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Submodular functions -- functions exhibiting diminishing returns -- are central to machine learning. When the objective is monotone and non-negative, the greedy algorithm achieves a tight $63\%$ approximation. But many practical objectives…

Machine Learning · Computer Science 2026-05-11 Yixin Chen , Alan Kuhnle

We consider parallel, or low adaptivity, algorithms for submodular function maximization. This line of work was recently initiated by Balkanski and Singer and has already led to several interesting results on the cardinality constraint and…

Data Structures and Algorithms · Computer Science 2018-12-03 Chandra Chekuri , Kent Quanrud

Submodular maximization has been widely studied over the past decades, mostly because of its numerous applications in real-world problems. It is well known that the standard greedy algorithm guarantees a worst-case approximation factor of…

Data Structures and Algorithms · Computer Science 2020-02-12 Alfredo Torrico , Mohit Singh , Sebastian Pokutta

We consider classes of objective functions of cardinality constrained maximization problems for which the greedy algorithm guarantees a constant approximation. We propose the new class of $\gamma$-$\alpha$-augmentable functions and prove…

Discrete Mathematics · Computer Science 2022-10-05 Yann Disser , David Weckbecker

This work provides performance guarantees for the greedy solution of experimental design problems. In particular, it focuses on A- and E-optimal designs, for which typical guarantees do not apply since the mean-square error and the maximum…

Machine Learning · Computer Science 2018-02-01 Luiz F. O. Chamon , Alejandro Ribeiro

In this note we study the greedy algorithm for combinatorial auctions with submodular bidders. It is well known that this algorithm provides an approximation ratio of $2$ for every order of the items. We show that if the valuations are…

Computer Science and Game Theory · Computer Science 2015-02-10 Shahar Dobzinski , Ami Mor

Bayesian Reinforcement Learning (RL) is capable of not only incorporating domain knowledge, but also solving the exploration-exploitation dilemma in a natural way. As Bayesian RL is intractable except for special cases, previous work has…

Artificial Intelligence · Computer Science 2013-06-14 Kenji Kawaguchi , Mauricio Araya

We study the problem of causal structure learning when the experimenter is limited to perform at most $k$ non-adaptive experiments of size $1$. We formulate the problem of finding the best intervention target set as an optimization problem,…

Machine Learning · Computer Science 2018-08-03 AmirEmad Ghassami , Saber Salehkaleybar , Negar Kiyavash , Elias Bareinboim

The paper gives a systematic study of the approximate versions of three greedy-type algorithms that are widely used in convex optimization. By approximate version we mean the one where some of evaluations are made with an error. Importance…

Machine Learning · Statistics 2014-12-11 Vladimir Temlyakov

This paper proposes a greedy algorithm named as Big step greedy set cover algorithm to compute approximate minimum set cover. The Big step greedy algorithm, in each step selects p sets such that the union of selected p sets contains…

Data Structures and Algorithms · Computer Science 2015-06-16 Drona Pratap Chandu

We provide new approximation guarantees for greedy low rank matrix estimation under standard assumptions of restricted strong convexity and smoothness. Our novel analysis also uncovers previously unknown connections between the low rank…

Machine Learning · Statistics 2017-03-09 Rajiv Khanna , Ethan Elenberg , Alexandros G. Dimakis , Sahand Negahban

We consider the problem of stochastic monotone submodular function maximization, subject to constraints. We give results on adaptivity gaps, and on the gap between the optimal offline and online solutions. We present a procedure that…

Data Structures and Algorithms · Computer Science 2015-04-28 Lisa Hellerstein , Devorah Kletenik , Patrick Lin

Adaptive sequential decision making is one of the central challenges in machine learning and artificial intelligence. In such problems, the goal is to design an interactive policy that plans for an action to take, from a finite set of $n$…

Machine Learning · Computer Science 2020-07-28 Hossein Esfandiari , Amin Karbasi , Vahab Mirrokni

We consider the optimisation problem of adding $k$ links to a given network, such that the resulting effective graph resistance is as small as possible. The problem was recently proven to be NP-hard, such that optimal solutions obtained…

Data Structures and Algorithms · Computer Science 2025-01-08 Massimo A. Achterberg , Robert E. Kooij

We demonstrate that from an algorithm guaranteeing an approximation factor for the ratio of submodular (RS) optimization problem, we can build another algorithm having a different kind of approximation guarantee -- weaker than the classical…

Data Structures and Algorithms · Computer Science 2022-09-12 Pierre Perrault , Jennifer Healey , Zheng Wen , Michal Valko

In this work, we consider the maximization of submodular functions constrained by independence systems. Because of the wide applicability of submodular functions, this problem has been extensively studied in the literature, on specialized…

Data Structures and Algorithms · Computer Science 2019-06-11 Alan Kuhnle

Greedy-GQ with linear function approximation, originally proposed in \cite{maei2010toward}, is a value-based off-policy algorithm for optimal control in reinforcement learning, and it has a non-linear two timescale structure with the…

Machine Learning · Computer Science 2024-05-03 Yue Wang , Yi Zhou , Shaofeng Zou

The frame algorithm uses a simple recursive formula to approximate an unknown vector from its frame coefficients. This note introduces an adaptive version of the frame algorithm that maximizes the error reduction between steps in terms of…

Functional Analysis · Mathematics 2025-06-24 Brody Dylan Johnson

We study the approximability of the maximum size independent set (MIS) problem in bounded degree graphs. This is one of the most classic and widely studied NP-hard optimization problems. We focus on the well known minimum degree greedy…

Data Structures and Algorithms · Computer Science 2020-02-03 Piotr Krysta , Mathieu Mari , Nan Zhi

We briefly discuss the greedy method and a couple of its more efficient variants for approximately maximizing monotone submodular functions.

Optimization and Control · Mathematics 2025-10-21 Alen Alexanderian