New method approximates non-submodular functions, offering first guarantees.
problem Minimizing non-submodular functions without theoretical guarantees.
method Extends submodularity relations to non-submodular functions, offering approximation guarantees.
result First approximation guarantees for non-submodular minimization, optimal under noise.
New method for probabilistic modeling of integer submodular functions.
problem Lack of probabilistic modeling for integer submodular functions.
method Proposed Generalized Multilinear Extension and block-coordinate ascent algorithm.
result Demonstrated effectiveness and viability on real-world datasets.
The paper studies continuous submodular functions and their optimization.
problem Maximizing continuous submodular functions in poly. time.
method Characterization of continuous submodularity, operations preserving it, and algorithms for constrained maximization.
result Continuous submodularity is equivalent to a weak DR property, leading to continuous DR-submodular functions with the full DR property.
A number of discrete and continuous optimization problems in machine learning are related to convex minimization problems under submodular constraints. In this paper, we deal with a submodular function with a directed graph structure, and we show that a wide range of convex optimization problems under submodular constr…
A new framework speeds up submodular optimization for large problems.
problem Large scale submodular optimization problems are hard to solve.
method Memoization framework for submodular functions with precomputed statistics.
result Significant speedups for various submodular optimization problems.
New variational method solves submodular maximum coverage problem efficiently.
problem Submodular maximum coverage problem in various applications.
method Variational optimization using Nemhauser divergence, alternating E and M steps.
result Efficient solution to submodular maximum coverage problem.
Scalable methods for maximizing regularized submodular functions with improved memory and communication complexity.
problem Maximizing submodular functions with negative values and constraints.
method Developed one-pass streaming and distributed algorithms for maximizing regularized submodular functions.
result Improved memory and communication complexity by a factor of O(1/ε) compared to existing work.
DR-submodular continuous functions are important objectives with wide real-world applications spanning MAP inference in determinantal point processes (DPPs), and mean-field inference for probabilistic submodular models, amongst others. DR-submodularity captures a subclass of non-convex functions that enables both exact…
In this paper we study the fundamental problems of maximizing a continuous non-monotone submodular function over the hypercube, both with and without coordinate-wise concavity. This family of optimization problems has several applications in machine learning, economics, and communication systems. Our main result is the…
We introduce a new convex optimization problem, termed quadratic decomposable submodular function minimization. The problem is closely related to decomposable submodular function minimization and arises in many learning on graphs and hypergraphs settings, such as graph-based semi-supervised learning and PageRank. We ap…
Submodularity is studied for convex risk measures, including Expected Shortfall.
problem Characterizing submodularity in convex risk measures.
method Analyzing submodularity properties of law-invariant coherent risk measures, including Expected Shortfall and Value-at-Risk.
result AES is submodular only when it reduces to ES, and empirical analysis shows AES violations are less frequent than VaR and ES violations.
Differentially private algorithms for submodular maximization under various constraints.
problem Maximizing decomposable submodular functions under constraints while preserving privacy.
method Designing differentially private algorithms for both monotone and non-monotone decomposable submodular maximization under general matroid constraints.
result Improved utility guarantees and competitive performance compared to non-private algorithms.
The paper introduces submodular information measures for machine learning applications.
problem Generalizing information-theoretic measures to non-random variables.
method Developing combinatorial information measures based on submodular functions.
result Submodular mutual information is submodular in one argument for certain submodular functions.
We introduce a method to learn a mixture of submodular "shells" in a large-margin setting. A submodular shell is an abstract submodular function that can be instantiated with a ground set and a set of parameters to produce a submodular function. A mixture of such shells can then also be so instantiated to produce a mor…
This thesis explores how submodularity aids in optimizing non-convex functions and validating algorithms.
problem Understanding which functions can be optimized efficiently in non-convex settings.
method Introducing continuous submodularity and developing algorithms for maximizing these functions.
result Characterization and optimization of continuous submodular functions with strong guarantees.
