EFFICIENT AND PERFECT DOMINATION ON ARCHIMEDEAN LATTICES

An Archimedean lattice is an infinite graph constructed from a vertex-transitive tiling of the plane by regular polygons. A set of vertices S is said to dominate a graph G=(V,E) if every vertex in V is either in the set S or is adjacent to a vertex in set S. A dominating set is a perfect dominating set if every vertex not in the dominating set is dominated exactly once. The domination ratio is the minimum proportion of vertices in a dominating set. The perfect domination ratio is the minimum proportion of vertices in a perfect dominating set. Dominating sets are provided to establish upper bounds for the domination ratios of all the Archimedean lattices. A dominating set is an efficient dominating set if every vertex is dominated exactly once. We show that seven of the eleven Archimedean lattices are efficiently dominated, which easily determine their domination ratios and perfect domination ratios. We prove that the other four Archimedean lattices cannot be efficiently dominated. For the four Archimedean lattices that cannot be efficiently dominated, we have determined their exact perfect domination ratios. Integer programming bounds for domination ratios are provided. A perfect domination proportion is the proportion of vertices in a perfect dominating set that is not necessarily minimal. We study nonisomorphic perfect dominating sets and possible perfect domination proportions of Archimedean lattices

Estimate-Then-Optimize Versus Integrated-Estimation-Optimization: A Stochastic Dominance Perspective

In data-driven stochastic optimization, model parameters of the underlying distribution need to be estimated from data in addition to the optimization task. Recent literature suggests the integration of the estimation and optimization processes, by selecting model parameters that lead to the best empirical objective performance. Such an integrated approach can be readily shown to outperform simple ``estimate then optimize" when the model is misspecified. In this paper, we argue that when the model class is rich enough to cover the ground truth, the performance ordering between the two approaches is reversed for nonlinear problems in a strong sense. Simple ``estimate then optimize" outperforms the integrated approach in terms of stochastic dominance of the asymptotic optimality gap, i,e, the mean, all other moments, and the entire asymptotic distribution of the optimality gap is always better. Analogous results also hold under constrained settings and when contextual features are available. We also provide experimental findings to support our theory

Implicit Two-Tower Policies

We present a new class of structured reinforcement learning policy-architectures, Implicit Two-Tower (ITT) policies, where the actions are chosen based on the attention scores of their learnable latent representations with those of the input states. By explicitly disentangling action from state processing in the policy stack, we achieve two main goals: substantial computational gains and better performance. Our architectures are compatible with both: discrete and continuous action spaces. By conducting tests on 15 environments from OpenAI Gym and DeepMind Control Suite, we show that ITT-architectures are particularly suited for blackbox/evolutionary optimization and the corresponding policy training algorithms outperform their vanilla unstructured implicit counterparts as well as commonly used explicit policies. We complement our analysis by showing how techniques such as hashing and lazy tower updates, critically relying on the two-tower structure of ITTs, can be applied to obtain additional computational improvements

Information rates in Kerr nonlinearity limited optical fiber communication systems

Achievable information rates of optical communication systems are inherently limited by nonlinear distortions due to the Kerr effect occurred in optical fibres. These nonlinear impairments become more significant for communication systems with larger transmission bandwidths, closer channel spacing and higher-order modulation formats. In this paper, the efficacy of nonlinearity compensation techniques, including both digital back-propagation and optical phase conjugation, for enhancing achievable information rates in lumped EDFA- and distributed Raman-amplified fully-loaded C −band systems is investigated considering practical transceiver limitations. The performance of multiple modulation formats, such as dual-polarisation quadrature phase shift keying (DP-QPSK), dual-polarisation 16 −ary quadrature amplitude modulation (DP-16QAM), DP-64QAM and DP-256QAM, has been studied in C −band systems with different transmission distances. It is found that the capabilities of both nonlinearity compensation techniques for enhancing achievable information rates strongly depend on signal modulation formats as well as target transmission distances

