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In this work, we develop a novel efficient quadrature and sparse grid based polynomial interpolation method to price American options with multiple underlying assets. The approach is based on first formulating the pricing of American options using dynamic programming, and then employing static sparse grids to interpolate the continuation value function at each time step. To achieve high efficiency, we first transform the domain from $\mathbb{R}^d$ to $(-1,1)^d$ via a scaled tanh map, and then remove the boundary singularity of the resulting multivariate function over $(-1,1)^d$ by a bubble function and simultaneously, to significantly reduce the number of interpolation points. We rigorously establish that with a proper choice of the bubble function, the resulting function has bounded mixed derivatives up to a certain order, which provides theoretical underpinnings for the use of sparse grids. Numerical experiments for American arithmetic and geometric basket put options with the number of underlying assets up to 16 are presented to validate the effectiveness of the approach.

In this paper, we aim at maximizing the weighted sum-rate (WSR) of rate splitting multiple access (RSMA) in multi-user multi-antenna transmission networks through the joint optimization of rate allocation and beamforming. Unlike conventional methods like weighted minimum mean square error (WMMSE) and standard fractional programming (FP), which tackle the non-convex WSR problem iteratively using disciplined convex subproblems and optimization toolboxes, our work pioneers a novel toolbox-free approach. For the first time, we identify the optimal beamforming structure and common rate allocation for WSR maximization in RSMA by leveraging FP and Lagrangian duality. Then we propose an algorithm based on FP and fixed point iteration to optimize the beamforming and common rate allocation without the need for optimization toolboxes. Our numerical results demonstrate that the proposed algorithm attains the same performance as standard FP and classical WMMSE methods while significantly reducing computational time.

In this paper, we propose simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) assisted non-orthogonal multiple access (NOMA) networks. The considered STAR-RIS utilizes the mode switching (MS) protocol to serve multiple NOMA users located on both sides of the RIS surface. Based on the MS protocol, each STAR-RIS element can operate in full transmission or reflection mode. Within this perspective, we propose a novel algorithm to partition the STAR-RIS surface among the available users. This algorithm aims to determine the proper number of transmitting/reflecting elements needs to be assigned to each user in order to maximize the system sum-rate while guaranteeing the quality-of-service requirements for individual users. For the proposed system, we derive closed-form analytical expressions for the outage probability (OP) and its corresponding asymptotic behavior under different user deployments. Finally, Monte Carlo simulations are performed in order to verify the correctness of the theoretical analysis. It is shown that the proposed system outperforms the classical NOMA and orthogonal multiple access systems in terms of OP and sum-rate.

In this paper, by constructing extremely hard examples of CSP (with large domains) and SAT (with long clauses), we prove that such examples cannot be solved without exhaustive search, which is stronger than P $\neq$ NP. This constructive approach for proving impossibility results is very different (and missing) from those currently used in computational complexity theory, but is similar to that used by Kurt G\"{o}del in proving his famous logical impossibility results. Just as shown by G\"{o}del's results that proving formal unprovability is feasible in mathematics, the results of this paper show that proving computational hardness is not hard in mathematics. Specifically, proving lower bounds for many problems, such as 3-SAT, can be challenging because these problems have various effective strategies available for avoiding exhaustive search. However, in cases of extremely hard examples, exhaustive search may be the only viable option, and proving its necessity becomes more straightforward. Consequently, it makes the separation between SAT (with long clauses) and 3-SAT much easier than that between 3-SAT and 2-SAT. Finally, the main results of this paper demonstrate that the fundamental difference between the syntax and the semantics revealed by G\"{o}del's results also exists in CSP and SAT.

In this paper, we propose three generic models of capacitated coverage and, more generally, submodular maximization to study task-worker assignment problems that arise in a wide range of gig economy platforms. Our models incorporate the following features: (1) Each task and worker can have an arbitrary matching capacity, which captures the limited number of copies or finite budget for the task and the working capacity of the worker; (2) Each task is associated with a coverage or, more generally, a monotone submodular utility function. Our objective is to design an allocation policy that maximizes the sum of all tasks' utilities, subject to capacity constraints on tasks and workers. We consider two settings: offline, where all tasks and workers are static, and online, where tasks are static while workers arrive dynamically. We present three LP-based rounding algorithms that achieve optimal approximation ratios of $1-1/\mathsf{e} \sim 0.632$ for offline coverage maximization, competitive ratios of $(19-67/\mathsf{e}^3)/27\sim 0.580$ and $0.436$ for online coverage and online monotone submodular maximization, respectively.

