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

Incentives Toward Conservation of Argaii Ovis Ammon: A Case Study of Trophy Hunting in Western China

We investigated management of wildlife, habitat and the hunting programme in Aksai County, Gansu Province, People\u27s Republic of China, during 1997-2000. Argali Ovis amnion is the focal species both for conservation and hunting. The hunting programme is intended to produce incentives to conserve wildlife and habitat. Poaching, a serious concern throughout western China, has been reduced in recent years in Aksai. Wildlife population trends are unknown because standardized surveys were begun only in 2000. Threats to argali in Aksai include livestock grazing, placer gold mining, and development of a dam, reservoir and aqueduct. The number of hunters participating in the programme (c. 3 per year) could provide considerable funding (c. $60,000 per year), but the allocation of these funds within China has provided too little for conservation at the local level, thus undermining the intended incentive system. Because local wildlife protection officials have been denied both funding and authority to deal with threats to the wildlife, the programme\u27s contribution to conservation has been minor. We recommend that hunters pay fees directly to county-level staff, thus increasing the proportion of funds retained at county-level, and that this added income is used to obtain wildlife grazing rights on important seasonal habitats for argali. These changes would promote local wildlife conservation without the need for additional external funding