Doubling Trick Research Articles

ACTUALIZATION OF PANCASILA VALUES IN PREVENTION AND ERADICATION EFFORTS NARCOTICS ABUSE IN INDONESIA

Pancasila is a state ideology that has been agreed upon as the basis for organizing social, national and state life in Indonesia. The practice of Pancasila values will certainly lead to the development of a society that is devout, humane, united, democratic and just. On the other hand, weak understanding and implementation of these basic values will cause various disorders that can threaten all areas of life, one of which is narcotics abuse. Sanctions or punishments for those who abuse narcotics themselves are different from dealers, couriers, dealers, and so on, because in the Narcotics Law there is a grouping of narcotics crimes. This is in accordance with the double trick system adopted by the Narcotics Law. Actualizing the values of Pancasila in efforts to prevent and eradicate narcotics abuse cannot be separated from the awareness of the entire community and law enforcement officials, in this case judges, in deciding narcotics abuse cases for the sake of justice based on God. This is because the values of Pancasila maintain the credibility of Indonesian culture and attitudes and have a major impact on the life and character of the nation by fighting narcotics abuse and breaking the chain of narcotics problems. We must understand the meaning of Pancasila values correctly, Pancasila as Indonesias national ideology for unity, as a national standard for preventing and eradicating narcotics abuse. The related Pancasila values are the value of God, the value of humanity, the value of unity, the value of people and the value of justice, so in everyday life you must adhere to these five precepts in order to avoid the dangers of narcotics.

Online Utility Optimization in Multi-User Interference Networks Under a Long-Term Budget Constraint

In this paper, we consider a multi-user interference network where a central controller allocates power resources to multiple base stations for maximizing the entire network utility under a long-term power budget constraint. The optimal power allocation strategy depends on accurate and instant channel state information (CSI). However, due to users’ mobility and the existence of channel fading and interference, timely channel estimation is unavailable. To overcome the difficulty of unknown channel states, we resort to the Lyapunov drift analysis framework and design an online power allocation algorithm based on historical observations. The algorithm can be proven to achieve sub-linear performance for both cumulative regret and power budget violation. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sub-linear regret</i> indicates the proposed algorithm can asymptotically achieve the optimal static power allocation performance in hindsight. Moreover, we use a general doubling trick to construct a parameter-free algorithm based on the aforementioned online algorithm without the knowledge of time horizon <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$T$</tex-math></inline-formula> , which can be proven to preserve the order of the regret and violation upper bound. Simulation results are provided to validate the performance of the proposed online algorithms compared with the offline cave-filling algorithms, as well as its robustness in the presence of adversarial interference.

Efficient Adaptive Online Learning via Frequent Directions.

By employing time-varying proximal functions, adaptive subgradient methods (ADAGRAD) have improved the regret bound and been widely used in online learning and optimization. However, ADAGRAD with full matrix proximal functions (ADA-FULL) cannot handle large-scale problems due to the impractical O(d³) time and O(d²) space complexities, though it has better performance when gradients are correlated. In this paper, we propose two efficient variants of ADA-FULL via a matrix sketching technique called frequent directions (FD). The first variant named as ADA-FD directly utilizes FD to maintain and manipulate low-rank matrices, which reduces the space and time complexities to O(τd) and O(τ²d) respectively, where d is the dimensionality and τ &lt;&lt; d is the sketching size. The second variant named as ADA-FFD further adopts a doubling trick to accelerate FD used in ADA-FD, which reduces the average time complexity to O(τd) while only doubles the space complexity of ADA-FD. Theoretical analysis reveals that the regret of ADA-FD and ADA-FFD is close to that of ADA-FULL as long as the outer product matrix of gradients is approximately low-rank. Experimental results demonstrate the efficiency and effectiveness of our algorithms.

Vector Gaussian Successive Refinement With Degraded Side Information

We investigate the problem of the successive refinement for Wyner-Ziv coding with degraded side information and obtain a complete characterization of the rate region for the quadratic vector Gaussian case. The achievability part is based on the evaluation of the Tian-Diggavi inner bound that involves Gaussian auxiliary random vectors. For the converse part, a matching outer bound is obtained with the aid of a new extremal inequality. Herein, the proof of this extremal inequality depends on the integration of the monotone path argument and the doubling trick as well as information-estimation relations.

