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1. A Single Recipe for Online Submodular Maximization with Adversarial or Stochastic Constraints

   Sadeghi, Omid ; Raut, Prasanna ; Fazel, Maryam ( December 2020 , Advances in neural information processing systems)

   null ; null ; null ; null ; null (Ed.)

   We consider an online optimization problem in which the reward functions are DR-submodular, and in addition to maximizing the total reward, the sequence of decisions must satisfy some convex constraints on average. Specifically, at each round t, upon committing to an action x_t, a DR-submodular utility function f_t and a convex constraint function g_t are revealed, and the goal is to maximize the overall utility while ensuring the average of the constraint functions is non-positive (so constraints are satisfied on average). Such cumulative constraints arise naturally in applications where the average resource consumption is required to remain below a specified threshold. We study this problem under an adversarial model and a stochastic model for the convex constraints, where the functions g_t can vary arbitrarily or according to an i.i.d. process over time. We propose a single algorithm which achieves sub-linear regret (with respect to the time horizon T) as well as sub-linear constraint violation bounds in both settings, without prior knowledge of the regime. Prior works have studied this problem in the special case of linear constraint functions. Our results not only improve upon the existing bounds under linear cumulative constraints, but also give the first sub-linear bounds for general convex long-term constraints. 

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2. Differentially Private Monotone Submodular Maximization Under Matroid and Knapsack Constraints

   Sadeghi, Omid ; Fazel, Maryam ( April 2021 , Proceedings of Machine Learning Research)

   Banerjee, Arindam ; Fukumizu, Kenji (Ed.)

   Numerous tasks in machine learning and artificial intelligence have been modeled as submodular maximization problems. These problems usually involve sensitive data about individuals, and in addition to maximizing the utility, privacy concerns should be considered. In this paper, we study the general framework of non-negative monotone submodular maximization subject to matroid or knapsack constraints in both offline and online settings. For the offline setting, we propose a differentially private $(1-\frac{\kappa}{e})$-approximation algorithm, where $\kappa\in[0,1]$ is the total curvature of the submodular set function, which improves upon prior works in terms of approximation guarantee and query complexity under the same privacy budget. In the online setting, we propose the first differentially private algorithm, and we specify the conditions under which the regret bound scales as $Ø(\sqrt{T})$, i.e., privacy could be ensured while maintaining the same regret bound as the optimal regret guarantee in the non-private setting. 

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3. Balancing Relevance and Diversity in Online Bipartite Matching via Submodularity

   Dickerson, John ; Sankararaman, Karthik ; Srinivasan, Aravind ; Xu, Pan ( January 2019 , AAAI Conference on Artificial Intelligence (AAAI))

   In bipartite matching problems, vertices on one side of a bipartite graph are paired with those on the other. In its online variant, one side of the graph is available offline, while the vertices on the other side arrive online. When a vertex arrives, an irrevocable and immediate decision should be made by the algorithm; either match it to an available vertex or drop it. Examples of such problems include matching workers to firms, advertisers to keywords, organs to patients, and so on. Much of the literature focuses on maximizing the total relevance—modeled via total weight—of the matching. However, in many real-world problems, it is also important to consider contributions of diversity: hiring a diverse pool of candidates, displaying a relevant but diverse set of ads, and so on. In this paper, we propose the Online Submodular Bipartite Matching (OSBM) problem, where the goal is to maximize a submodular function f over the set of matched edges. This objective is general enough to capture the notion of both diversity (e.g., a weighted coverage function) and relevance (e.g., the traditional linear function)—as well as many other natural objective functions occurring in practice (e.g., limited total budget in advertising settings). We propose novel algorithms that have provable guarantees and are essentially optimal when restricted to various special cases. We also run experiments on real-world and synthetic datasets to validate our algorithms. 

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4. Online Restless Multi-Armed Bandits with Long-Term Fairness Constraints

   https://doi.org/10.1609/aaai.v38i14.29489  

   Wang, Shufan ; Xiong, Guojun ; Li, Jian ( March 2024 , Proceedings of the AAAI Conference on Artificial Intelligence)

   Restless multi-armed bandits (RMAB) have been widely used to model sequential decision making problems with constraints. The decision maker (DM) aims to maximize the expected total reward over an infinite horizon under an “instantaneous activation constraint” that at most B arms can be activated at any decision epoch, where the state of each arm evolves stochastically according to a Markov decision process (MDP). However, this basic model fails to provide any fairness guarantee among arms. In this paper, we introduce RMAB-F, a new RMAB model with “long-term fairness constraints”, where the objective now is to maximize the longterm reward while a minimum long-term activation fraction for each arm must be satisfied. For the online RMAB-F setting (i.e., the underlying MDPs associated with each arm are unknown to the DM), we develop a novel reinforcement learning (RL) algorithm named Fair-UCRL. We prove that Fair-UCRL ensures probabilistic sublinear bounds on both the reward regret and the fairness violation regret. Compared with off-the-shelf RL methods, our Fair-UCRL is much more computationally efficient since it contains a novel exploitation that leverages a low-complexity index policy for making decisions. Experimental results further demonstrate the effectiveness of our Fair-UCRL.

    

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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 & 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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