A Simple, Optimal and Efficient Algorithm for Online Exp-Concave Optimization

Online eXp-concave Optimization (OXO) is a fundamental problem in online learning. The standard algorithm, Online Newton Step (ONS), balances statistical optimality and computational practicality, guaranteeing an optimal regret of $O(d \log T)$, where $d$ is the dimension and $T$ is the time horizon. ONS faces a computational bottleneck due to the Mahalanobis projections at each round. This step costs $Ω(d^ω)$ arithmetic operations for bounded domains, even for the unit ball, where $ω\in (2,3]$ is the matrix-multiplication exponent. As a result, the total runtime can reach $\tilde{O}(d^ωT)$, particularly when iterates frequently oscillate near the domain boundary. For Stochastic eXp-concave Optimization (SXO), computational cost is also a challenge. Deploying ONS with online-to-batch conversion for SXO requires $T = \tilde{O}(d/ε)$ rounds to achieve an excess risk of $ε$, and thereby necessitates an $\tilde{O}(d^{ω+1}/ε)$ runtime. A COLT'13 open problem posed by Koren [2013] asks for an SXO algorithm with runtime less than $\tilde{O}(d^{ω+1}/ε)$. This paper proposes a simple variant of ONS, LightONS, which reduces the total runtime to $O(d^2 T + d^ω\sqrt{T \log T})$ while preserving the optimal $O(d \log T)$ regret. LightONS implies an SXO method with runtime $\tilde{O}(d^3/ε)$, thereby answering the open problem. Importantly, LightONS preserves the elegant structure of ONS by leveraging domain-conversion techniques from parameter-free online learning to introduce a hysteresis mechanism that delays expensive Mahalanobis projections until necessary. This design enables LightONS to serve as an efficient plug-in replacement of ONS in broader scenarios, even beyond regret minimization, including gradient-norm adaptive regret, parametric stochastic bandits, and memory-efficient online learning.

Adaptive Three Layer Hybrid Reconfigurable Intelligent Surface for 6G Wireless Communication: Trade-offs and Performance

A potential candidate technology for the development of future 6G networks has been recognized as Reconfigurable Intelligent Surface (RIS). However, due to the variation in radio link quality, traditional passive RISs only accomplish a minimal signal gain in situations with strong direct links between user equipment (UE) and base station (BS). In order to get over this fundamental restriction of smaller gain, the idea of active RISs might be a suitable solution. In contrast to current passive RIS, which simply reflects and directs signals without any additional amplification, active RISs have the ability to enhance reflected signals by the incorporation of amplifiers inside its elements. However, with additional amplifiers, apart from the relatively complex attributes of RIS-assisted arrangements, the additional energy consumption of such technologies is often disregarded. So, there might be a tradeoff between the additional energy consumption for the RIS technologies and the overall gain acquired by deploying this potential advancement. The objective of this work is to provide a primary idea of a three-layer hybrid RIS-assisted configuration that is responsive to both active and passive RIS, as well as an additional dormant or inactive state. The single RIS structure should be capable of adjusting its overall configuration in response to fluctuations in transmit power and radio link quality. Furthermore, our fabricated passive RIS-assisted structure verifies a portion of the proposed idea, with simulations highlighting its advantages over standalone passive or active RIS-assisted technologies.