λ-Deformations in the upper-half plane

We formulate λ-deformed σ-models as QFTs in the upper-half plane. For different boundary conditions we compute correlation functions of currents and primary operators, exactly in the deformation parameter λ and for large values of the level k of the underlying WZW model. To perform our computations we use either conformal perturbation theory in association with Cardy's doubling trick, as well as meromorphicity arguments and a non-perturbative symmetry in the parameter space (λ,k), or standard QFT techniques based on the free field expansion of the σ-model action, with the free fields obeying appropriate boundary conditions. Both methods have their own advantages yielding consistent and rich, compared to those in the absence of a boundary, complementary results. We pay particular attention, albeit not exclusively, to integrability preserving boundary conditions.

Sample Efficient Reinforcement Learning with REINFORCE

Policy gradient methods are among the most effective methods for large-scale reinforcement learning, and their empirical success has prompted several works that develop the foundation of their global convergence theory. However, prior works have either required exact gradients or state-action visitation measure based mini-batch stochastic gradients with a diverging batch size, which limit their applicability in practical scenarios. In this paper, we consider classical policy gradient methods that compute an approximate gradient with a single trajectory or a fixed size mini-batch of trajectories under soft-max parametrization and log-barrier regularization, along with the widely-used REINFORCE gradient estimation procedure. By controlling the number of "bad" episodes and resorting to the classical doubling trick, we establish an anytime sub-linear high probability regret bound as well as almost sure global convergence of the average regret with an asymptotically sub-linear rate. These provide the first set of global convergence and sample efficiency results for the well-known REINFORCE algorithm and contribute to a better understanding of its performance in practice.

Privacy-Preserving Distributed Online Optimization Over Unbalanced Digraphs via Subgradient Rescaling

In this article, we investigate a distributed online constrained optimization problem with differential privacy where the network is modeled by an unbalanced digraph with a row-stochastic adjacency matrix. To address such a problem, a distributed differentially private algorithm without introducing a trusted third-party is proposed to preserve the privacy of the participating nodes. Under mild conditions, we show that the proposed algorithm attains an O(log T) expected regret bound for strongly convex local cost functions, where T is the time horizon. Moreover, we remove the need for knowing the time horizon T in advance by adopting doubling trick scheme, and derive an O(√T) expected regret bound for general convex local cost functions. Our results coincide with the best theoretical regrets that can be achieved in the state-of-the-art algorithms. Finally, simulation results are conducted to validate the efficiency of our proposed algorithm.

Cost‐efficient monitoring of continuous‐time stochastic processes based on discrete observations

AbstractPlanning a cost‐efficient monitoring policy of stochastic processes arises from many industrial problems. We formulate a simple discrete‐time monitoring problem of continuous‐time stochastic processes with its applications to several industrial problems. A key in our model is a doubling trick of the variables, with which we can construct an algorithm to solve the problem. The cost‐efficient monitoring policy balancing between the observation cost and information loss is governed by an optimality equation of a fixed point type, which is solvable with an iterative algorithm based on the Feynman‐Kac formula. This is a new linkage between monitoring problems and mathematical sciences. We show regularity results of the optimization problem and present a numerical algorithm for its approximation. A problem having model ambiguity is presented as well. The presented model is applied to problems of environment, ecology, and energy, having qualitatively different target stochastic processes with each other.

Selfish Bandit-Based Cognitive Anti-Jamming Strategy for Aeronautic Swarm Network in Presence of Multiple Jammer

In order to enhance the anti-jamming capability of aeronautic swarm tactical network in the complicated electromagnetic environment, we address the problem of bandit-based cognitive anti-jamming strategy for enabling reliable information transmission. We first present an adversarial multiuser multi-armed bandit model for the aeronautic swarm network employing airborne cognitive radios with the same-frequency simultaneous transmit and receive feature. Then, we utilize the improved energy detection method to perform jamming sensing and derive the closed expression of false alarm probability, false detection probability, and the optimal decision threshold in the case of single and multi-jammer. Finally, using the jamming sensing output to calculate reward and with the objective of maximizing the throughput of each airborne radio, a decentralized selfish doubling trick kl-UCB <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">++</sup> anti-jamming strategy is developed to allocate an optimal configuration of transmitting power and spectrum channel to each radio. This anytime bandit strategy is simultaneously minimaxed optimal and asymptotically optimal. The simulation results validate that the aggregate average throughput, cumulative regret obtained with the proposed anti-jamming strategy outperform the well-known UCB, kl-UCB <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">++</sup> bandit algorithm.

A Forward-Reverse Brascamp-Lieb Inequality: Entropic Duality and Gaussian Optimality.

