Coverage Analysis for Digital Cousin Selection -- Improving Multi-Environment Q-Learning

Q-learning is widely employed for optimizing various large-dimensional networks with unknown system dynamics. Recent advancements include multi-environment mixed Q-learning (MEMQ) algorithms, which utilize multiple independent Q-learning algorithms across multiple, structurally related but distinct environments and outperform several state-of-the-art Q-learning algorithms in terms of accuracy, complexity, and robustness. We herein conduct a comprehensive probabilistic coverage analysis to ensure optimal data coverage conditions for MEMQ algorithms. First, we derive upper and lower bounds on the expectation and variance of different coverage coefficients (CC) for MEMQ algorithms. Leveraging these bounds, we develop a simple way of comparing the utilities of multiple environments in MEMQ algorithms. This approach appears to be near optimal versus our previously proposed partial ordering approach. We also present a novel CC-based MEMQ algorithm to improve the accuracy and complexity of existing MEMQ algorithms. Numerical experiments are conducted using random network graphs with four different graph properties. Our algorithm can reduce the average policy error (APE) by 65% compared to partial ordering and is 95% faster than the exhaustive search. It also achieves 60% less APE than several state-of-the-art reinforcement learning and prior MEMQ algorithms. Additionally, we numerically verify the theoretical results and show their scalability with the action-space size.

A Multi-Agent Multi-Environment Mixed Q-Learning for Partially Decentralized Wireless Network Optimization

Q-learning is a powerful tool for network control and policy optimization in wireless networks, but it struggles with large state spaces. Recent advancements, like multi-environment mixed Q-learning (MEMQ), improves performance and reduces complexity by integrating multiple Q-learning algorithms across multiple related environments so-called digital cousins. However, MEMQ is designed for centralized single-agent networks and is not suitable for decentralized or multi-agent networks. To address this challenge, we propose a novel multi-agent MEMQ algorithm for partially decentralized wireless networks with multiple mobile transmitters (TXs) and base stations (BSs), where TXs do not have access to each other's states and actions. In uncoordinated states, TXs act independently to minimize their individual costs. In coordinated states, TXs use a Bayesian approach to estimate the joint state based on local observations and share limited information with leader TX to minimize joint cost. The cost of information sharing scales linearly with the number of TXs and is independent of the joint state-action space size. The proposed scheme is 50% faster than centralized MEMQ with only a 20% increase in average policy error (APE) and is 25% faster than several advanced decentralized Q-learning algorithms with 40% less APE. The convergence of the algorithm is also demonstrated.

Coverage Analysis of Multi-Environment Q-Learning Algorithms for Wireless Network Optimization

Q-learning is widely used to optimize wireless networks with unknown system dynamics. Recent advancements include ensemble multi-environment hybrid Q-learning algorithms, which utilize multiple Q-learning algorithms across structurally related but distinct Markovian environments and outperform existing Q-learning algorithms in terms of accuracy and complexity in large-scale wireless networks. We herein conduct a comprehensive coverage analysis to ensure optimal data coverage conditions for these algorithms. Initially, we establish upper bounds on the expectation and variance of different coverage coefficients. Leveraging these bounds, we present an algorithm for efficient initialization of these algorithms. We test our algorithm on two distinct real-world wireless networks. Numerical simulations show that our algorithm can achieve %50 less policy error and %40 less runtime complexity than state-of-the-art reinforcement learning algorithms. Furthermore, our algorithm exhibits robustness to changes in network settings and parameters. We also numerically validate our theoretical results.

Leveraging Digital Cousins for Ensemble Q-Learning in Large-Scale Wireless Networks

Optimizing large-scale wireless networks, including optimal resource management, power allocation, and throughput maximization, is inherently challenging due to their non-observable system dynamics and heterogeneous and complex nature. Herein, a novel ensemble Q-learning algorithm that addresses the performance and complexity challenges of the traditional Q-learning algorithm for optimizing wireless networks is presented. Ensemble learning with synthetic Markov Decision Processes is tailored to wireless networks via new models for approximating large state-space observable wireless networks. In particular, digital cousins are proposed as an extension of the traditional digital twin concept wherein multiple Q-learning algorithms on multiple synthetic Markovian environments are run in parallel and their outputs are fused into a single Q-function. Convergence analyses of key statistics and Q-functions and derivations of upper bounds on the estimation bias and variance are provided. Numerical results across a variety of real-world wireless networks show that the proposed algorithm can achieve up to 50% less average policy error with up to 40% less runtime complexity than the state-of-the-art reinforcement learning algorithms. It is also shown that theoretical results properly predict trends in the experimental results.

Multi-Timescale Ensemble Q-learning for Markov Decision Process Policy Optimization

Reinforcement learning (RL) is a classical tool to solve network control or policy optimization problems in unknown environments. The original Q-learning suffers from performance and complexity challenges across very large networks. Herein, a novel model-free ensemble reinforcement learning algorithm which adapts the classical Q-learning is proposed to handle these challenges for networks which admit Markov decision process (MDP) models. Multiple Q-learning algorithms are run on multiple, distinct, synthetically created and structurally related Markovian environments in parallel; the outputs are fused using an adaptive weighting mechanism based on the Jensen-Shannon divergence (JSD) to obtain an approximately optimal policy with low complexity. The theoretical justification of the algorithm, including the convergence of key statistics and Q-functions are provided. Numerical results across several network models show that the proposed algorithm can achieve up to 55% less average policy error with up to 50% less runtime complexity than the state-of-the-art Q-learning algorithms. Numerical results validate assumptions made in the theoretical analysis.