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Determinantal point processes (DPPs) are popular probabilistic models that arise in many machine learning tasks, where distributions of diverse sets are characterized by matrix determinants. In this paper, we develop fast algorithms to find…
Multi-step greedy policies have been extensively used in model-based reinforcement learning (RL), both when a model of the environment is available (e.g.,~in the game of Go) and when it is learned. In this paper, we explore their benefits…
We introduce a transformation framework that can be utilized to develop online algorithms with low $\epsilon$-approximate regret in the random-order model from offline approximation algorithms. We first give a general reduction theorem that…
Online algorithms for detecting changepoints, or abrupt shifts in the behavior of a time series, are often deployed with limited resources, e.g., to edge computing settings such as mobile phones or industrial sensors. In these scenarios it…
We provide a distributed online algorithm for multi-agent submodular maximization under communication delays. We are motivated by the future distributed information-gathering tasks in unknown and dynamic environments, where utility…
Submodular optimization is a special class of combinatorial optimization arising in several machine learning problems, but also in cooperative control of complex systems. In this paper, we consider agents in an asynchronous, unreliable and…
Multiobjective optimization plays an increasingly important role in modern applications, where several objectives are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to…
Recovery type a posteriori error estimators are popular, particularly in the engineering community, for their computationally inexpensive, easy to implement, and generally asymptotically exactness. Unlike the residual type error estimators,…
This paper presents a model order reduction (MOR) approach for high dimensional problems in the analysis of financial risk. To understand the financial risks and possible outcomes, we have to perform several thousand simulations of the…
In this paper we prove the efficacy of a simple greedy algorithm for a finite horizon online resource allocation/matching problem, when the corresponding static planning linear program (SPP) exhibits a non-degeneracy condition called the…
The maximization of submodular functions is an NP-Hard problem for certain subclasses of functions, for which a simple greedy algorithm has been shown to guarantee a solution whose quality is within 1/2 of the optimal. When this algorithm…
We investigate model reduction of parametric linear time-invariant (LTI) dynamical systems. When posed in the frequency domain, this problem can be formulated as seeking a low-order rational function approximation of a high-order rational…
We consider an online two-stage stochastic optimization with long-term constraints over a finite horizon of $T$ periods. At each period, we take the first-stage action, observe a model parameter realization and then take the second-stage…
The classical problem of maximizing a submodular function under a matroid constraint is considered. Defining a new measure for the increments made by the greedy algorithm at each step, called the discriminant, improved approximation ratio…
This paper focuses on the development of novel greedy techniques for distributed learning under sparsity constraints. Greedy techniques have widely been used in centralized systems due to their low computational requirements and at the same…
This work introduces a natural variant of the online machine scheduling problem on unrelated machines, which we refer to as the favorite machine model. In this model, each job has a minimum processing time on a certain set of machines,…
Identifying breakpoints in piecewise regression is critical in enhancing the reliability and interpretability of data fitting. In this paper, we propose novel algorithms based on the greedy algorithm to accurately and efficiently identify…
Many problems in signal processing and machine learning can be formalized as weak submodular optimization tasks. For such problems, a simple greedy algorithm (\textsc{Greedy}) is guaranteed to find a solution achieving the objective with a…
By a high-order numerical homogenization method, a heterogeneous multiscale scheme was developed in Jin & Li (2022) for evolving differential equations containing two time scales. In this paper, we further explore the technique to propose…
Offline optimization is an emerging problem in many experimental engineering domains including protein, drug or aircraft design, where online experimentation to collect evaluation data is too expensive or dangerous. To avoid that, one has…