Inspired by the forward and the reverse channels from the image-size characterization problem in network information theory, we introduce a functional inequality that unifies both the Brascamp-Lieb inequality and Barthe’s inequality, which is a reverse form of the Brascamp-Lieb inequality. For Polish spaces, we prove its equivalent entropic formulation using the Legendre-Fenchel duality theory. Capitalizing on the entropic formulation, we elaborate on a “doubling trick” used by Lieb and Geng-Nair to prove the Gaussian optimality in this inequality for the case of Gaussian reference measures.

A continuous-time approach to online optimization

We consider a family of mirror descent strategies for online optimization in continuous-time and we show that they lead to no regret. From a more traditional, discrete-time viewpoint, this continuous-time approach allows us to derive the no-regret properties of a large class of discrete-time algorithms including as special cases the exponential weights algorithm, online mirror descent, smooth fictitious play and vanishingly smooth fictitious play. In so doing, we obtain a unified view of many classical regret bounds, and we show that they can be decomposed into a term stemming from continuous-time considerations and a term which measures the disparity between discrete and continuous time. This generalizes the continuous-time based analysis of the exponential weights algorithm from [ 29 ]. As a result, we obtain a general class of infinite horizon learning strategies that guarantee an \begin{document}$\mathcal{O}(n^{-1/2})$ \end{document} regret bound without having to resort to a doubling trick.

Scattering theory for the defocusing fourth-order Schrödinger equation

In this paper, we study the global well-posedness and scattering theory for the defocusing fourth-order nonlinear Schrödinger equation (FNLS) in dimensions . We prove that if the solution u is apriorily bounded in the critical Sobolev space, that is, with all if p is an even integer or otherwise, then u is global and scatters. We will give a uniform way to treat the energy-subcritical, energy-critical and energy-supercritical FNLS by making use of the strategy derived from concentration compactness ideas, and we are able to overcome the logarithmic blowup in the double Duhamel trick in dimension eight by exploiting the refined dispersive estimate which is in sharp contrast to the Schrödinger equation.

The defocusing energy-supercritical Hartree equation

In this paper, we study the global well-posedness and scattering problem for the energysupercritical Hartree equation \(iu_t + \Delta u - (|x|^{ - \gamma } * |u|^2 )u = 0\) with γ > 4 in dimension d > γ. We prove that if the solution u is apriorily bounded in the critical Sobolev space, that is, u ∈ Lt∞ (I; 547-2 (ℝd)) with \(s_c : = \tfrac{\gamma } {2} - 1 > 1 \), then u is global and scatters. The impetus to consider this problem stems from a series of recent works for the energy-supercritical nonlinear wave equation (NLW) and nonlinear Schrodinger equation (NLS). We utilize the strategy derived from concentration compactness ideas to show that the proof of the global well-posedness and scattering is reduced to disprove the existence of three scenarios: finite time blowup; soliton-like solution and low to high frequency cascade. Making use of the No-waste Duhamel formula, we deduce that the energy of the finite time blow-up solution is zero and so get a contradiction. Finally, we adopt the double Duhamel trick, the interaction Morawetz estimate and interpolation to kill the last two scenarios.

Follow the leader if you can, hedge if you must

Follow-the-Leader (FTL) is an intuitive sequential prediction strategy that guarantees constant regret in the stochastic setting, but has poor performance for worst-case data. Other hedging strategies have better worst-case guarantees but may perform much worse than FTL if the data are not maximally adversarial. We introduce the FlipFlop algorithm, which is the first method that provably combines the best of both worlds. As a stepping stone for our analysis, we develop AdaHedge, which is a new way of dynamically tuning the learning rate in Hedge without using the doubling trick. AdaHedge refines a method by Cesa-Bianchi, Mansour, and Stoltz (2007), yielding improved worst-case guarantees. By interleaving AdaHedge and FTL, FlipFlop achieves regret within a constant factor of the FTL regret, without sacrificing AdaHedge's worst-case guarantees. AdaHedge and FlipFlop do not need to know the range of the losses in advance; moreover, unlike earlier methods, both have the intuitive property that the issued weights are invariant under rescaling and translation of the losses. The losses are also allowed to be negative, in which case they may be interpreted as gains.

