Near-optimal irrevocable sample selection for periodic data streams with applications to marine robotics

We consider the task of monitoring spatiotemporal phenomena in real-time by deploying limited sampling resources at locations of interest irrevocably and without knowledge of future observations. This task can be modeled as an instance of the classical secretary problem. Although this problem has been studied extensively in theoretical domains, existing algorithms require that data arrive in random order to provide performance guarantees. These algorithms will perform arbitrarily poorly on data streams such as those encountered in robotics and environmental monitoring domains, which tend to have spatiotemporal structure. We focus on the problem of selecting representative samples from phenomena with periodic structure and introduce a novel sample selection algorithm that recovers a near-optimal sample set according to any monotone submodular utility function. We evaluate our algorithm on a seven-year environmental dataset collected at the Martha's Vineyard Coastal Observatory and show that it selects phytoplankton sample locations that are nearly optimal in an information-theoretic sense for predicting phytoplankton concentrations in locations that were not directly sampled. The proposed periodic secretary algorithm can be used with theoretical performance guarantees in many real-time sensing and robotics applications for streaming, irrevocable sample selection from periodic data streams.Comment: 8 pages, accepted for presentation in IEEE Int. Conf. on Robotics and Automation, ICRA '18, Brisbane, Australia, May 201

On Conceptually Simple Algorithms for Variants of Online Bipartite Matching

We present a series of results regarding conceptually simple algorithms for bipartite matching in various online and related models. We first consider a deterministic adversarial model. The best approximation ratio possible for a one-pass deterministic online algorithm is $1/2$, which is achieved by any greedy algorithm. D\"urr et al. recently presented a $2$-pass algorithm called Category-Advice that achieves approximation ratio $3/5$. We extend their algorithm to multiple passes. We prove the exact approximation ratio for the $k$-pass Category-Advice algorithm for all $k \ge 1$, and show that the approximation ratio converges to the inverse of the golden ratio $2/(1+\sqrt{5}) \approx 0.618$ as $k$ goes to infinity. The convergence is extremely fast --- the $5$-pass Category-Advice algorithm is already within $0.01\%$ of the inverse of the golden ratio. We then consider a natural greedy algorithm in the online stochastic IID model---MinDegree. This algorithm is an online version of a well-known and extensively studied offline algorithm MinGreedy. We show that MinDegree cannot achieve an approximation ratio better than $1-1/e$, which is guaranteed by any consistent greedy algorithm in the known IID model. Finally, following the work in Besser and Poloczek, we depart from an adversarial or stochastic ordering and investigate a natural randomized algorithm (MinRanking) in the priority model. Although the priority model allows the algorithm to choose the input ordering in a general but well defined way, this natural algorithm cannot obtain the approximation of the Ranking algorithm in the ROM model

Constrained Non-Monotone Submodular Maximization: Offline and Secretary Algorithms

Constrained submodular maximization problems have long been studied, with near-optimal results known under a variety of constraints when the submodular function is monotone. The case of non-monotone submodular maximization is less understood: the first approximation algorithms even for the unconstrainted setting were given by Feige et al. (FOCS '07). More recently, Lee et al. (STOC '09, APPROX '09) show how to approximately maximize non-monotone submodular functions when the constraints are given by the intersection of p matroid constraints; their algorithm is based on local-search procedures that consider p-swaps, and hence the running time may be n^Omega(p), implying their algorithm is polynomial-time only for constantly many matroids. In this paper, we give algorithms that work for p-independence systems (which generalize constraints given by the intersection of p matroids), where the running time is poly(n,p). Our algorithm essentially reduces the non-monotone maximization problem to multiple runs of the greedy algorithm previously used in the monotone case. Our idea of using existing algorithms for monotone functions to solve the non-monotone case also works for maximizing a submodular function with respect to a knapsack constraint: we get a simple greedy-based constant-factor approximation for this problem. With these simpler algorithms, we are able to adapt our approach to constrained non-monotone submodular maximization to the (online) secretary setting, where elements arrive one at a time in random order, and the algorithm must make irrevocable decisions about whether or not to select each element as it arrives. We give constant approximations in this secretary setting when the algorithm is constrained subject to a uniform matroid or a partition matroid, and give an O(log k) approximation when it is constrained by a general matroid of rank k.Comment: In the Proceedings of WINE 201

Statistical models and decision making for robotic scientific information gathering

