which resulted in poorer results or results not worth the extra cost were dropped from the repertoire.

scholarly journals Following Forrelation – quantum algorithms in exploring Boolean functions' spectra

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Suman Dutta ◽  
Subhamoy Maitra ◽  
Chandra Sekhar Mukherjee
Keyword(s):  
Boolean Functions ◽  
Cross Correlation ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Sampling Technique ◽  
Linear Functions ◽  
Query Complexity ◽  
Walsh Spectrum ◽  
Correlation Spectrum ◽  
The Cross

<p style='text-indent:20px;'>Here we revisit the quantum algorithms for obtaining Forrelation [Aaronson et al., 2015] values to evaluate some of the well-known cryptographically significant spectra of Boolean functions, namely the Walsh spectrum, the cross-correlation spectrum, and the autocorrelation spectrum. We introduce the existing 2-fold Forrelation formulation with bent duality-based promise problems as desirable instantiations. Next, we concentrate on the 3-fold version through two approaches. First, we judiciously set up some of the functions in 3-fold Forrelation so that given oracle access, one can sample from the Walsh Spectrum of <inline-formula><tex-math id="M1">\begin{document}$ f $\end{document}</tex-math></inline-formula>. Using this, we obtain improved results than what one can achieve by exploiting the Deutsch-Jozsa algorithm. In turn, it has implications in resiliency checking. Furthermore, we use a similar idea to obtain a technique in estimating the cross-correlation (and thus autocorrelation) value at any point, improving upon the existing algorithms. Finally, we tweak the quantum algorithm with the superposition of linear functions to obtain a cross-correlation sampling technique. This is the first cross-correlation sampling algorithm with constant query complexity to the best of our knowledge. This also provides a strategy to check if two functions are uncorrelated of degree <inline-formula><tex-math id="M2">\begin{document}$ m $\end{document}</tex-math></inline-formula>. We further modify this using Dicke states so that the time complexity reduces, particularly for constant values of <inline-formula><tex-math id="M3">\begin{document}$ m $\end{document}</tex-math></inline-formula>.</p>

scholarly journals Revisiting Variable Output Length XOR Pseudorandom Function

2018 ◽  
pp. 314-335 ◽  
Author(s):  
Srimanta Bhattacharya ◽  
Mridul Nandi
Keyword(s):  
Linear Equations ◽  
Security Analysis ◽  
Basic Structure ◽  
Authenticated Encryption ◽  
Security Proof ◽  
Simple Variant ◽  
Encryption Algorithms ◽  
The Cost ◽  
Mirror Theory ◽  
Pseudorandom Function

Let σ be some positive integer and C ⊆ {(i, j) : 1 ≤ i < j ≤ σ}. The theory behind finding a lower bound on the number of distinct blocks P1, . . . , Pσ ∈ {0, 1}n satisfying a set of linear equations {Pi ⊕Pj = ci,j : (i, j) ∈ C} for some ci,j ∈ {0, 1}n, is called mirror theory. Patarin introduced the mirror theory and provided a proof for this. However, the proof, even for a special class of equations, is complex and contains several non-trivial gaps. As an application of mirror theory, XORP[w] (known as XOR construction) returning (w−1) block output, is a pseudorandom function (PRF) for some parameter w, called width. The XOR construction can be seen as a basic structure of some encryption algorithms, e.g., the CENC encryption and the CHM authenticated encryption, proposed by Iwata in 2006. Due to potential application of XORP[w] and the nontrivial gaps in the proof of mirror theory, an alternative simpler analysis of PRF-security of XORP[w] would be much desired. Recently (in Crypto 2017) Dai et al. introduced a tool, called the χ2 method, for analyzing PRF-security. Using this tool, the authors have provided a proof of PRF-security of XORP[2] without relying on the mirror theory. In this paper, we resolve the general case; we apply the χ2 method to obtain a simpler security proof of XORP[w] for any w ≥ 2. For w = 2, we obtain a tighter bound for a wider range of parameters than that of Dai et al.. Moreover, we consider variable width construction XORP[∗] (in which the widths are chosen by adversaries adaptively), and also provide variable output length pseudorandom function (VOLPRF) security analysis for it. As an application of VOLPRF, we propose an authenticated encryption which is a simple variant of CHM or AES-GCM and provides much higher security than those at the cost of one extra blockcipher call for every message.

scholarly journals Evolutionary Computing Techniques for Resolving Load Dispatch Problem

2020 ◽  
Vol 2 (1) ◽  
pp. 47-56
Author(s):  
Dr. Jennifer S. Raj
Keyword(s):  
Evolutionary Computing ◽  
Vital Role ◽  
Linear Functions ◽  
Economic Load Dispatch ◽  
Generation System ◽  
Cost Curves ◽  
Plant Operations ◽  
Network Operations ◽  
Power Generation System ◽  
The Cost

To have an effective scheduling of the generators in order to achieve a perfect planning and functioning of the electric power generation system so as to satisfy the demands required, the economic load dispatch is important. The economic load dispatch is very essential in the network operations in the market with the derestricted electricity and takes a vital role in the power plant operations. ELD problem scopes to meet the load demands fulfilling the various constraints in the operation and minimizing the cost of the operations. The conventional methods put forth to find the solution were found unsuitable as the cost curves of the units were assume to be uneventfully increasing linear functions and whereas the practical systems are nonlinear. So the evolutionary computing engaging the GA in combination with the PSO to resolve the economic load dispatching problem

scholarly journals Changes and Perspectives in Food Studies

2012 ◽  
Vol 1 (2) ◽  
Author(s):  
Elisabeth Dumoulin
Keyword(s):  
Teaching And Learning ◽  
Raw Materials ◽  
Food Studies ◽  
Team Work ◽  
Human Beings ◽  
Food Engineering ◽  
New Ideas ◽  
New Students ◽  
Desire To Conceive ◽  
The Cost

