787 research outputs found
On Unconstrained Quasi-Submodular Function Optimization
With the extensive application of submodularity, its generalizations are
constantly being proposed. However, most of them are tailored for special
problems. In this paper, we focus on quasi-submodularity, a universal
generalization, which satisfies weaker properties than submodularity but still
enjoys favorable performance in optimization. Similar to the diminishing return
property of submodularity, we first define a corresponding property called the
{\em single sub-crossing}, then we propose two algorithms for unconstrained
quasi-submodular function minimization and maximization, respectively. The
proposed algorithms return the reduced lattices in iterations,
and guarantee the objective function values are strictly monotonically
increased or decreased after each iteration. Moreover, any local and global
optima are definitely contained in the reduced lattices. Experimental results
verify the effectiveness and efficiency of the proposed algorithms on lattice
reduction.Comment: 11 page
Parsimonious Black-Box Adversarial Attacks via Efficient Combinatorial Optimization
Solving for adversarial examples with projected gradient descent has been
demonstrated to be highly effective in fooling the neural network based
classifiers. However, in the black-box setting, the attacker is limited only to
the query access to the network and solving for a successful adversarial
example becomes much more difficult. To this end, recent methods aim at
estimating the true gradient signal based on the input queries but at the cost
of excessive queries. We propose an efficient discrete surrogate to the
optimization problem which does not require estimating the gradient and
consequently becomes free of the first order update hyperparameters to tune.
Our experiments on Cifar-10 and ImageNet show the state of the art black-box
attack performance with significant reduction in the required queries compared
to a number of recently proposed methods. The source code is available at
https://github.com/snu-mllab/parsimonious-blackbox-attack.Comment: Accepted and to appear at ICML 201
Attention and Anticipation in Fast Visual-Inertial Navigation
We study a Visual-Inertial Navigation (VIN) problem in which a robot needs to
estimate its state using an on-board camera and an inertial sensor, without any
prior knowledge of the external environment. We consider the case in which the
robot can allocate limited resources to VIN, due to tight computational
constraints. Therefore, we answer the following question: under limited
resources, what are the most relevant visual cues to maximize the performance
of visual-inertial navigation? Our approach has four key ingredients. First, it
is task-driven, in that the selection of the visual cues is guided by a metric
quantifying the VIN performance. Second, it exploits the notion of
anticipation, since it uses a simplified model for forward-simulation of robot
dynamics, predicting the utility of a set of visual cues over a future time
horizon. Third, it is efficient and easy to implement, since it leads to a
greedy algorithm for the selection of the most relevant visual cues. Fourth, it
provides formal performance guarantees: we leverage submodularity to prove that
the greedy selection cannot be far from the optimal (combinatorial) selection.
Simulations and real experiments on agile drones show that our approach ensures
state-of-the-art VIN performance while maintaining a lean processing time. In
the easy scenarios, our approach outperforms appearance-based feature selection
in terms of localization errors. In the most challenging scenarios, it enables
accurate visual-inertial navigation while appearance-based feature selection
fails to track robot's motion during aggressive maneuvers.Comment: 20 pages, 7 figures, 2 table
Resilient Monotone Submodular Function Maximization
In this paper, we focus on applications in machine learning, optimization,
and control that call for the resilient selection of a few elements, e.g.
features, sensors, or leaders, against a number of adversarial
denial-of-service attacks or failures. In general, such resilient optimization
problems are hard, and cannot be solved exactly in polynomial time, even though
they often involve objective functions that are monotone and submodular.
Notwithstanding, in this paper we provide the first scalable,
curvature-dependent algorithm for their approximate solution, that is valid for
any number of attacks or failures, and which, for functions with low curvature,
guarantees superior approximation performance. Notably, the curvature has been
known to tighten approximations for several non-resilient maximization
problems, yet its effect on resilient maximization had hitherto been unknown.
We complement our theoretical analyses with supporting empirical evaluations.Comment: Improved suboptimality guarantees on proposed algorithm and corrected
typo on Algorithm 1's statemen
The Lov\'asz Hinge: A Novel Convex Surrogate for Submodular Losses
Learning with non-modular losses is an important problem when sets of
predictions are made simultaneously. The main tools for constructing convex
surrogate loss functions for set prediction are margin rescaling and slack
rescaling. In this work, we show that these strategies lead to tight convex
surrogates iff the underlying loss function is increasing in the number of
incorrect predictions. However, gradient or cutting-plane computation for these
functions is NP-hard for non-supermodular loss functions. We propose instead a
novel surrogate loss function for submodular losses, the Lov\'asz hinge, which
leads to O(p log p) complexity with O(p) oracle accesses to the loss function
to compute a gradient or cutting-plane. We prove that the Lov\'asz hinge is
convex and yields an extension. As a result, we have developed the first
tractable convex surrogates in the literature for submodular losses. We
demonstrate the utility of this novel convex surrogate through several set
prediction tasks, including on the PASCAL VOC and Microsoft COCO datasets
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