Practical Bilevel Optimization: Algorithms and Applications

By J. Bard. 1998

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In Mathematical Optimization

Citations in the corpus

Certified Defenses for Data Poisoning Attacks (2017, methodology): “Separately, the bound L(θ̂) / M was useful because M admits the natural minimax formulation (5), but the worst-case L(θ̂) can be expressed directly as a bilevel optimization problem (Mei and Zhu, 2015b), which is intractable in general but admits a number of heuristics (Bard, 1999).”
Using Machine Teaching to Identify Optimal Training-Set Attacks on Machine Learners (2015, background): “This is a bilevel optimization problem (Bard 1998).”
On Differentiating Parameterized Argmin and Argmax Problems with Application to Bi-level Optimization (2016, methodology): “As such, many techniques have been proposed for solving diﬀerent kinds of bi-level optimization problems [Bard, 1998, Dempe and Franke, 2015].”
Coresets via Bilevel Optimization for Continual Learning and Streaming (2020, background): “Provably correct solvers rely on branch and bound techniques [5].”
Bilevel Programming for Hyperparameter Optimization and Meta-Learning (2018, background): “Bilevel programming (Bard, 2013) has been suggested before in machine learning in the context of kernel methods and support vector machines (Keerthi et al., 2007; Kunapuli et al., 2008), multitask learning (Flamary et al., 2014), and more recently HO (Pedregosa, 2016), but never in the context of…”
MetaPoison: Practical General-purpose Clean-label Data Poisoning (2020, background): “Note that (1) is a bi-level optimization problem (Bard, 2013) – the minimization for X p involves the weights θ ∗ ( X p ) , which are themselves the minimizer of the training problem, where L train is the standard cross entropy loss, and Y ∈ N + n contains the correct labels of the clean and poison…”
Planning Regional Water Resources System Using an Interval Fuzzy Bi-Level Programming Method (2010, background): “Therefore, the linear BLP can be formulated as follows (Lai et al., 1996; Bard, 1998; Emam, 2006): [Upper-level]”
Deep Declarative Networks (2019, methodology): “Formally, we can think of the learning problem as an upper optimization problem and the network output as being obtained from a lower optimization problemwithin a bi-level optimization framework [7], [53].”
Annotated Bibliography on Bilevel Programming and Mathematical Programs with Equilibrium Constraints (2003, methodology): “The most comprehensive overview over the historical development of bilevel programming can be found in the monograph [31].”
Strategic bidding of transmission-constrained GENCOs with incomplete information (2005, methodology): “During the last two decades, numerical methods have been proposed for solving the bilevel problem, including the branch and bound algorithm, steepest descent direction, and heuristics methods [ 17 ], [18].”
Defense Against Adversarial Attacks Using Feature Scattering-based Adversarial Training (2019, background): “More specifically, it can be regarded as an instance of the more general bilevel optimization problem [13, 3].”
Optknock: A bilevel programming framework for identifying gene knockout strategies for microbial strain optimization (2003, background): “This multilayered optimization structure involving two competing optimal strategists (i.e., cellular objective and chemical production) is referred to as a bilevel optimization problem ( Bard, 1998 ).”
A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applications (2017, methodology): “To highlight the kind of complexities induced in the presence of discrete variables, we consider a simple linear bilevel problem described in [18] and [166] to show how the inducible region changes based on the upper, lower or both level variables being discrete or continuous.”
BlackIoT: IoT Botnet of High Wattage Devices Can Disrupt the Power Grid (2018, background): “The interdependency between failures in power grids and communication networks, and their propagation has also been recently studied [16, 38, 46], but these works focused on attacks and failures that target both the power grid’s and the communication network’s physical infrastructure at the same tim”