In this paper, we study an intelligent reflecting surface (IRS)-aided communication system with single-antenna transmitter and receiver, under imperfect channel state information (CSI). More specifically, we deal with the robust selection of binary (on/off) states of the IRS elements in order to maximize the worst-case energy efficiency (EE), given a bounded CSI uncertainty, while satisfying a minimum signal-to-noise ratio (SNR). In addition, we consider not only continuous but also discrete IRS phase shifts. First, we derive closed-form expressions of the worst-case SNRs, and then formulate the robust (discrete) optimization problems for each case. In the case of continuous phase shifts, we design a dynamic programming (DP) algorithm that is theoretically guaranteed to achieve the global maximum with polynomial complexity $O(L\,{\log L})$, where $L$ is the number of IRS elements. In the case of discrete phase shifts, we develop a convex-relaxation-based method (CRBM) to obtain a feasible (sub-optimal) solution in polynomial time $O(L^{3.5})$, with a posteriori performance guarantee. Furthermore, numerical simulations provide useful insights and confirm the theoretical results. In particular, the proposed algorithms are several orders of magnitude faster than the exhaustive search when $L$ is large, thus being highly scalable and suitable for practical applications. Moreover, both algorithms outperform a baseline scheme, namely, the activation of all IRS elements.

This paper presents a case for exemplar parallelism of neural networks using Go as parallelization framework. Further it is shown that also limited multi-core hardware systems are feasible for these parallelization tasks, as notebooks and single board computer systems. The main question was how much speedup can be generated when using concurrent Go goroutines specifically. A simple concurrent feedforward network for MNIST digit recognition with the programming language Go was created to find the answer. The first findings when using a notebook (Lenovo Yoga 2) showed a speedup of 252% when utilizing 4 goroutines. Testing a single board computer (Banana Pi M3) delivered more convincing results: 320% with 4 goroutines, and 432% with 8 goroutines.

In this paper, we proposed to apply meta learning approach for low-resource automatic speech recognition (ASR). We formulated ASR for different languages as different tasks, and meta-learned the initialization parameters from many pretraining languages to achieve fast adaptation on unseen target language, via recently proposed model-agnostic meta learning algorithm (MAML). We evaluated the proposed approach using six languages as pretraining tasks and four languages as target tasks. Preliminary results showed that the proposed method, MetaASR, significantly outperforms the state-of-the-art multitask pretraining approach on all target languages with different combinations of pretraining languages. In addition, since MAML's model-agnostic property, this paper also opens new research direction of applying meta learning to more speech-related applications.

In this paper, we propose a deep reinforcement learning framework called GCOMB to learn algorithms that can solve combinatorial problems over large graphs. GCOMB mimics the greedy algorithm in the original problem and incrementally constructs a solution. The proposed framework utilizes Graph Convolutional Network (GCN) to generate node embeddings that predicts the potential nodes in the solution set from the entire node set. These embeddings enable an efficient training process to learn the greedy policy via Q-learning. Through extensive evaluation on several real and synthetic datasets containing up to a million nodes, we establish that GCOMB is up to 41% better than the state of the art, up to seven times faster than the greedy algorithm, robust and scalable to large dynamic networks.

In this paper, we propose a conceptually simple and geometrically interpretable objective function, i.e. additive margin Softmax (AM-Softmax), for deep face verification. In general, the face verification task can be viewed as a metric learning problem, so learning large-margin face features whose intra-class variation is small and inter-class difference is large is of great importance in order to achieve good performance. Recently, Large-margin Softmax and Angular Softmax have been proposed to incorporate the angular margin in a multiplicative manner. In this work, we introduce a novel additive angular margin for the Softmax loss, which is intuitively appealing and more interpretable than the existing works. We also emphasize and discuss the importance of feature normalization in the paper. Most importantly, our experiments on LFW BLUFR and MegaFace show that our additive margin softmax loss consistently performs better than the current state-of-the-art methods using the same network architecture and training dataset. Our code has also been made available at //github.com/happynear/AMSoftmax