Convergence Analysis of Mixed Timescale Cross-Layer Stochastic Optimization

This paper considers a cross-layer optimization problem driven by multi-timescale stochastic exogenous processes in wireless communication networks. Due to the hierarchical information structure in a wireless network, a mixed timescale stochastic iterative algorithm is proposed to track the time-varying optimal solution of the cross-layer optimization problem, where the variables are partitioned into short-term controls updated in a faster timescale, and long-term controls updated in a slower timescale. We focus on establishing a convergence analysis framework for such multi-timescale algorithms, which is difficult due to the timescale separation of the algorithm and the time-varying nature of the exogenous processes. To cope with this challenge, we model the algorithm dynamics using stochastic differential equations (SDEs) and show that the study of the algorithm convergence is equivalent to the study of the stochastic stability of a virtual stochastic dynamic system (VSDS). Leveraging the techniques of Lyapunov stability, we derive a sufficient condition for the algorithm stability and a tracking error bound in terms of the parameters of the multi-timescale exogenous processes. Based on these results, an adaptive compensation algorithm is proposed to enhance the tracking performance. Finally, we illustrate the framework by an application example in wireless heterogeneous network

Scheduling and Power Control for Wireless Multicast Systems via Deep Reinforcement Learning

Multicasting in wireless systems is a natural way to exploit the redundancy in user requests in a Content Centric Network. Power control and optimal scheduling can significantly improve the wireless multicast network's performance under fading. However, the model based approaches for power control and scheduling studied earlier are not scalable to large state space or changing system dynamics. In this paper, we use deep reinforcement learning where we use function approximation of the Q-function via a deep neural network to obtain a power control policy that matches the optimal policy for a small network. We show that power control policy can be learnt for reasonably large systems via this approach. Further we use multi-timescale stochastic optimization to maintain the average power constraint. We demonstrate that a slight modification of the learning algorithm allows tracking of time varying system statistics. Finally, we extend the multi-timescale approach to simultaneously learn the optimal queueing strategy along with power control. We demonstrate scalability, tracking and cross layer optimization capabilities of our algorithms via simulations. The proposed multi-timescale approach can be used in general large state space dynamical systems with multiple objectives and constraints, and may be of independent interest.Comment: arXiv admin note: substantial text overlap with arXiv:1910.0530

Flatter, faster: scaling momentum for optimal speedup of SGD

Commonly used optimization algorithms often show a trade-off between good generalization and fast training times. For instance, stochastic gradient descent (SGD) tends to have good generalization; however, adaptive gradient methods have superior training times. Momentum can help accelerate training with SGD, but so far there has been no principled way to select the momentum hyperparameter. Here we study training dynamics arising from the interplay between SGD with label noise and momentum in the training of overparametrized neural networks. We find that scaling the momentum hyperparameter $1-\beta$ with the learning rate to the power of $2/3$ maximally accelerates training, without sacrificing generalization. To analytically derive this result we develop an architecture-independent framework, where the main assumption is the existence of a degenerate manifold of global minimizers, as is natural in overparametrized models. Training dynamics display the emergence of two characteristic timescales that are well-separated for generic values of the hyperparameters. The maximum acceleration of training is reached when these two timescales meet, which in turn determines the scaling limit we propose. We confirm our scaling rule for synthetic regression problems (matrix sensing and teacher-student paradigm) and classification for realistic datasets (ResNet-18 on CIFAR10, 6-layer MLP on FashionMNIST), suggesting the robustness of our scaling rule to variations in architectures and datasets.Comment: v2: expanded introduction section, corrected minor typos. v1: 12+13 pages, 3 figure

A streamwise-constant model of turbulent pipe flow

A streamwise-constant model is presented to investigate the basic mechanisms responsible for the change in mean flow occuring during pipe flow transition. Using a single forced momentum balance equation, we show that the shape of the velocity profile is robust to changes in the forcing profile and that both linear non-normal and nonlinear effects are required to capture the change in mean flow associated with transition to turbulence. The particularly simple form of the model allows for the study of the momentum transfer directly by inspection of the equations. The distribution of the high- and low-speed streaks over the cross-section of the pipe produced by our model is remarkably similar to one observed in the velocity field near the trailing edge of the puff structures present in pipe flow transition. Under stochastic forcing, the model exhibits a quasi-periodic self-sustaining cycle characterized by the creation and subsequent decay of "streamwise-constant puffs", so-called due to the good agreement between the temporal evolution of their velocity field and the projection of the velocity field associated with three-dimensional puffs in a frame of reference moving at the bulk velocity. We establish that the flow dynamics are relatively insensitive to the regeneration mechanisms invoked to produce near-wall streamwise vortices and that using small, unstructured background disturbances to regenerate the streamwise vortices is sufficient to capture the formation of the high- and low-speed streaks and their segregation leading to the blunting of the velocity profile characteristic of turbulent pipe flow

Learning for Cross-layer Resource Allocation in the Framework of Cognitive Wireless Networks

The framework of cognitive wireless networks is expected to endow wireless devices with a cognition-intelligence ability with which they can efficiently learn and respond to the dynamic wireless environment. In this dissertation, we focus on the problem of developing cognitive network control mechanisms without knowing in advance an accurate network model. We study a series of cross-layer resource allocation problems in cognitive wireless networks. Based on model-free learning, optimization and game theory, we propose a framework of self-organized, adaptive strategy learning for wireless devices to (implicitly) build the understanding of the network dynamics through trial-and-error. The work of this dissertation is divided into three parts. In the first part, we investigate a distributed, single-agent decision-making problem for real-time video streaming over a time-varying wireless channel between a single pair of transmitter and receiver. By modeling the joint source-channel resource allocation process for video streaming as a constrained Markov decision process, we propose a reinforcement learning scheme to search for the optimal transmission policy without the need to know in advance the details of network dynamics. In the second part of this work, we extend our study from the single-agent to a multi-agent decision-making scenario, and study the energy-efficient power allocation problems in a two-tier, underlay heterogeneous network and in a self-sustainable green network. For the heterogeneous network, we propose a stochastic learning algorithm based on repeated games to allow individual macro- or femto-users to find a Stackelberg equilibrium without flooding the network with local action information. For the self-sustainable green network, we propose a combinatorial auction mechanism that allows mobile stations to adaptively choose the optimal base station and sub-carrier group for transmission only from local payoff and transmission strategy information. In the third part of this work, we study a cross-layer routing problem in an interweaved Cognitive Radio Network (CRN), where an accurate network model is not available and the secondary users that are distributed within the CRN only have access to local action/utility information. In order to develop a spectrum-aware routing mechanism that is robust against potential insider attackers, we model the uncoordinated interaction between CRN nodes in the dynamic wireless environment as a stochastic game. Through decomposition of the stochastic routing game, we propose two stochastic learning algorithm based on a group of repeated stage games for the secondary users to learn the best-response strategies without the need of information flooding