Proximal Multitask Learning over Networks with Sparsity-inducing Coregularization

In this work, we consider multitask learning problems where clusters of nodes are interested in estimating their own parameter vector. Cooperation among clusters is beneficial when the optimal models of adjacent clusters have a good number of similar entries. We propose a fully distributed algorithm for solving this problem. The approach relies on minimizing a global mean-square error criterion regularized by non-differentiable terms to promote cooperation among neighboring clusters. A general diffusion forward-backward splitting strategy is introduced. Then, it is specialized to the case of sparsity promoting regularizers. A closed-form expression for the proximal operator of a weighted sum of $\ell_1$-norms is derived to achieve higher efficiency. We also provide conditions on the step-sizes that ensure convergence of the algorithm in the mean and mean-square error sense. Simulations are conducted to illustrate the effectiveness of the strategy

Quantization for decentralized learning under subspace constraints

In this paper, we consider decentralized optimization problems where agents have individual cost functions to minimize subject to subspace constraints that require the minimizers across the network to lie in low-dimensional subspaces. This constrained formulation includes consensus or single-task optimization as special cases, and allows for more general task relatedness models such as multitask smoothness and coupled optimization. In order to cope with communication constraints, we propose and study an adaptive decentralized strategy where the agents employ differential randomized quantizers to compress their estimates before communicating with their neighbors. The analysis shows that, under some general conditions on the quantization noise, and for sufficiently small step-sizes $\mu$, the strategy is stable both in terms of mean-square error and average bit rate: by reducing $\mu$, it is possible to keep the estimation errors small (on the order of $\mu$) without increasing indefinitely the bit rate as $\mu\rightarrow 0$. Simulations illustrate the theoretical findings and the effectiveness of the proposed approach, revealing that decentralized learning is achievable at the expense of only a few bits

Distributed adaptive estimation over multitask networks

L’apprentissage adaptatif distribué sur les réseaux permet à un ensemble d’agents de résoudre des problèmes d’estimation de paramètres en ligne en se basant sur des calculs locaux et sur des échanges locaux avec les voisins immédiats. La littérature sur l’estimation distribuée considère essentiellement les problèmes à simple tâche, où les agents disposant de fonctions objectives séparables doivent converger vers un vecteur de paramètres commun. Cependant, dans de nombreuses applications nécessitant des modèles plus complexes et des algorithmes plus flexibles, les agents ont besoin d’estimer et de suivre plusieurs vecteurs de paramètres simultanément. Nous appelons ce type de réseau, où les agents doivent estimer plusieurs vecteurs de paramètres, réseau multitâche. Bien que les agents puissent avoir différentes tâches à résoudre, ils peuvent capitaliser sur le transfert inductif entre eux afin d’améliorer les performances de leurs estimés. Le but de cette thèse est de proposer et d’étudier de nouveaux algorithmes d’estimation distribuée sur les réseaux multitâches. Dans un premier temps, nous présentons l’algorithme diffusion LMS qui est une stratégie efficace pour résoudre les problèmes d’estimation à simple-tâche et nous étudions théoriquement ses performances lorsqu’il est mis en oeuvre dans un environnement multitâche et que les communications entre les noeuds sont bruitées. Ensuite, nous présentons une stratégie de clustering non-supervisé permettant de regrouper les noeuds réalisant une même tâche en clusters, et de restreindre les échanges d’information aux seuls noeuds d’un même clusterDistributed adaptive learning allows a collection of interconnected agents to perform parameterestimation tasks from streaming data by relying solely on local computations and interactions with immediate neighbors. Most prior literature on distributed inference is concerned with single-task problems, where agents with separable objective functions need to agree on a common parameter vector. However, many network applications require more complex models and flexible algorithms than single-task implementations since their agents involve the need to estimate and track multiple objectives simultaneously. Networks of this kind, where agents need to infer multiple parameter vectors, are referred to as multitask networks. Although agents may generally have distinct though related tasks to perform, they may still be able to capitalize on inductive transfer between them to improve their estimation accuracy. This thesis is intended to bring forth advances on distributed inference over multitask networks. First, we present the well-known diffusion LMS strategies to solve single-task estimation problems and we assess their performance when they are run in multitask environments in the presence of noisy communication links. An improved strategy allowing the agents to adapt their cooperation to neighbors sharing the same objective is presented in order to attain improved learningand estimation over networks. Next, we consider the multitask diffusion LMS strategy which has been proposed to solve multitask estimation problems where the network is decomposed into clusters of agents seeking differen

