Reconfigurable intelligent surfaces (RISs) have received considerable attention as a key enabler for envisioned 6G networks, for the purpose of improving the network capacity, coverage, efficiency, and security with low energy consumption and low hardware cost. However, integrating RISs into the existing infrastructure greatly increases the network management complexity, especially for controlling a significant number of RIS elements. To realize the full potential of RISs, efficient optimization approaches are of great importance. This work provides a comprehensive survey of optimization techniques for RIS-aided wireless communications, including model-based, heuristic, and machine learning (ML) algorithms. In particular, we first summarize the problem formulations in the literature with diverse objectives and constraints, e.g., sumrate maximization, power minimization, and imperfect channel state information constraints. Then, we introduce model-based algorithms that have been used in the literature, such as alternating optimization, the majorization-minimization method, and successive convex approximation. Next, heuristic optimization is discussed, which applies heuristic rules for obtaining lowcomplexity solutions. Moreover, we present state-of-the-art ML algorithms and applications towards RISs, i.e., supervised and unsupervised learning, reinforcement learning, federated learning, graph learning, transfer learning, and hierarchical learning-based approaches. Model-based, heuristic, and ML approaches are compared in terms of stability, robustness, optimality and so on, providing a systematic understanding of these techniques. Finally, we highlight RIS-aided applications towards 6G networks and identify future challenges.

中文翻译：

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RIS 辅助无线网络中基于模型、启发式和机器学习优化方法的调查


可重构智能表面（RIS）作为设想的 6G 网络的关键推动者受到了广泛关注，其目的是在低能耗和低硬件成本的情况下提高网络容量、覆盖范围、效率和安全性。然而，将 RIS 集成到现有基础设施中会大大增加网络管理的复杂性，尤其是控制大量 RIS 元素时。为了充分发挥 RIS 的潜力，有效的优化方法非常重要。这项工作对 RIS 辅助无线通信的优化技术进行了全面的调查，包括基于模型、启发式和机器学习 (ML) 算法。特别是，我们首先总结了文献中具有不同目标和约束的问题表述，例如总速率最大化、功率最小化和不完善的信道状态信息约束。然后，我们介绍文献中使用的基于模型的算法，例如交替优化、主最小化方法和逐次凸逼近。接下来，讨论启发式优化，它应用启发式规则来获得低复杂度的解决方案。此外，我们还展示了针对 RIS 的最先进的 ML 算法和应用，即监督和无监督学习、强化学习、联邦学习、图学习、迁移学习和基于分层学习的方法。基于模型、启发式和机器学习方法在稳定性、鲁棒性、最优性等方面进行了比较，提供了对这些技术的系统理解。最后，我们重点介绍 RIS 辅助的 6G 网络应用并确定未来的挑战。