Submitted in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering and Computer Science at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 2018.Mobile robots and autonomous sensors have seen increasing use in scientific applications, from planetary rovers surveying for signs of life on Mars, to environmental buoys measuring and logging oceanographic conditions in coastal regions. This thesis makes contributions in both planning algorithms and model design for autonomous scientific information gathering, demonstrating how theory from machine learning, decision theory, theory of optimal experimental design, and statistical inference can be used to develop online algorithms for robotic information gathering that are robust to modeling errors, account for spatiotemporal structure in scientific data, and have probabilistic performance guarantees. This thesis first introduces a novel sample selection algorithm for online, irrevocable sampling in data streams that have spatiotemporal structure, such as those that commonly arise in robotics and environmental monitoring. Given a limited sampling capacity, the proposed periodic secretary algorithm uses an information-theoretic reward function to select samples in real-time that maximally reduce posterior uncertainty in a given scientific model. Additionally, we provide a lower bound on the quality of samples selected by the periodic secretary algorithm by leveraging the submodularity of the information-theoretic reward function. Finally, we demonstrate the robustness of the proposed approach by employing the periodic secretary algorithm to select samples irrevocably from a seven-year oceanographic data stream collected at the Martha’s Vineyard Coastal Observatory off the coast of Cape Cod, USA. Secondly, we consider how scientific models can be specified in environments – such as the deep sea or deep space – where domain scientists may not have enough a priori knowledge to formulate a formal scientific model and hypothesis. These domains require scientific models that start with very little prior information and construct a model of the environment online as observations are gathered. We propose unsupervised machine learning as a technique for science model-learning in these environments. To this end, we introduce a hybrid Bayesian-deep learning model that learns a nonparametric topic model of a visual environment. We use this semantic visual model to identify observations that are poorly explained in the current model, and show experimentally that these highly perplexing observations often correspond to scientifically interesting phenomena. On a marine dataset collected by the SeaBED AUV on the Hannibal Sea Mount, images of high perplexity in the learned model corresponded, for example, to a scientifically novel crab congregation in the deep sea. The approaches presented in this thesis capture the depth and breadth of the problems facing the field of autonomous science. Developing robust autonomous systems that enhance our ability to perform exploratory science in environments such as the oceans, deep space, agricultural and disaster-relief zones will require insight and techniques from classical areas of robotics, such as motion and path planning, mapping, and localization, and from other domains, including machine learning, spatial statistics, optimization, and theory of experimental design. This thesis demonstrates how theory and practice from these diverse disciplines can be unified to address problems in autonomous scientific information gathering

Statistical models and decision making for robotic scientific information gathering

Thesis: S.M., Joint Program in Applied Ocean Physics and Engineering (Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science; and the Woods Hole Oceanographic Institution), 2018.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (pages 97-107).Mobile robots and autonomous sensors have seen increasing use in scientific applications, from planetary rovers surveying for signs of life on Mars, to environmental buoys measuring and logging oceanographic conditions in coastal regions. This thesis makes contributions in both planning algorithms and model design for autonomous scientific information gathering, demonstrating how theory from machine learning, decision theory, theory of optimal experimental design, and statistical inference can be used to develop online algorithms for robotic information gathering that are robust to modeling errors, account for spatiotemporal structure in scientific data, and have probabilistic performance guarantees. This thesis first introduces a novel sample selection algorithm for online, irrevocable sampling in data streams that have spatiotemporal structure, such as those that commonly arise in robotics and environmental monitoring. Given a limited sampling capacity, the proposed periodic secretary algorithm uses an information-theoretic reward function to select samples in real-time that maximally reduce posterior uncertainty in a given scientific model. Additionally, we provide a lower bound on the quality of samples selected by the periodic secretary algorithm by leveraging the submodularity of the information-theoretic reward function. Finally, we demonstrate the robustness of the proposed approach by employing the periodic secretary algorithm to select samples irrevocably from a seven-year oceanographic data stream collected at the Martha's Vineyard Coastal Observatory off the coast of Cape Cod, USA. Secondly, we consider how scientific models can be specified in environments - such as the deep sea or deep space - where domain scientists may not have enough a priori knowledge to formulate a formal scientific model and hypothesis. These domains require scientific models that start with very little prior information and construct a model of the environment online as observations are gathered. We propose unsupervised machine learning as a technique for science model-learning in these environments. To this end, we introduce a hybrid Bayesian-deep learning model that learns a nonparametric topic model of a visual environment. We use this semantic visual model to identify observations that are poorly explained in the current model, and show experimentally that these highly perplexing observations often correspond to scientifically interesting phenomena. On a marine dataset collected by the SeaBED AUV on the Hannibal Sea Mount, images of high perplexity in the learned model corresponded, for example, to a scientifically novel crab congregation in the deep sea. The approaches presented in this thesis capture the depth and breadth of the problems facing the field of autonomous science. Developing robust autonomous systems that enhance our ability to perform exploratory science in environments such as the oceans, deep space, agricultural and disaster-relief zones will require insight and techniques from classical areas of robotics, such as motion and path planning, mapping, and localization, and from other domains, including machine learning, spatial statistics, optimization, and theory of experimental design. This thesis demonstrates how theory and practice from these diverse disciplines can be unified to address problems in autonomous scientific information gathering.by Genevieve Elaine Flaspohler.S.M