Estimation distribuée adaptative sur les réseaux multitâches

Distributed adaptive learning allows a collection of interconnected agents to perform parameterestimation tasks from streaming data by relying solely on local computations and interactions with immediate neighbors. Most prior literature on distributed inference is concerned with single-task problems, where agents with separable objective functions need to agree on a common parameter vector. However, many network applications require more complex models and flexible algorithms than single-task implementations since their agents involve the need to estimate and track multiple objectives simultaneously. Networks of this kind, where agents need to infer multiple parameter vectors, are referred to as multitask networks. Although agents may generally have distinct though related tasks to perform, they may still be able to capitalize on inductive transfer between them to improve their estimation accuracy. This thesis is intended to bring forth advances on distributed inference over multitask networks. First, we present the well-known diffusion LMS strategies to solve single-task estimation problems and we assess their performance when they are run in multitask environments in the presence of noisy communication links. An improved strategy allowing the agents to adapt their cooperation to neighbors sharing the same objective is presented in order to attain improved learningand estimation over networks. Next, we consider the multitask diffusion LMS strategy which has been proposed to solve multitask estimation problems where the network is decomposed into clusters of agents seeking differentL’apprentissage adaptatif distribué sur les réseaux permet à un ensemble d’agents de résoudre des problèmes d’estimation de paramètres en ligne en se basant sur des calculs locaux et sur des échanges locaux avec les voisins immédiats. La littérature sur l’estimation distribuée considère essentiellement les problèmes à simple tâche, où les agents disposant de fonctions objectives séparables doivent converger vers un vecteur de paramètres commun. Cependant, dans de nombreuses applications nécessitant des modèles plus complexes et des algorithmes plus flexibles, les agents ont besoin d’estimer et de suivre plusieurs vecteurs de paramètres simultanément. Nous appelons ce type de réseau, où les agents doivent estimer plusieurs vecteurs de paramètres, réseau multitâche. Bien que les agents puissent avoir différentes tâches à résoudre, ils peuvent capitaliser sur le transfert inductif entre eux afin d’améliorer les performances de leurs estimés. Le but de cette thèse est de proposer et d’étudier de nouveaux algorithmes d’estimation distribuée sur les réseaux multitâches. Dans un premier temps, nous présentons l’algorithme diffusion LMS qui est une stratégie efficace pour résoudre les problèmes d’estimation à simple-tâche et nous étudions théoriquement ses performances lorsqu’il est mis en oeuvre dans un environnement multitâche et que les communications entre les noeuds sont bruitées. Ensuite, nous présentons une stratégie de clustering non-supervisé permettant de regrouper les noeuds réalisant une même tâche en clusters, et de restreindre les échanges d’information aux seuls noeuds d’un même cluste