New algorithm maximizes non-monotone adaptive submodular functions in linear time.
problem Maximizing non-monotone adaptive submodular functions subject to a cardinality constraint.
method Developed a linear-time algorithm for non-monotone adaptive submodular maximization.
result Achieved a 1/e−ε approximation ratio with O(nε−2logε−1) value oracle queries. Paper tackles stochastic k-submodular bandits with full feedback, achieving sublinear regret.
problem Online optimization of k-submodular functions with full-bandit feedback. method Proposes online algorithms for various k-submodular stochastic combinatorial multi-armed bandit problems. result Achieves sublinear α-regret bounds for multiple k-submodular stochastic combinatorial multi-armed bandit problems. Improved model capacity for graph cut algorithms by relaxing submodularity constraints.
problem Improving graph cut algorithms for complex image processing tasks.
method Enforce probably approximately submodular pairwise potentials instead of guaranteed submodular ones.
result Substantial improvement in model capacity with reduced inference error.
Study private submodular maximization in streaming data.
problem Private maximization of submodular functions in streaming data.
method Established differentially private baselines and derived better trade-offs for decomposable submodular functions.
result Improved trade-offs between privacy and utility for decomposable submodular functions.
Greedy policy achieves good results for adaptive submodular problems.
problem Sequential decision making with adaptive stochastic optimization.
method Adaptive submodularity ratio to analyze greedy policy performance.
result Greedy policy achieves approximation guarantees for a broader class of problems.
New framework tackles submodular welfare with multi-agent combinatorial bandits.
problem Maximizing total welfare among agents with shared constraints and submodular utilities under bandit feedback.
method Proposes an explore-then-commit strategy with randomized assignments for multi-agent combinatorial bandits.
result Achieves ildeO(T2/3) regret, first for partition-based submodular welfare problem under bandit feedback. The paper tackles feature cross search for linear models, providing approximation algorithms and structural results.
problem Maximizing AUC of a linear model trained on feature crosses.
method Submodular optimization, greedy algorithm, and connections to total variation and kernel matrices.
result Simple greedy (1−1/e)-approximation algorithm for maximizing AUC. Derives an approximation algorithm for continuous submodular maximization without derivative information.
problem Maximizing a continuous submodular function with only function values and no derivative information.
method Black-box Continuous Greedy algorithm for DR-submodular functions, extended to stochastic setting.
result Achieves a (1−1/e)OPT−ε approximation guarantee with O(d/ε3) function evaluations. Three online algorithms for submodular maximization with varying feedback types.
problem Maximizing submodular functions under different feedback models.
method Mono-Frank-Wolfe, Bandit-Frank-Wolfe, Responsive-Frank-Wolfe.
result Achieved (1−1/e)-regret bounds for each algorithm. The ability to integrate information in the brain is considered to be an essential property for cognition and consciousness. Integrated Information Theory (IIT) hypothesizes that the amount of integrated information (Φ) in the brain is related to the level of consciousness. IIT proposes that to quantify information i…
Paper improves greedy algorithm for non-submodular matroid constraints.
problem Maximizing non-submodular functions subject to matroid constraints.
method Developed and analyzed a greedy algorithm with approximation guarantees.
result Greedy algorithm offers approximation factors for matroid constraints.
New algorithms solve DR-submodular maximization with faster convergence.
problem Maximizing monotone DR-submodular functions under convex constraints.
method Introduced strongly DR-submodular functions and proposed SDRFW and PGA algorithms.
result SDRFW achieves optimal approximation ratio after fewer iterations.
Adaptive cascade submodular maximization tackles sequential selection under uncertainty.
problem Maximizing expected utility from a set of items with unknown states and continuation probabilities.
method Proposed adaptive cascade submodular functions and a 0.12 approximation algorithm.
result Identified a class of functions (adaptive cascade submodular) that many practical applications satisfy.
A new method learns interpretable decision rules using submodular optimization.
problem Learning interpretable decision rules from data.
method Submodular optimization approach for selecting rules from a large set.
result The method effectively learns interpretable rule sets from real datasets.
New algorithm speeds up feature selection and experimental design.
problem Designing efficient parallel algorithms for statistical subset selection.
method Differential submodularity and adaptive sampling.
result Logarithmic parallel runtime for feature selection and experimental design.
Algorithm improves recommendation subset selection in the presence of biases.
problem Maximizing submodular functions for recommendation in the presence of social biases.
method Algorithm for submodular maximization with fairness constraints.
result Algorithm provably outputs subsets with near-optimal utility and proportional representation.
Paper tackles non-monotone DR-submodular maximization with approximation and regret guarantees.
problem Maximizing non-monotone DR-submodular functions over specific sets.
method Frank-Wolfe algorithm for general convex sets, Stochastic Gradient Ascent for down-closed convex sets.
result First approximation guarantees for both offline and online settings.
