Despite significant economic and ecological effects, a higher level of renewable energy generation leads to increased uncertainty and variability in power injections, thus compromising grid reliability. In order to improve power grid security, we investigate a joint chance-constrained (CC) direct current (DC) optimal power flow (OPF) problem. The problem aims to find economically optimal power generation while guaranteeing that all power generation, line flows, and voltages simultaneously remain within their bounds with a pre-defined probability. Unfortunately, the problem is computationally intractable even if the distribution of renewables fluctuations is specified. Moreover, existing approximate solutions to the joint CC OPF problem are overly conservative, and therefore have less value for the operational practice. This paper proposes an importance sampling approach to the CC DC OPF problem, which yields better complexity and accuracy than current state-of-the-art methods. The algorithm efficiently reduces the number of scenarios by generating and using only the most important of them, thus enabling real-time solutions for test cases with up to several hundred buses.
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In the storied Colonel Blotto game, two colonels allocate $a$ and $b$ troops, respectively, to $k$ distinct battlefields. A colonel wins a battle if they assign more troops to that particular battle, and each colonel seeks to maximize their total number of victories. Despite the problem's formulation in 1921, the first polynomial-time algorithm to compute Nash equilibrium (NE) strategies for this game was discovered only quite recently. In 2016, \citep{ahmadinejad_dehghani_hajiaghayi_lucier_mahini_seddighin_2019} formulated a breakthrough algorithm to compute NE strategies for the Colonel Blotto game in computational complexity $O(k^{14}\max\{a,b\}^{13})$, receiving substantial media coverage (e.g. \citep{Insider}, \citep{NSF}, \citep{ScienceDaily}). As of this work, this is the only known provably efficient algorithm (to our knowledge) for the Colonel Blotto game with general parameters. In this work, we present the first known algorithm to compute $\eps$-approximate NE strategies in the two-player Colonel Blotto game in runtime $\widetilde{O}(\eps^{-4} k^8 \max\{a,b\})$ for arbitrary settings of these parameters. Moreover, this algorithm is the first known efficient algorithm to compute approximate coarse correlated equilibrium strategies in the multiplayer Colonel Blotto game (when there are $\ell > 2$ colonels) with runtime $\widetilde{O}(\ell \eps^{-4} k^8 \max\{a,b\} + \ell^2 \eps^{-2} k^3 \max\{a,b\})$. Prior to this work, no polynomial-time algorithm was known to compute exact or approximate equilibrium (in any sense) strategies for multiplayer Colonel Blotto with arbitrary parameters. Our algorithm computes these approximate equilibria by implicitly performing multiplicative weights update over the exponentially many strategies available to each player.
This paper addresses the problem of determining all optimal integer solutions of a linear integer network flow problem, which we call the all optimal integer flow (AOF) problem. We derive an O(F (m + n) + mn + M ) time algorithm to determine all F many optimal integer flows in a directed network with n nodes and m arcs, where M is the best time needed to find one minimum cost flow. We remark that stopping Hamacher's well-known method for the determination of the K best integer flows at the first sub-optimal flow results in an algorithm with a running time of O(F m(n log n + m) + M ) for solving the AOF problem. Our improvement is essentially made possible by replacing the shortest path sub-problem with a more efficient way to determine a so called proper zero cost cycle using a modified depth-first search technique. As a byproduct, our analysis yields an enhanced algorithm to determine the K best integer flows that runs in O(Kn3 + M ). Besides, we give lower and upper bounds for the number of all optimal integer and feasible integer solutions. Our bounds are based on the fact that any optimal solution can be obtained by an initial optimal tree solution plus a conical combination of incidence vectors of all induced cycles with bounded coefficients.
Exact-approximate sequential Monte Carlo (SMC) methods target the exact posterior of intractable likelihood models by using a non-negative unbiased estimator of the likelihood when the likelihood is computationally intractable. For state-space models, a particle filter estimator can be used to obtain an unbiased estimate of the likelihood. The efficiency of exact-approximate SMC greatly depends on the variance of the likelihood estimator, and therefore on the number of state particles used within the particle filter. We introduce a novel method to adaptively select the number of state particles within exact-approximate SMC. We also utilise the expected squared jumping distance to trigger the adaptation, and modify the exchange importance sampling method of Chopin et al. (2012) to replace the current set of state particles with the new set. The resulting algorithm is fully adaptive, and can significantly improve current methods. Code for our methods is available at //github.com/imkebotha/adaptive-exact-approximate-smc.
Obtaining first-order regret bounds -- regret bounds scaling not as the worst-case but with some measure of the performance of the optimal policy on a given instance -- is a core question in sequential decision-making. While such bounds exist in many settings, they have proven elusive in reinforcement learning with large state spaces. In this work we address this gap, and show that it is possible to obtain regret scaling as $\mathcal{O}(\sqrt{V_1^\star K})$ in reinforcement learning with large state spaces, namely the linear MDP setting. Here $V_1^\star$ is the value of the optimal policy and $K$ is the number of episodes. We demonstrate that existing techniques based on least squares estimation are insufficient to obtain this result, and instead develop a novel robust self-normalized concentration bound based on the robust Catoni mean estimator, which may be of independent interest.
