Double-Active-IRS Aided Wireless Communication: Deployment Optimization and Capacity Scaling

In this letter, we consider a double-active-intelligent reflecting surface (IRS) aided wireless communication system, where two active IRSs are properly deployed to assist the communication from a base station (BS) to multiple users located in a given zone via the double-reflection links. Under the assumption of fixed per-element amplification power for each active-IRS element, we formulate a rate maximization problem subject to practical constraints on the reflection design, elements allocation, and placement of active IRSs. To solve this non-convex problem, we first obtain the optimal active-IRS reflections and BS beamforming, based on which we then jointly optimize the active-IRS elements allocation and placement by using the alternating optimization (AO) method. Moreover, we show that given the fixed per-element amplification power, the received signal-to-noise ratio (SNR) at the user increases asymptotically with the square of the number of reflecting elements; while given the fixed number of reflecting elements, the SNR does not increase with the per-element amplification power when it is asymptotically large. Last, numerical results are presented to validate the effectiveness of the proposed AO-based algorithm and compare the rate performance of the considered double-active-IRS aided wireless system with various benchmark systems

Extremal problems for disjoint graphs

For a simple graph $F$, let $\mathrm{EX}(n, F)$ and $\mathrm{EX_{sp}}(n,F)$ be the set of graphs with the maximum number of edges and the set of graphs with the maximum spectral radius in an $n$-vertex graph without any copy of the graph $F$, respectively. Let $F$ be a graph with $\mathrm{ex}(n,F)=e(T_{n,r})+O(1)$. In this paper, we show that $\mathrm{EX_{sp}}(n,kF)\subseteq \mathrm{EX}(n,kF)$ for sufficiently large $n$. This generalizes a result of Wang, Kang and Xue [J. Comb. Theory, Ser. B, 159(2023) 20-41]. We also determine the extremal graphs of $kF$ in term of the extremal graphs of $F$.Comment: 23 pages. arXiv admin note: text overlap with arXiv:2306.1674

Spectral extremal graphs for edge blow-up of star forests

The edge blow-up of a graph $G$, denoted by $G^{p+1}$, is obtained by replacing each edge of $G$ with a clique of order $p+1$, where the new vertices of the cliques are all distinct. Yuan [J. Comb. Theory, Ser. B, 152 (2022) 379-398] determined the range of the Tur\'{a}n numbers for edge blow-up of all bipartite graphs and the exact Tur\'{a}n numbers for edge blow-up of all non-bipartite graphs. In this paper we prove that the graphs with the maximum spectral radius in an $n$-vertex graph without any copy of edge blow-up of star forests are the extremal graphs for edge blow-up of star forests when $n$ is sufficiently large.Comment: 22. arXiv admin note: text overlap with arXiv:2208.0655

Beyond OOD State Actions: Supported Cross-Domain Offline Reinforcement Learning

Offline reinforcement learning (RL) aims to learn a policy using only pre-collected and fixed data. Although avoiding the time-consuming online interactions in RL, it poses challenges for out-of-distribution (OOD) state actions and often suffers from data inefficiency for training. Despite many efforts being devoted to addressing OOD state actions, the latter (data inefficiency) receives little attention in offline RL. To address this, this paper proposes the cross-domain offline RL, which assumes offline data incorporate additional source-domain data from varying transition dynamics (environments), and expects it to contribute to the offline data efficiency. To do so, we identify a new challenge of OOD transition dynamics, beyond the common OOD state actions issue, when utilizing cross-domain offline data. Then, we propose our method BOSA, which employs two support-constrained objectives to address the above OOD issues. Through extensive experiments in the cross-domain offline RL setting, we demonstrate BOSA can greatly improve offline data efficiency: using only 10\% of the target data, BOSA could achieve {74.4\%} of the SOTA offline RL performance that uses 100\% of the target data. Additionally, we also show BOSA can be effortlessly plugged into model-based offline RL and noising data augmentation techniques (used for generating source-domain data), which naturally avoids the potential dynamics mismatch between target-domain data and newly generated source-domain data