Towards Zero Shot Learning in Restless Multi-armed Bandits

Restless multi-arm bandits (RMABs), a class of resource allocation problems with broad application in areas such as healthcare, online advertising, and anti-poaching, have recently been studied from a multi-agent reinforcement learning perspective. Prior RMAB research suffers from several limitations, e.g., it fails to adequately address continuous states, and requires retraining from scratch when arms opt-in and opt-out over time, a common challenge in many real world applications. We address these limitations by developing a neural network-based pre-trained model (PreFeRMAB) that has general zero-shot ability on a wide range of previously unseen RMABs, and which can be fine-tuned on specific instances in a more sample-efficient way than retraining from scratch. Our model also accommodates general multi-action settings and discrete or continuous state spaces. To enable fast generalization, we learn a novel single policy network model that utilizes feature information and employs a training procedure in which arms opt-in and out over time. We derive a new update rule for a crucial $\lambda$-network with theoretical convergence guarantees and empirically demonstrate the advantages of our approach on several challenging, real-world inspired problems

Information rates in Kerr nonlinearity limited optical fibre communication systems

Achievable information rates of optical communication systems are inherently limited by nonlinear distortions due to the Kerr effect occurred in optical fibres. These nonlinear impairments become more significant for communication systems with larger transmission bandwidths, closer channel spacing and higher-order modulation formats. In this paper, the efficacy of nonlinearity compensation techniques, including both digital back-propagation and optical phase conjugation, for enhancing achievable information rates in lumped EDFA- and distributed Raman-amplified fully-loaded C −band systems is investigated considering practical transceiver limitations. The performance of multiple modulation formats, such as dual-polarisation quadrature phase shift keying (DP-QPSK), dual-polarisation 16 −ary quadrature amplitude modulation (DP-16QAM), DP-64QAM and DP-256QAM, has been studied in C −band systems with different transmission distances. It is found that the capabilities of both nonlinearity compensation techniques for enhancing achievable information rates strongly depend on signal modulation formats as well as target transmission distances

Influence of equalization enhanced phase noise on digital nonlinearity compensation in Nyquist-spaced superchannel transmission systems

In digital signal processing (DSP) based coherent optical communication systems, the effect of equalization enhanced phase noise (EEPN) will seriously degrade the transmission performance of high-capacity optical transmission system. In this paper, we have investigated the influence of EEPN on 9-channel 32-Gbaud dual-polarization 64-ary quadrature amplitude modulation (DP-64QAM) Nyquist-spaced superchannel optical field trial by using electronic dispersion compensation (EDC) and multi-channel digital backpropagation (MC-DBP). The deteriorations caused by EEPN on the signal-to-noise-ratio (SNR) and achievable information rates (AIRs) in high-speed optical communication systems have been studied. The system performance versus back-propagated bandwidth under different laser linewidth have also been demonstrated. The SNR penalty due to the distortion of EEPN achieves ~5.11 dB when FF-DBP is implemented, which informs that FF-DBP is more susceptible to EEPN, especially when the LO laser linewidth is larger. The system AIR versus different transmission distance under different EEPN interference using EDC-only and MC-DBP have also been evaluated, which show that there is a trade-off on the selection of lasers and back-propagated bandwidths to achieve a target AIR

Carrier phase recovery in optical fiber communication systems using high-order modulation formats

Nowadays, the coherent optical communication system plays an important role in communication field because of large capability and bandwidth. A coherent optical communication, based on high-order modulation and digital signal processing technologies, consists of optical transmitters, optical fiber lines, optical amplifiers and optical receivers. In the high-speed coherent optical communication system, the phase noise from the transmitter laser and the local oscillator laser can significantly degrade the performance of the signal transmission and detection, especially for the systems using high-order modulation format, such as m-ary phase shift keying (mPSK) and m-ary quadrature amplitude modulation (m-QAM). Therefore, investigations on laser phase noise compensation algorithm based on digital signal processing technologies has become more and more significant. In this work, a multi-ring carrier phase recovery algorithm is developed for compensating the laser phase noise in optical fiber communication systems using high-order modulation formats. Degradations on the performance of communication systems due to the laser phase noise have been investigated. The system performance using the proposed algorithm and the conventional Viterbi-Viterbi algorithm were also evaluated in 9-channel and 15- channel, 32-Gbaud, Nyquist-spaced QPSK, 16-QAM, 64-QAM and 256-QAM coherent transmission systems with considering the impact of the laser phase noise. It is found that the phase noise leads to stricter constraints on the linewidths of transmitter-side and receiver-side lasers, and it can greatly degrade the achievable information rates in communication systems. Besides, compared to the conventional Viterbi-Viterbi algorithm, which is usually applied in the QPSK system, our proposed algorithm can also well mitigate the laser phase noise in 16-QAM, 64-QAM and 256-QAM optical communication systems