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New Exploration and Identification schemes for Linear Dynamics: the cases of Convex costs and Censored Data
No full textAdaptive control, i.e., learning to control an unknown linear dynamical system, has a long history in statistics and control theory. However, sharp non-asymptotic bounds were only recently obtained, and are outputs of an ongoing research program aiming to apply tools from learning theory and optimization, to control theory. A common feature of all the major results of the program has been the learning-part of the proposed algorithms, i.e., the exploration strategy. All these algorithms apply the so-called "certainty-equivalence", where the learner spends the first steps applying random controls (e.g. Gaussian noise), then estimates the dynamics via least-squares, and thereafter optimizes the control-policy using these estimates. Even though this is the simplest exploration strategy, it is optimal for the classical linear quadratic regulator (LQR). In this thesis, I study 1) the problem of adaptive control when the cost can be any convex function (thus generalizing LQR), and 2) the problem of learning a linear dynamical system (LDS) from "censored" observations, i.e., the state is observed only when it falls inside some set (e.g., the state can be the position of an object and the set can be the camera-frame). For the first problem, certainty-equivalence is suboptimal. For the second, the least-squares solution is not even consistent. The contribution of the thesis is the development of new computationally and statistically efficient algorithms for both problems. Specifically,
1. For adaptive control with convex costs, we consider the objective of regret with respect to the benchmark of stabilizing linear control policies. Leveraging ideas from convex geometry, we design an exploration strategy that achieves optimal regret, in terms of the dependence on the time-horizon. Our result improves upon the previous best known bounds, which correspond to algorithms applying certainty-equivalence.
2. In the problem of learning an LDS from censored observations, the learner observes the state if and only if belongs to some set . This setting was first considered by Lee and Maddala (1985), and Zeger and Brookmeyer (1986). We develop the first computationally and statistically efficient algorithm for learning the system, assuming only membership-oracle access to the sets (which can be arbitrarily complex sets, e.g., non-convex). Our algorithm, Stochastic Online Newton with Switching Gradients, is a novel second-order method that builds on the Online Newton Step of Hazan et al. (2007)
Learning from Censored and Dependent Data: The case of Linear Dynamics
Get PDFObservations from dynamical systems often exhibit irregularities, such as
censoring, where values are recorded only if they fall within a certain range.
Censoring is ubiquitous in practice, due to saturating sensors,
limit-of-detection effects, and image-frame effects. In light of recent
developments on learning linear dynamical systems (LDSs), and on censored
statistics with independent data, we revisit the decades-old problem of
learning an LDS, from censored observations (Lee and Maddala (1985); Zeger and
Brookmeyer (1986)). Here, the learner observes the state
if and only if belongs to some set . We
develop the first computationally and statistically efficient algorithm for
learning the system, assuming only oracle access to the sets . Our
algorithm, Stochastic Online Newton with Switching Gradients, is a novel
second-order method that builds on the Online Newton Step (ONS) of Hazan et al.
(2007). Our Switching-Gradient scheme does not always use (stochastic)
gradients of the function we want to optimize, which we call "censor-aware"
function. Instead, in each iteration, it performs a simple test to decide
whether to use the censor-aware, or another "censor-oblivious" function, for
getting a stochastic gradient.
In our analysis, we consider a "generic" Online Newton method, which uses
arbitrary vectors instead of gradients, and we prove an error-bound for it.
This can be used to appropriately design these vectors, leading to our
Switching-Gradient scheme. This framework significantly deviates from the
recent long line of works on censored statistics (e.g., Daskalakis et al.
(2018); Kontonis et al. (2019); Daskalakis et al. (2019)), which apply
Stochastic Gradient Descent (SGD), and their analysis reduces to establishing
conditions for off-the-shelf SGD-bounds
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Geometric Exploration for Online Control
No full textWe study the control of an \emph{unknown} linear dynamical system under general convex costs. The objective is minimizing regret vs the class of strongly-stable linear policies. In this work, we first consider the case of known cost functions, for which we design the first polynomial-time algorithm with n 3 √ T -regret, where n is the dimension of the state plus the dimension of control input. The √ T -horizon dependence is optimal, and improves upon the previous best known bound of T 2 / 3 . The main component of our algorithm is a novel geometric exploration strategy: we adaptively construct a sequence of barycentric spanners in an over-parameterized policy space. Second, we consider the case of bandit feedback, for which we give the first polynomial-time algorithm with p o l y ( n ) √ T -regret, building on Stochastic Bandit Convex Optimization
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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