A Multi-Plane Block-Coordinate Frank-Wolfe Algorithm for Training Structural SVMs with a Costly max-Oracle

Structural support vector machines (SSVMs) are amongst the best performing models for structured computer vision tasks, such as semantic image segmentation or human pose estimation. Training SSVMs, however, is computationally costly, because it requires repeated calls to a structured prediction subroutine (called \emph{max-oracle}), which has to solve an optimization problem itself, e.g. a graph cut. In this work, we introduce a new algorithm for SSVM training that is more efficient than earlier techniques when the max-oracle is computationally expensive, as it is frequently the case in computer vision tasks. The main idea is to (i) combine the recent stochastic Block-Coordinate Frank-Wolfe algorithm with efficient hyperplane caching, and (ii) use an automatic selection rule for deciding whether to call the exact max-oracle or to rely on an approximate one based on the cached hyperplanes. We show experimentally that this strategy leads to faster convergence to the optimum with respect to the number of requires oracle calls, and that this translates into faster convergence with respect to the total runtime when the max-oracle is slow compared to the other steps of the algorithm. A publicly available C++ implementation is provided at http://pub.ist.ac.at/~vnk/papers/SVM.html

Efficient Semidefinite Branch-and-Cut for MAP-MRF Inference

We propose a Branch-and-Cut (B&C) method for solving general MAP-MRF inference problems. The core of our method is a very efficient bounding procedure, which combines scalable semidefinite programming (SDP) and a cutting-plane method for seeking violated constraints. In order to further speed up the computation, several strategies have been exploited, including model reduction, warm start and removal of inactive constraints. We analyze the performance of the proposed method under different settings, and demonstrate that our method either outperforms or performs on par with state-of-the-art approaches. Especially when the connectivities are dense or when the relative magnitudes of the unary costs are low, we achieve the best reported results. Experiments show that the proposed algorithm achieves better approximation than the state-of-the-art methods within a variety of time budgets on challenging non-submodular MAP-MRF inference problems.Comment: 21 page

Energy Beamforming with One-Bit Feedback

Wireless energy transfer (WET) has attracted significant attention recently for providing energy supplies wirelessly to electrical devices without the need of wires or cables. Among different types of WET techniques, the radio frequency (RF) signal enabled far-field WET is most practically appealing to power energy constrained wireless networks in a broadcast manner. To overcome the significant path loss over wireless channels, multi-antenna or multiple-input multiple-output (MIMO) techniques have been proposed to enhance the transmission efficiency and distance for RF-based WET. However, in order to reap the large energy beamforming gain in MIMO WET, acquiring the channel state information (CSI) at the energy transmitter (ET) is an essential task. This task is particularly challenging for WET systems, since existing channel training and feedback methods used for communication receivers may not be implementable at the energy receiver (ER) due to its hardware limitation. To tackle this problem, in this paper we consider a multiuser MIMO system for WET, where a multiple-antenna ET broadcasts wireless energy to a group of multiple-antenna ERs concurrently via transmit energy beamforming. By taking into account the practical energy harvesting circuits at the ER, we propose a new channel learning method that requires only one feedback bit from each ER to the ET per feedback interval. The feedback bit indicates the increase or decrease of the harvested energy by each ER between the present and previous intervals, which can be measured without changing the existing hardware at the ER. Based on such feedback information, the ET adjusts transmit beamforming in different training intervals and at the same time obtains improved estimates of the MIMO channels to ERs by applying a new approach termed analytic center cutting plane method (ACCPM).Comment: This is the longer version of a paper to appear in IEEE Transactions on Signal Processin

Block-Coordinate Frank-Wolfe Optimization for Structural SVMs

We propose a randomized block-coordinate variant of the classic Frank-Wolfe algorithm for convex optimization with block-separable constraints. Despite its lower iteration cost, we show that it achieves a similar convergence rate in duality gap as the full Frank-Wolfe algorithm. We also show that, when applied to the dual structural support vector machine (SVM) objective, this yields an online algorithm that has the same low iteration complexity as primal stochastic subgradient methods. However, unlike stochastic subgradient methods, the block-coordinate Frank-Wolfe algorithm allows us to compute the optimal step-size and yields a computable duality gap guarantee. Our experiments indicate that this simple algorithm outperforms competing structural SVM solvers.Comment: Appears in Proceedings of the 30th International Conference on Machine Learning (ICML 2013). 9 pages main text + 22 pages appendix. Changes from v3 to v4: 1) Re-organized appendix; improved & clarified duality gap proofs; re-drew all plots; 2) Changed convention for Cf definition; 3) Added weighted averaging experiments + convergence results; 4) Clarified main text and relationship with appendi