Jungian Metaphor within the Selected Works of H.D., W.B. Yeats, and James Joyce

This thesis will argue for the centrality of Carl Jung’s theory of individuation and alchemy in modernist poetics. Jung’s position in this context is relatively unexamined, and published works often represent misreadings and distortions of Jung’s theory in this field; in particular, Jungian literary criticism’s use of Jung’s theories of the anima, the collective unconscious, alchemy, and individuation. The specific works discussed in this novel context are H.D.’s Trilogy, Yeats’s poems and A Vision, and Joyce’s A Portrait of the Artist as a Young Man, Ulysses, and Finnegans Wake. These works will be read in light of Jung’s central theme of alchemy, which is a metaphor for ‘individuation’, or personal development, a process attained through an ‘alchemical marriage’, or union of antinomial (‘male’ and ‘female’) elements of the psyche. In the works of H.D., Yeats, and Joyce, there are attempts at developing a related alchemical model, a Jungian poetics, which serves to expand a reader’s understanding of modernist uses of language. While critical reading of Jung and his revisionists establishes the ground for this thesis’s discussion of the alchemical theme of transformation, the first chapter considers the personal philosophies of the writers pertinent to this study, surveys modernist poetics, and pays attention to Arthur Rimbaud’s ‘alchemy of the word’. The following chapters observe aspects of a Jungian poetics in each of H.D., Yeats, and Joyce’s works, examining H.D.’s verbal alchemy, Yeats’s visionary alchemy, and Joyce’s textual individuation. First, H.D. is shown to adopt alchemy as a style, through which she aims to recreate a feminine principle and establish a new mythos. The following chapter critically considers a Jungian reading of Yeats’s works in terms of the ‘evocative’ nature of poetry, as a manifestation of creativity, capable of giving the individual access to a collective unconscious. Finally, the fourth chapter continues the examination of the central alchemical theme and writing style in Joyce’s novels, through which he aims to transform both text and protagonist

Adaptation and Learning Over Networks Under Subspace Constraints & x2014;Part II: Performance Analysis

Part & x00A0;I of this paper considered optimization problems over networks where agents have individual objectives to meet, or individual parameter vectors to estimate, subject to subspace constraints that require the objectives across the network to lie in low-dimensional subspaces. Starting from the centralized projected gradient descent, an iterative and distributed solution was proposed that responds to streaming data and employs stochastic approximations in place of actual gradient vectors, which are generally unavailable. We examined the second-order stability of the learning algorithm and we showed that, for small step-sizes , the proposed strategy leads to small estimation errors on the order of . This Part & x00A0;II examines steady-state performance. The results reveal explicitly the influence of the gradient noise, data characteristics, and subspace constraints, on the network performance. The results also show that in the small step-size regime, the iterates generated by the distributed algorithm achieve the centralized steady-state performance

Distributed Inference Over Networks Under Subspace Constraints

This paper considers optimization problems over networks where agents have individual objectives to meet, or individual parameter vectors to estimate, subject to subspace constraints that enforce the objectives across the network to lie in a low-dimensional subspace. This constrained formulation includes consensus optimization as a special case, and allows for more general task relatedness models such as smoothness. While such formulations can be solved via projected gradient descent, the resulting algorithm is not distributed. Motivated by the centralized solution, we propose an iterative and distributed implementation of the projection step, which runs in parallel with the gradient descent update. We establish that, for small step-sizes mu, the proposed distributed adaptive strategy leads to small estimation errors on the order of mu

Adaptation and Learning Over Networks Under Subspace Constraints-Part I: Stability Analysis

This paper considers optimization problems over networks where agents have individual objectives to meet, or individual parameter vectors to estimate, subject to subspace constraints that require the objectives across the network to lie in low-dimensional subspaces. This constrained formulation includes consensus optimization as a special case, and allows for more general task relatedness models such as smoothness. While such formulations can be solved via projected gradient descent, the resulting algorithm is not distributed. Starting from the centralized solution, we propose an iterative and distributed implementation of the projection step, which runs in parallel with the stochastic gradient descent update. We establish in this Part I of the work that, for small step-sizes $\mu$, the proposed distributed adaptive strategy leads to small estimation errors on the order of $\mu$. We examine in the accompanying Part II (R. Nassif, S. Vlaski, and A. H. Sayed, 2019) the steady-state performance. The results will reveal explicitly the influence of the gradient noise, data characteristics, and subspace constraints, on the network performance. The results will also show that in the small step-size regime, the iterates generated by the distributed algorithm achieve the centralized steady-state performance