arXiv subjects

Vikram Krishnamurthy

Publications and source records attributed to Vikram Krishnamurthy.

At least 91 records · Page 5Linked to original sources

arXiv2020

Identifying Cognitive Radars -- Inverse Reinforcement Learning using Revealed Preferences

We consider an inverse reinforcement learning problem involving us versus an enemy radar equipped with a Bayesian tracker. By observing the emissions of the enemy radar,how can we identify if the radar is cognitive (constrained utility maximizer)? Given the observed sequence of actions taken by the enemy's radar, we consider three problems: (i) Are the enemy radar's actions (waveform choice, beam scheduling) consistent with constrained utility maximization? If so how can we estimate the cognitive radar's utility function that is consistent with its actions. We formulate and solve the problem in terms of the spectra (eigenvalues) of the state and observation noise covariance matrices, and the algebraic Riccati equation. (ii) How to construct a statistical test for detecting a cognitive radar (constrained utility maximization) when we observe the radar's actions in noise or the radar observes our probe signal in noise? We propose a statistical detector with a tight Type-II error bound. (iii) How can we optimally probe (interrogate) the enemy's radar by choosing our state to minimize the Type-II error of detecting if the radar is deploying an economic rational strategy, subject to a constraint on the Type-I detection error? We present a stochastic optimization algorithm to optimize our probe signal. The main analysis framework used in this paper is that of revealed preferences from microeconomics.

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arXiv2020

Policy Gradient using Weak Derivatives for Reinforcement Learning

This paper considers policy search in continuous state-action reinforcement learning problems. Typically, one computes search directions using a classic expression for the policy gradient called the Policy Gradient Theorem, which decomposes the gradient of the value function into two factors: the score function and the Q-function. This paper presents four results:(i) an alternative policy gradient theorem using weak (measure-valued) derivatives instead of score-function is established; (ii) the stochastic gradient estimates thus derived are shown to be unbiased and to yield algorithms that converge almost surely to stationary points of the non-convex value function of the reinforcement learning problem; (iii) the sample complexity of the algorithm is derived and is shown to be $O(1/\sqrt(k))$; (iv) finally, the expected variance of the gradient estimates obtained using weak derivatives is shown to be lower than those obtained using the popular score-function approach. Experiments on OpenAI gym pendulum environment show superior performance of the proposed algorithm.

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arXiv2020

Rationally Inattentive Inverse Reinforcement Learning Explains YouTube Commenting Behavior

We consider a novel application of inverse reinforcement learning with behavioral economics constraints to model, learn and predict the commenting behavior of YouTube viewers. Each group of users is modeled as a rationally inattentive Bayesian agent which solves a contextual bandit problem. Our methodology integrates three key components. First, to identify distinct commenting patterns, we use deep embedded clustering to estimate framing information (essential extrinsic features) that clusters users into distinct groups.Second, we present an inverse reinforcement learning algorithm that uses Bayesian revealed preferences to test for rationality: does there exist a utility function that rationalizes the given data, and if yes, can it be used to predict commenting behavior? Finally, we impose behavioral economics constraints stemming from rational inattention to characterize the attention span of groups of users. The test imposes a R{é}nyi mutual information cost constraint which impacts how the agent can select attention strategies to maximize their expected utility. After a careful analysis of a massive YouTube dataset, our surprising result is that in most YouTube user groups, the commenting behavior is consistent with optimizing a Bayesian utility with rationally inattentive constraints. The paper also highlights how the rational inattention model can accurately predict commenting behavior. The massive YouTube dataset and analysis used in this paper are available on GitHub and completely reproducible.

