Quantization-Based Optimization: Alternative Stochastic Approximation of Global Optimization

In this study, we propose a global optimization algorithm based on quantizing the energy level of an objective function in an NP-hard problem. According to the white noise hypothesis for a quantization error with a dense and uniform distribution, we can regard the quantization error as i.i.d. white noise. From stochastic analysis, the proposed algorithm converges weakly only under conditions satisfying Lipschitz continuity, instead of local convergence properties such as the Hessian constraint of the objective function. This shows that the proposed algorithm ensures global optimization by Laplace's condition. Numerical experiments show that the proposed algorithm outperforms conventional learning methods in solving NP-hard optimization problems such as the traveling salesman problem.Comment: 25 pages, 3 figures, NeurIPS 2022 workshop OPT 2022 (14th Annual Workshop on Optimization for Machine Learning

Quantization-based Optimization with Perspective of Quantum Mechanics

Statistical and stochastic analysis based on thermodynamics has been the main analysis framework for stochastic global optimization. Recently, appearing quantum annealing or quantum tunneling algorithm for global optimization, we require a new researching framework for global optimization algorithms. In this paper, we provide the analysis for quantization-based optimization based on the Schr\"odinger equation to reveal what property in quantum mechanics enables global optimization. We present that the tunneling effect derived by the Schr\"odinger equation in quantization-based optimization enables to escape of a local minimum. Additionally, we confirm that this tunneling effect is the same property included in quantum mechanics-based global optimization. Experiments with standard multi-modal benchmark functions represent that the proposed analysis is valid.Comment: Preprint for ICTC conferenc

Towards optimal symbolization for time series comparisons

The abundance and value of mining large time series data sets has long been acknowledged. Ubiquitous in fields ranging from astronomy, biology and web science the size and number of these datasets continues to increase, a situation exacerbated by the exponential growth of our digital footprints. The prevalence and potential utility of this data has led to a vast number of time-series data mining techniques, many of which require symbolization of the raw time series as a pre-processing step for which a number of well used, pre-existing approaches from the literature are typically employed. In this work we note that these standard approaches are sub-optimal in (at least) the broad application area of time series comparison leading to unnecessary data corruption and potential performance loss before any real data mining takes place. Addressing this we present a novel quantizer based upon optimization of comparison fidelity and a computationally tractable algorithm for its implementation on big datasets. We demonstrate empirically that our new approach provides a statistically significant reduction in the amount of error introduced by the symbolization process compared to current state-of-the-art. The approach therefore provides a more accurate input for the vast number of data mining techniques in the literature, providing the potential of increased real world performance across a wide range of existing data mining algorithms and applications

Maximizing Energy Efficiency in Multiple Access Channels by Exploiting Packet Dropping and Transmitter Buffering

Quality of service (QoS) for a network is characterized in terms of various parameters specifying packet delay and loss tolerance requirements for the application. The unpredictable nature of the wireless channel demands for application of certain mechanisms to meet the QoS requirements. Traditionally, medium access control (MAC) and network layers perform these tasks. However, these mechanisms do not take (fading) channel conditions into account. In this paper, we investigate the problem using cross layer techniques where information flow and joint optimization of higher and physical layer is permitted. We propose a scheduling scheme to optimize the energy consumption of a multiuser multi-access system such that QoS constraints in terms of packet loss are fulfilled while the system is able to maximize the advantages emerging from multiuser diversity. Specifically, this work focuses on modeling and analyzing the effects of packet buffering capabilities of the transmitter on the system energy for a packet loss tolerant application. We discuss low complexity schemes which show comparable performance to the proposed scheme. The numerical evaluation reveals useful insights about the coupling effects of different QoS parameters on the system energy consumption and validates our analytical results.Comment: in IEEE trans. Wireless communications, 201