Submodular functions are a broad class of set functions, which naturally arise in diverse areas. Many algorithms have been suggested for the maximization of these functions. Unfortunately, once the function deviates from submodularity, the known algorithms may perform arbitrarily poorly. Amending this issue, by obtaini…
New algorithms reduce regret for online submodular maximization under various conditions.
problem Online optimization of submodular functions with adversarial or random utilities.
method Characterized strongly DR-submodular functions and derived bounds for different utility classes.
result Logarithmic regret bounds for adversarial strongly DR-submodular functions and submodular functions with random order.
Unified framework for robust submodular optimization with various constraints.
problem Robust optimization in machine learning applications.
method Unified framework for minimization and maximization under combinatorial constraints.
result Scalable approximation algorithms for various submodular optimization problems.
This paper studies robust payoff allocation in submodular games, especially against replication.
problem Payoff allocation in submodular games, especially robustness against replication.
method Systematically studied replication manipulation in submodular games, introduced replication robustness metric, and validated with empirical ML data market.
result Conditions characterizing robustness of semivalues in submodular games.
Generative Flow Networks use submodular upper bounds to generate more data.
problem Generating data from unknown, complex reward functions efficiently.
method Introduce submodular upper bounds to estimate reward, use Optimism in the Face of Uncertainty principle to train GFNs.
result SUBo-GFN generates significantly more data than classical GFNs.
Fast algorithms developed for adaptive and fully adaptive submodular maximization problems.
problem Maximizing submodular functions subject to constraints in linear time.
method Developed linear-time algorithms for two submodular maximization problems: adaptive and fully adaptive.
result Achieved (1−1/e−ε) approximation ratio for adaptive submodular maximization and $ rac{1-1/e-ε}{4-2/e-2ε}$ for fully adaptive submodular maximization. New method improves submodular maximization for machine learning applications.
problem Inexact monotonicity in submodular functions limits traditional algorithms' performance.
method Introduces monotonicity ratio as a continuous version of monotonicity, leading to improved approximation guarantees.
result Improved approximation ratios for movie recommendation, quadratic programming, and image summarization.
The scalability of submodular optimization methods is critical for their usability in practice. In this paper, we study the reducibility of submodular functions, a property that enables us to reduce the solution space of submodular optimization problems without performance loss. We introduce the concept of reducibility…
We extend the work of Narasimhan and Bilmes [30] for minimizing set functions representable as a dierence between submodular functions. Similar to [30], our new algorithms are guaranteed to monotonically reduce the objective function at every step. We empirically and theoretically show that the per-iteration cost of ou…
New technique improves submodular maximization with barrier functions.
problem Maximizing submodular functions under complex constraints.
method Inspired by barrier functions in continuous optimization, a novel potential function is proposed for approximate minimization.
result Guaranteed 2(k+1+ε)-approximation factor for feasible sets. Paper tackles online DR-submodular maximization with various convex sets.
problem Maximizing DR-submodular functions online over different convex sets.
method Develops online algorithms with approximation guarantees for various convex sets.
result Achieves 1/e-approximation ratio with O(T2/3) regret for down-closed sets. This paper tackles robust submodular minimization for image segmentation and correspondence.
problem Robust submodular minimization for image segmentation and correspondence.
method Constrained submodular minimization with scalable approximation algorithms for various combinatorial constraints.
result First work on robust submodular minimization under broad combinatorial constraints.
Submodular extensions of an energy function can be used to efficiently compute approximate marginals via variational inference. The accuracy of the marginals depends crucially on the quality of the submodular extension. To identify the best possible extension, we show an equivalence between the submodular extensions of…
Many tasks in machine learning and data mining, such as data diversification, non-parametric learning, kernel machines, clustering etc., require extracting a small but representative summary from a massive dataset. Often, such problems can be posed as maximizing a submodular set function subject to a cardinality constr…
New algorithm for maximizing submodular functions in real-time data changes.
problem Maximizing submodular functions under dynamic constraints.
method Randomized algorithm with O(k2) amortized update time. result 4-approximate solution to submodular maximization problem.
We consider active, semi-supervised learning in an offline transductive setting. We show that a previously proposed error bound for active learning on undirected weighted graphs can be generalized by replacing graph cut with an arbitrary symmetric submodular function. Arbitrary non-symmetric submodular functions can be…