This paper presents a continuum mechanics-based approach for real-time deployment (RTD) of a multi-quadcopter system between moving initial and final configurations arbitrarily distributed in a 3-D motion space. The proposed RTD problem is decomposed into spatial planning, temporal planning and acquisition sub-problems. For the spatial planning, the RTD desired coordination is defined by integrating (i) rigid-body rotation, (ii) one-dimensional homogeneous deformation, and (ii) one-dimensional heterogeneous coordination such that necessary conditions for inter-agent collision avoidance between every two quadcopter UAVs are satisfied. By the RTD temporal planning, this paper suffices the inter-agent collision avoidance between every two individual quadcopters, and assures the boundedness of the rotor angular speeds for every individual quadcopter. For the RTD acquisition, each quadcopter modeled by a nonlinear dynamics applies a nonlinear control to stably and safely track the desired RTD trajectory such that the angular speeds of each quadcopter remain bounded and do not exceed a certain upper limit.
Due to the COVID 19 pandemic, smartphone-based proximity tracing systems became of utmost interest. Many of these systems use Bluetooth Low Energy (BLE) signals to estimate the distance between two persons. The quality of this method depends on many factors and, therefore, does not always deliver accurate results. In this paper, we present a multi-channel approach to improve proximity estimation, and a novel, publicly available dataset that contains matched IEEE 802.11 (2.4 GHz and 5 GHz) and BLE signal strength data, measured in four different environments. We have developed and evaluated a combined classification model based on BLE and IEEE 802.11 signals. Our approach significantly improves the distance estimation and consequently also the contact tracing accuracy. We are able to achieve good results with our approach in everyday public transport scenarios. However, in our implementation based on IEEE 802.11 probe requests, we also encountered privacy problems and limitations due to the consistency and interval at which such probes are sent. We discuss these limitations and sketch how our approach could be improved to make it suitable for real-world deployment.
Millimeter-wave self-backhauled small cells are a key component of next-generation wireless networks. Their dense deployment will increase data rates, reduce latency, and enable efficient data transport between the access and backhaul networks, providing greater flexibility not previously possible with optical fiber. Despite their high potential, operating dense self-backhauled networks optimally is an open challenge, particularly for radio resource management (RRM). This paper presents, RadiOrchestra, a holistic RRM framework that models and optimizes beamforming, rate selection as well as user association and admission control for self-backhauled networks. The framework is designed to account for practical challenges such as hardware limitations of base stations (e.g., computational capacity, discrete rates), the need for adaptability of backhaul links, and the presence of interference. Our framework is formulated as a nonconvex mixed-integer nonlinear program, which is challenging to solve. To approach this problem, we propose three algorithms that provide a trade-off between complexity and optimality. Furthermore, we derive upper and lower bounds to characterize the performance limits of the system. We evaluate the developed strategies in various scenarios, showing the feasibility of deploying practical self-backhauling in future networks.
Many representative graph neural networks, $e.g.$, GPR-GNN and ChebyNet, approximate graph convolutions with graph spectral filters. However, existing work either applies predefined filter weights or learns them without necessary constraints, which may lead to oversimplified or ill-posed filters. To overcome these issues, we propose $\textit{BernNet}$, a novel graph neural network with theoretical support that provides a simple but effective scheme for designing and learning arbitrary graph spectral filters. In particular, for any filter over the normalized Laplacian spectrum of a graph, our BernNet estimates it by an order-$K$ Bernstein polynomial approximation and designs its spectral property by setting the coefficients of the Bernstein basis. Moreover, we can learn the coefficients (and the corresponding filter weights) based on observed graphs and their associated signals and thus achieve the BernNet specialized for the data. Our experiments demonstrate that BernNet can learn arbitrary spectral filters, including complicated band-rejection and comb filters, and it achieves superior performance in real-world graph modeling tasks.
Human pose estimation - the process of recognizing human keypoints in a given image - is one of the most important tasks in computer vision and has a wide range of applications including movement diagnostics, surveillance, or self-driving vehicle. The accuracy of human keypoint prediction is increasingly improved thanks to the burgeoning development of deep learning. Most existing methods solved human pose estimation by generating heatmaps in which the ith heatmap indicates the location confidence of the ith keypoint. In this paper, we introduce novel network structures referred to as multiresolution representation learning for human keypoint prediction. At different resolutions in the learning process, our networks branch off and use extra layers to learn heatmap generation. We firstly consider the architectures for generating the multiresolution heatmaps after obtaining the lowest-resolution feature maps. Our second approach allows learning during the process of feature extraction in which the heatmaps are generated at each resolution of the feature extractor. The first and second approaches are referred to as multi-resolution heatmap learning and multi-resolution feature map learning respectively. Our architectures are simple yet effective, achieving good performance. We conducted experiments on two common benchmarks for human pose estimation: MS-COCO and MPII dataset.
Graph convolution is the core of most Graph Neural Networks (GNNs) and usually approximated by message passing between direct (one-hop) neighbors. In this work, we remove the restriction of using only the direct neighbors by introducing a powerful, yet spatially localized graph convolution: Graph diffusion convolution (GDC). GDC leverages generalized graph diffusion, examples of which are the heat kernel and personalized PageRank. It alleviates the problem of noisy and often arbitrarily defined edges in real graphs. We show that GDC is closely related to spectral-based models and thus combines the strengths of both spatial (message passing) and spectral methods. We demonstrate that replacing message passing with graph diffusion convolution consistently leads to significant performance improvements across a wide range of models on both supervised and unsupervised tasks and a variety of datasets. Furthermore, GDC is not limited to GNNs but can trivially be combined with any graph-based model or algorithm (e.g. spectral clustering) without requiring any changes to the latter or affecting its computational complexity. Our implementation is available online.
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