This work examines a distributed learning problem where the agents of a network form their beliefs about certain hypotheses of interest Each agent collects streaming (private) data and updates continually its belief by means of a diffusion strategy, which blends the agent's data with the beliefs of its neighbors We focus on weakly-connected graphs, where the network is partitioned into sending and receiving sub-networks, and we allow for heterogeneous models across the agents First, we examine what agents learn ( social learning ) and provide an analytical characterization for the long-term beliefs at the agents Among other effects, the analysis predicts when a leader-follower behavior is possible, where some sending agents control the beliefs of the receiving agents by forcing them to choose a particular and possibly fake hypothesis Second, we consider the dual or reverse learning problem that reveals how agents learn: given the beliefs collected at a receiving agent, we would like to discover the influence that any sending sub-network might have exerted on this receiving agent ( topology learning ) An unexpected interplay between social and topology learning emerges: given $H$ hypotheses and $S$ sending sub-networks, topology learning can be feasible when $H\geq S$  The latter being only a necessary condition, we then examine the feasibility of topology learning for two useful classes of problems The analysis reveals that a critical element to enable topology learning is a sufficient degree of diversity in the statistical models of the sending sub-networks

/pdf/interplay-between-topology-and-social-learning-over-weak-22ub0lyowt.pdf

Interplay Between Topology and Social Learning Over Weak Graphs

We consider a social learning problem, where a network of agents is interested in selecting one among a finite number of hypotheses. We focus on weakly-connected graphs where the network is partitioned into a sending part and a receiving part. The data collected by the agents might be heterogeneous. For example, some sub-networks might intentionally generate data from a fake hypothesis in order to influence other agents. The social learning task is accomplished via a diffusion strategy where each agent: i) updates individually its belief using its private data; ii) computes a new belief by exponentiating a linear combination of the log-beliefs of its neighbors. First, we examine what agents learn over weak graphs (social learning problem). We obtain analytical formulas for the beliefs at the different agents, which reveal how the agents' detection capability and the network topology interact to influence the beliefs. In particular, the formulas allow us to predict when a leader-follower behavior is possible, where some sending agents can control the mind of the receiving agents by forcing them to choose a particular hypothesis. Second, we consider the dual or reverse learning problem that reveals how agents learned: given a stream of beliefs collected at a receiving agent, we would like to discover the global influence that any sending component exerts on this receiving agent (topology learning problem). A remarkable and perhaps unexpected interplay between social and topology learning is observed: given $H$ hypotheses and $S$ sending components, topology learning can be feasible when $H\geq S$. The latter being only a necessary condition, we examine the feasibility of topology learning for two useful classes of problems. The analysis reveals that a critical element to enable faithful topology learning is the diversity in the statistical models of the sending sub-networks.

Interplay between Topology and Social Learning over Weak Graphs.

In this paper a generalized tuning methodology for proportional-integral-derivative (PID) controllers is proposed. The methodology is akin to the Ziegler-Nichols forced oscillation method, inheriting fully its practical appeal, but can be applied to much more general classes of plants. This generalization is achieved by employing a relay with adjustable phase (RAP) in a relay feedback experiment, and the tuning consists of formulas based on measurements obtained from this experiment. Experimental results in a liquid processing plant with of-the-shelf industrial equipments illustrate the performance of the methodology and the practical procedures involved in its application, which can be fully automated.

The generalized forced oscillation method for tuning PID controllers.

