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We develop an algorithmic framework for solving convex optimization problems using no-regret game dynamics. By converting the problem of minimizing a convex function into an auxiliary problem of solving a min-max game in a sequential…
Submodular function maximization has been studied extensively in recent years under various constraints and models. The problem plays a major role in various disciplines. We study a natural online variant of this problem in which elements…
Despite strong performance in numerous applications, the fragility of deep learning to input perturbations has raised serious questions about its use in safety-critical domains. While adversarial training can mitigate this issue in…
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…
In this paper, the distributed resource allocation optimization problem is investigated. The allocation decisions are made to minimize the sum of all the agents' local objective functions while satisfying both the global network resource…
Maximizing submodular functions under cardinality constraints lies at the core of numerous data mining and machine learning applications, including data diversification, data summarization, and coverage problems. In this work, we study this…
The research of influence propagation in social networks via word-of-mouth processes has been given considerable attention in recent years. Arguably, the most fundamental problem in this domain is influence maximization, where the goal is…
In this paper, we introduce a novel technique for constrained submodular maximization, inspired by barrier functions in continuous optimization. This connection not only improves the running time for constrained submodular maximization but…
We consider the problem of influence maximization in fixed networks for contagion models in an adversarial setting. The goal is to select an optimal set of nodes to seed the influence process, such that the number of influenced nodes at the…
In this work we study a special minimax problem where there are linear constraints that couple both the minimization and maximization decision variables. The problem is a generalization of the traditional saddle point problem (which does…
We propose a novel approach to allocating resources for expensive simulations of high fidelity models when used in a multifidelity framework. Allocation decisions that distribute computational resources across several simulation models…
The greedy strategy is an approximation algorithm to solve optimization problems arising in decision making with multiple actions. How good is the greedy strategy compared to the optimal solution? In this survey, we mainly consider two…
For effective decision support in scenarios with conflicting objectives, sets of potentially optimal solutions can be presented to the decision maker. We explore both what policies these sets should contain and how such sets can be computed…
Greedy algorithms are widely used for problems in machine learning such as feature selection and set function optimization. Unfortunately, for large datasets, the running time of even greedy algorithms can be quite high. This is because for…
Many engineering problems have multiple objectives, and the overall aim is to optimize a non-linear function of these objectives. In this paper, we formulate the problem of maximizing a non-linear concave function of multiple long-term…
Many large-scale machine learning problems--clustering, non-parametric learning, kernel machines, etc.--require selecting a small yet representative subset from a large dataset. Such problems can often be reduced to maximizing a submodular…
We propose a distributionally robust formulation of the traditional risk parity portfolio optimization problem. Distributional robustness is introduced by targeting the discrete probabilities attached to each observation used during…
Two optimization algorithms are proposed for solving a stochastic programming problem for which the objective function is given in the form of the expectation of convex functions and the constraint set is defined by the intersection of…
We consider minimax (saddle-point) problems of the form max_{c \in C} min_{\beta \in S} g(c; \beta), where C and S are compact convex sets, and g is concave-convex. Applying the Alternating Direction Method of Multipliers (ADMM) requires…
We provide theoretical bounds on the worst case performance of the greedy algorithm in seeking to maximize a normalized, monotone, but not necessarily submodular objective function under a simple partition matroid constraint. We also…