The double CFTP method

We consider the problem of the exact simulation of random variables Z that satisfy the distributional identity Z = L VY + (1- V ) Z , where V ∈ [0,1] and Y are independent, and = L denotes equality in distribution. Equivalently, Z is the limit of a Markov chain driven by that map. We give an algorithm that can be automated under the condition that we have a source capable of generating independent copies of Y , and that V has a density that can be evaluated in a black-box format. The method uses a doubling trick for inducing coalescence in coupling from the past. Applications include exact samplers for many Dirichlet means, some two-parameter Poisson--Dirichlet means, and a host of other distributions related to occupation times of Bessel bridges that can be described by stochastic fixed point equations.

Extending the Range of Error Estimates for Radial Approximation in Euclidean Space and on Spheres

We adapt Schaback's error doubling trick [R. Schaback, Math. Comp., 68 (1999), pp. 201–216] to give error estimates for radial interpolation of functions with smoothness lying (in some sense) between that of the usual native space and the subspace with double the smoothness. We do this for both bounded subsets of ${\mathbb{R}}^d$ and spheres. As a step on the way to our ultimate goal we also show convergence of pseudoderivatives of the interpolation error.

Infinitely many hyperbolic Coxeter groups through dimension 19

We prove the following: there are infinitely many finite-covolume (resp. cocompact) Coxeter groups acting on hyperbolic space Hn for every n≤19 (resp. n≤6). When n=7 or 8, they may be taken to be nonarithmetic. Furthermore, for 2≤n≤19, with the possible exceptions n=16 and 17, the number of essentially distinct Coxeter groups in Hn with noncompact fundamental domain of volume≤V grows at least exponentially with respect to V. The same result holds for cocompact groups for n≤6. The technique is a doubling trick and variations on it; getting the most out of the method requires some work with the Leech lattice.

Integrable open spin chains and the doubling trick in Script N = 2 SYM with fundamental matter

We demonstrate that the one-loop anomalous dimension matrix in N = 2 SYM with a single chiral hypermultiplet of fundamental matter, which is dual to AdS_5 X S^5 with a D7-brane filling AdS_5 and wrapped around an $^3 in the S^5, is an integrable open spin chain Hamiltonian. We also use the doubling trick to relate these open spin chains to closed spin chains in pure N = 4 SYM. By using the AdS/CFT correspondence, we find a relation between the corresponding open and closed strings that differs from a simple doubling trick by terms that vanish in the semiclassical limit. We also demonstrate that in some cases the closed string is simpler and easier to study than the corresponding open string, and we speculate on the nature of corrections due to the presence of D-branes that this implies.

Open spinning strings and AdS/dCFT duality

We consider open spinning string solutions on an AdS_4 x S^2-brane (D5-brane) in the bulk AdS_5 x S^5 background. By taking account of the breaking of SO(6)_R to SO(3)_H x SO(3)_V due to the presence of the AdS-brane, the open rotating string ansatz is discussed. We construct the elliptic folded/circular open string solutions in the SU(2) and the SL(2) sectors, so that they satisfy the appropriate boundary conditions. On the other hand, in the SU(2) sector of the gauge theory, we compute the matrix of anomalous dimension of the defect operator, which turns out to be the Hamiltonian of an open integrable spin chain. Then we consider the coordinate Bethe ansatz with arbitrary number of impurities, and compare the boundary condition of the Bethe wavefunction with that of the corresponding open string solution. We also discuss the Bethe ansatz for the open SL(2) spin chain with several supports from the string theory side. Then, in both SU(2) and SL(2) sectors, we analyze the Bethe equations in the thermodynamic limit and formulate the `doubling trick' on the Riemann surface associated with the gauge theory.

Non-BPS D-branes in light-cone Green-Schwarz formalism

Non-BPS D-branes are difficult to describe covariantly in a manifestly supersymmetric formalism. For definiteness we concentrate on type IIB string theory in flat background in light-cone Green-Schwarz formalism. We study both the boundary state and the boundary conformal field theory descriptions of these D-branes with manifest SO(8) covariance and go through various consistency checks. We analyze Sen's original construction of non-BPS D-branes given in terms of an orbifold boundary conformal field theory. We also directly study the relevant world-sheet theory by deriving the open string boundary condition from the covariant boundary state. Both these methods give the same open string spectrum which is consistent with the boundary state, as required by the world-sheet duality. The boundary condition found in the second method is given in terms of bi-local fields that are quadratic in Green-Schwarz fermions. We design a special ``doubling trick'' suitable to handle such boundary conditions and prescribe rules for computing all possible correlation functions without boundary insertions. This prescription has been tested by computing disk one-point functions of several classes of closed string states and comparing the results with the boundary state computation.