This work proposes a novel strategy for social learning by introducing the critical feature of adaptation . In social learning, several distributed agents update continually their belief about a phenomenon of interest through: $i$ ) direct observation of streaming data that they gather locally ; and $ii$ ) diffusion of their beliefs through local cooperation with their neighbors. Traditional social learning implementations are known to learn well the underlying hypothesis (which means that the belief of every individual agent peaks at the true hypothesis), achieving steady improvement in the learning accuracy under stationary conditions. However, these algorithms do not perform well under nonstationary conditions commonly encountered in online learning, exhibiting a significant inertia to track drifts in the streaming data. In order to address this gap, we propose an Adaptive Social Learning (ASL) strategy, which relies on a small step-size parameter to tune the adaptation degree. First, we provide a detailed characterization of the learning performance by means of a steady-state analysis. Focusing on the small step-size regime, we establish that the ASL strategy achieves consistent learning under standard global identifiability assumptions. We derive reliable Gaussian approximations for the probability of error (i.e., of choosing a wrong hypothesis) at each individual agent. We carry out a large deviations analysis revealing the universal behavior of adaptive social learning: the error probabilities decrease exponentially fast with the inverse of the step-size, and we characterize the resulting exponential learning rate. Second, we characterize the adaptation performance by means of a detailed transient analysis, which allows us to obtain useful analytical formulas relating the adaptation time to the step-size. The revealed dependence of the adaptation time and the error probabilities on the step-size highlights the fundamental trade-off between adaptation and learning emerging in adaptive social learning.

/pdf/adaptive-social-learning-2xvgni2j2u.pdf

Adaptive Social Learning

In order to achieve stable and dexterous grasping of objects, prehension force control is quite a significant parameter for prosthetic hands. Commercially available hands such as bebionic, i-limb quantum and Michelangelo offer the precise grasping capability to perform activities of daily living (ADLs). However, the cost of such hands is too expensive for amputees residing in low-income countries. This paper introduces a low-cost, simple and efficient system for controlling the prehension force of a self-designed myoelectric prosthetic hand. A hand prototype was developed employing 3D printing technology and an intrinsic actuation approach. The hand fingers were equipped with a pre-calibrated force sensor for the online estimation of the grasp force. A closed-loop proportional-derivative (PD) based position control system was designed considering actuator as plant, electromyography (EMG) as a reference and grasp force as a feedback signal. The results showed highly improved parameters, i.e. overshoot, offset and settling time of the proposed system than a simple open-loop system. These parameters guarantee faster closing of hand fingers and the production of accurate prehension force during finger-object interaction. Further, the myoelectric hand with a developed control scheme was successfully tested on five different transradial amputees for performing precise and faster grasping of different shaped objects.

A low-cost system to control prehension force of a custom-made myoelectric hand prosthesis

This work studies the learning abilities of agents sharing partial beliefs over social networks. The agents observe data that could have risen from one of several hypotheses and interact locally to decide whether the observations they are receiving have risen from a particular hypothesis of interest. To do so, we establish the conditions under which it is sufficient to share partial information about the agents’ belief in relation to the hypothesis of interest. Some interesting convergence regimes arise.

Social Learning with Partial Information Sharing

This work addresses the problem of sharing partial information within social learning strategies. In traditional social learning, agents solve a distributed multiple hypothesis testing problem by performing two operations at each instant: first, agents incorporate information from private observations to form their beliefs over a set of hypotheses; second, agents combine the entirety of their beliefs locally among neighbors. Within a sufficiently informative environment and as long as the connectivity of the network allows information to diffuse across agents, these algorithms enable agents to learn the true hypothesis. Instead of sharing the entirety of their beliefs, this work considers the case in which agents will only share their beliefs regarding one hypothesis of interest, with the purpose of evaluating its validity, and draws conditions under which this policy does not affect truth learning. We propose two approaches for sharing partial information, depending on whether agents behave in a self-aware manner or not. The results show how different learning regimes arise, depending on the approach employed and on the inherent characteristics of the inference problem. Furthermore, the analysis interestingly points to the possibility of deceiving the network, as long as the evaluated hypothesis of interest is close enough to the truth.

Virginia Bordignon

Papers

Interplay Between Topology and Social Learning Over Weak Graphs

Interplay between Topology and Social Learning over Weak Graphs.

Adaptive Social Learning

Social Learning with Partial Information Sharing

Social Learning with Partial Information Sharing