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1. Online Continuous DR-Submodular Maximization with Long-Term Budget Constraints

   Sadeghi, Omid ; Fazel, Maryam ( August 2020 , Proceedings of Machine Learning Research)

   In this paper, we study a class of online optimization problems with long-term budget constraints where the objective functions are not necessarily concave (nor convex), but they instead satisfy the Diminishing Returns (DR) property. In this online setting, a sequence of monotone DR-submodular objective functions and linear budget functions arrive over time and assuming a limited total budget, the goal is to take actions at each time, before observing the utility and budget function arriving at that round, to achieve sub-linear regret bound while the total budget violation is sub-linear as well. Prior work has shown that achieving sub-linear regret and total budget violation simultaneously is impossible if the utility and budget functions are chosen adversarially. Therefore, we modify the notion of regret by comparing the agent against the best fixed decision in hindsight which satisfies the budget constraint proportionally over any window of length W. We propose the Online Saddle Point Hybrid Gradient (OSPHG) algorithm to solve this class of online problems. For W = T, we recover the aforementioned impossibility result. However, if W is sublinear in T, we show that it is possible to obtain sub-linear bounds for both the regret and the total budget violation. 

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2. Fast First-Order Methods for Monotone Strongly DR-Submodular Maximization

   Sadeghi, Omid ; Fazel, Maryam ( January 2023 , Proceedings of SIAM Conference on Applied and Computational Discrete Algorithms)

   Berry, Jonathan ; Shmoys, David ; Cowen, Lenore ; Naumann, Uwe (Ed.)

   Continuous DR-submodular functions are a class of functions that satisfy the Diminishing Returns (DR) property, which implies that they are concave along non-negative directions. Existing works have studied monotone continuous DR-submodular maximization subject to a convex constraint and have proposed efficient algorithms with approximation guarantees. However, in many applications, e. g., computing the stability number of a graph and mean-field inference for probabilistic log-submodular models, the DR-submodular function has the additional property of being strongly concave along non-negative directions that could be utilized for obtaining faster convergence rates. In this paper, we first introduce and characterize the class of strongly DR-submodular functions and show how such a property implies strong concavity along non-negative directions. Then, we study L-smooth monotone strongly DR-submodular functions that have bounded curvature, and we show how to exploit such additional structure to obtain algorithms with improved approximation guarantees and faster convergence rates for the maximization problem. In particular, we propose the SDRFW algorithm that matches the provably optimal approximation ratio after only iterations, where c ∈ [0,1] and μ ≥ 0 are the curvature and the strong DR-submodularity parameter. Furthermore, we study the Projected Gradient Ascent (PGA) method for this problem and provide a refined analysis of the algorithm with an improved approximation ratio (compared to ½ in prior works) and a linear convergence rate. Given that both algorithms require knowledge of the smoothness parameter L, we provide a novel characterization of L for DR-submodular functions showing that in many cases, computing L could be formulated as a convex optimization problem, i. e., a geometric program, that could be solved efficiently. Experimental results illustrate and validate the efficiency and effectiveness of our algorithms. 

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3. Submodular maximization with matroid and packing constraints in parallel

   https://doi.org/10.1145/3313276.3316389  

   Ene, Alina ; Nguyen, Huy L. ; Vladu, Adrian ( June 2019 , ACM SIGACT Symposium on Theory of Computing)

   We consider the problem of maximizing the multilinear extension of a submodular function subject a single matroid constraint or multiple packing constraints with a small number of adaptive rounds of evaluation queries. We obtain the first algorithms with low adaptivity for submodular maximization with a matroid constraint. Our algorithms achieve a $1-1/e-\epsilon$ approximation for monotone functions and a $1/e-\epsilon$ approximation for non-monotone functions, which nearly matches the best guarantees known in the fully adaptive setting. The number of rounds of adaptivity is $O(\log^2{n}/\epsilon^3)$, which is an exponential speedup over the existing algorithms. We obtain the first parallel algorithm for non-monotone submodular maximization subject to packing constraints. Our algorithm achieves a $1/e-\epsilon$ approximation using $O(\log(n/\epsilon) \log(1/\epsilon) \log(n+m)/ \epsilon^2)$ parallel rounds, which is again an exponential speedup in parallel time over the existing algorithms. For monotone functions, we obtain a $1-1/e-\epsilon$ approximation in $O(\log(n/\epsilon)\log(m)/\epsilon^2)$ parallel rounds. The number of parallel rounds of our algorithm matches that of the state of the art algorithm for solving packing LPs with a linear objective (Mahoney et al., 2016). Our results apply more generally to the problem of maximizing a diminishing returns submodular (DR-submodular) function. 

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4. Fairness-Aware Online Meta-learning

   Zhao, Chen ; Chen, Feng ; Thuraisingham, Bhavani ( August 2021 , In Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining)

   null (Ed.)

   Fairness in AI and Machine Learning is emerging to be a crucial research area to ensure social good. In contrast to offline working fashions, two research paradigms are devised for online learning: (1) Online Meta-Learning (OML learns good priors over model parameters (or learning to learn) in a sequential setting where tasks are revealed one after another. Although it provides a sub-linear regret bound, such techniques completely ignore the importance of learning with fairness which is a significant hallmark of human intelligence. (2) Online Fairness-Aware Learning that captures many classification problems for which fairness is a concern. But it aims to attain zero-shot generalization without any task-specific adaptation. This, therefore, limits the capability of a model to adapt to newly arrived data. To overcome such issues and bridge the gap, this paper is the first to propose a novel online meta-learning algorithm, namely FFML, which is under the setting of unfairness prevention. The key part of FFML is to learn good priors of an online fair classification model's primal and dual parameters that are associated with the model's accuracy and fairness, respectively. The problem is formulated in the form of a bi-level convex-concave optimization. The theoretic analysis provides sub-linear upper bounds for loss regret and violation of cumulative fairness constraints. The experiments demonstrate the versatility of FFML by applying it to classification on three real-world datasets and show substantial improvements over the best prior work on the tradeoff between fairness and classification accuracy. 

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5. Fairness-Aware Online Meta-learning

   Zhao, Chen ; Chen, Feng ; Thuraisingham, Bhavani ( August 2021 , In Proceedings of the 27th ACM SIGKDD conference on knowledge discovery and data mining (KDD 2021),)

   null (Ed.)

   Fairness in AI and Machine Learning is emerging to be a crucial research area to ensure social good. In contrast to offline working fashions, two research paradigms are devised for online learning: (1) Online Meta-Learning (OML learns good priors over model parameters (or learning to learn) in a sequential setting where tasks are revealed one after another. Although it provides a sub-linear regret bound, such techniques completely ignore the importance of learning with fairness which is a significant hallmark of human intelligence. (2) Online Fairness-Aware Learning that captures many classification problems for which fairness is a concern. But it aims to attain zero-shot generalization without any task-specific adaptation. This, therefore, limits the capability of a model to adapt to newly arrived data. To overcome such issues and bridge the gap, this paper is the first to propose a novel online meta-learning algorithm, namely FFML, which is under the setting of unfairness prevention. The key part of FFML is to learn good priors of an online fair classification model's primal and dual parameters that are associated with the model's accuracy and fairness, respectively. The problem is formulated in the form of a bi-level convex-concave optimization. The theoretic analysis provides sub-linear upper bounds for loss regret and violation of cumulative fairness constraints. The experiments demonstrate the versatility of FFML by applying it to classification on three real-world datasets and show substantial improvements over the best prior work on the tradeoff between fairness and classification accuracy. 

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