Food Studies represent the bases for multidisciplinary knowledge in food science, food engineering, food management, and how to use these scientific bases in a food worldwide context. Teaching and learning must be adapted to the new students, to the new tools, considering the cost of studies and equipment. The international availability of raw materials, the diversity of cultures, tastes and habits must be taken into account in the controlled food processes. Food engineering must be taught with reference to nutrition, health and security, but also to packaging, logistics, international rules, management of water, energy, wastes and cost. So how do we teach the present and future food engineers, to help them to acquire and build their own knowledge, to develop curiosity, an open mind and team work? How do we teach them to use, in an efficient way, computers, data bases, the internet, but also to learn and practice in the lab, on pilot equipment, in the plant during long internships? How do we give them the desire to conceive, to create, to manage, to communicate and to continue to learn during their professional life? International networks of universities, with associated people from research and industry, with teachers in elementary and secondary schools, with students, represent a main factor for reciprocal knowledge and exchanges, to preserve and use diversity to develop new ideas for teaching and learning. The objectives are to contribute to the development of our society, to feed in an harmonized way the world made of human beings, consumers, and workers in industry, research and universities.

scholarly journals Evolutionary Gradient Descent for Non-convex Optimization

2021 ◽  
Author(s):  
Ke Xue ◽  
Chao Qian ◽  
Ling Xu ◽  
Xudong Fei
Keyword(s):  
Convex Optimization ◽  
Stationary Point ◽  
Gradient Descent ◽  
Saddle Points ◽  
Global Optimum ◽  
General Purpose ◽  
Good Ability ◽  
Derivative Free Optimization ◽  
Derivative Free ◽  
Low Efficiency

Non-convex optimization is often involved in artificial intelligence tasks, which may have many saddle points, and is NP-hard to solve. Evolutionary algorithms (EAs) are general-purpose derivative-free optimization algorithms with a good ability to find the global optimum, which can be naturally applied to non-convex optimization. Their performance is, however, limited due to low efficiency. Gradient descent (GD) runs efficiently, but only converges to a first-order stationary point, which may be a saddle point and thus arbitrarily bad. Some recent efforts have been put into combining EAs and GD. However, previous works either utilized only a specific component of EAs, or just combined them heuristically without theoretical guarantee. In this paper, we propose an evolutionary GD (EGD) algorithm by combining typical components, i.e., population and mutation, of EAs with GD. We prove that EGD can converge to a second-order stationary point by escaping the saddle points, and is more efficient than previous algorithms. Empirical results on non-convex synthetic functions as well as reinforcement learning (RL) tasks also show its superiority.

Time-optimal path tracking for robots under dynamics constraints based on convex optimization

Robotica ◽  
2015 ◽  
Vol 34 (9) ◽  
pp. 2116-2139 ◽  
Author(s):  
Qiang Zhang ◽  
Shurong Li ◽  
Jian-Xin Guo ◽  
Xiao-Shan Gao
Keyword(s):  
Convex Optimization ◽  
High Speed ◽  
Optimal Path ◽  
Robotic Manipulators ◽  
Path Tracking ◽  
Minimum Time ◽  
Linear Functions ◽  
Change Rate ◽  
Time Path ◽  
Motion Time

SUMMARYTo fully utilize the dynamic performance of robotic manipulators and enforce minimum motion time in path tracking, the problem of minimum time path tracking for robotic manipulators under confined torque, change rate of the torque, and voltage of the DC motor is considered. The main contribution is the introduction of the concepts of virtual change rate of the torque and the virtual voltage, which are linear functions in the state and control variables and are shown to be very tight approximation to the real ones. As a result, the computationally challenging non-convex minimum time path tracking problem is reduced to a convex optimization problem which can be solved efficiently. It is also shown that introducing dynamics constraints can significantly improve the motion precision without costing much in motion time, especially in the case of high speed motion. Extensive simulations are presented to demonstrate the effectiveness of the proposed approach.

THE PROBLEM OF PARTITIONING WITH DUPLICATIONS AND ITS APPLICATIONS

1994 ◽  
Vol 03 (03) ◽  
pp. 395-405
Author(s):  
J. HARALAMBIDES ◽  
S. TRAGOUDAS
Keyword(s):  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Vlsi Layout ◽  
Optimal Polynomial ◽  
Partitioning Problem ◽  
Polynomially Solvable ◽  
The Cost ◽  
Parallel Graph ◽  
Special Case

The problem of partitioning the elements of a graph G=(V, E) into two equal size sets A and B that share at most d elements such that the total number of edges (u, v), u∈A−B, v∈B−A is minimized, arises in the areas of Hypermedia Organization, Network Integrity, and VLSI Layout. We formulate the problem in terms of element duplication, where each element c∈A∩B is substituted by two copies c′∈A and c″∈B As a result, edges incident to c′ or c″ need not count in the cost of the partition. We show that this partitioning problem is NP-hard in general, and we present a solution which utilizes an optimal polynomial time algorithm for the special case where G is a series-parallel graph. We also discuss special other cases where the partitioning problem or variations are polynomially solvable.

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