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arXiv2020

Controlled Sequential Information Fusion with Social Sensors

A sequence of social sensors estimate an unknown parameter (modeled as a state of nature) by performing Bayesian Social Learning, and myopically optimize individual reward functions. The decisions of the social sensors contain quantized information about the underlying state. How should a fusion center dynamically incentivize the social sensors for acquiring information about the underlying state? This paper presents five results. First, sufficient conditions on the model parameters are provided under which the optimal policy for the fusion center has a threshold structure. The optimal policy is determined in closed form, and is such that it switches between two exactly specified incentive policies at the threshold. Second, it is shown that the optimal incentive sequence is a sub-martingale, i.e, the optimal incentives increase on average over time. Third, it is shown that it is possible for the fusion center to learn the true state asymptotically by employing a sub-optimal policy; in other words, controlled information fusion with social sensors can be consistent. Fourth, uniform bounds on the average additional cost incurred by the fusion center for employing a sub-optimal policy are provided. This characterizes the trade-off between the cost of information acquisition and consistency for the fusion center. Finally, when it is sufficient to estimate the state with a degree of confidence, uniform bounds on the budget saved by employing policies that guarantee state estimation in finite time are provided.

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arXiv2020

Adversarial Radar Inference. From Inverse Tracking to Inverse Reinforcement Learning of Cognitive Radar

Cognitive sensing refers to a reconfigurable sensor that dynamically adapts its sensing mechanism by using stochastic control to optimize its sensing resources. For example, cognitive radars are sophisticated dynamical systems; they use stochastic control to sense the environment, learn from it relevant information about the target and background, then adapt the radar sensor to satisfy the needs of their mission. The last two decades have witnessed intense research in cognitive/adaptive radars.This paper discusses addresses the next logical step, namely inverse cognitive sensing. By observing the emissions of a sensor (e.g. radar or in general a controlled stochastic dynamical system) in real time, how can we detect if the sensor is cognitive (rational utility maximizer) and how can we predict its future actions? The scientific challenges involve extending Bayesian filtering, inverse reinforcement learning and stochastic optimization of dynamical systems to a data-driven adversarial setting. Our methodology transcends classical statistical signal processing (sensing and estimation/detection theory) to address the deeper issue of how to infer strategy from sensing. The generative models, adversarial inference algorithms and associated mathematical analysis will lead to advances in understanding how sophisticated adaptive sensors such as cognitive radars operate.

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arXiv2020

Inverse Filtering for Hidden Markov Models with Applications to Counter-Adversarial Autonomous Systems

Bayesian filtering deals with computing the posterior distribution of the state of a stochastic dynamic system given noisy observations. In this paper, motivated by applications in counter-adversarial systems, we consider the following inverse filtering problem: Given a sequence of posterior distributions from a Bayesian filter, what can be inferred about the transition kernel of the state, the observation likelihoods of the sensor and the measured observations? For finite-state Markov chains observed in noise (hidden Markov models), we show that a least-squares fit for estimating the parameters and observations amounts to a combinatorial optimization problem with non-convex objective. Instead, by exploiting the algebraic structure of the corresponding Bayesian filter, we propose an algorithm based on convex optimization for reconstructing the transition kernel, the observation likelihoods and the observations. We discuss and derive conditions for identifiability. As an application of our results, we illustrate the design of counter-adversarial systems: By observing the actions of an autonomous enemy, we estimate the accuracy of its sensors and the observations it has received. The proposed algorithms are evaluated in numerical examples.

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arXiv2019

Convex Stochastic Dominance in Bayesian Localization, Filtering and Controlled Sensing POMDPs

This paper provides conditions on the observation probability distribution in Bayesian localization and optimal filtering so that the conditional mean estimate satisfies convex stochastic dominance. Convex dominance allows us to compare the unconditional mean square error between two optimal Bayesian state estimators over arbitrary time horizons instead of using brute force Monte-Carlo computations. The proof uses two key ideas from microeconomics, namely, integral precision dominance and aggregation of single crossing.The convex dominance result is then used to give sufficient conditions so that the optimal policy of a controlled sensing two-state partially observed Markov decision process (POMDP) is lower bounded by a myopic policy. Numerical examples are presented where the Shannon capacity of the observation distribution using one sensor dominates that of another, and convex dominance holds but Blackwell dominance does not hold. These illustrate the usefulness of the main result in localization, filtering and controlled sensing applications.

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arXiv2019

What Did Your Adversary Believe? Optimal Filtering and Smoothing in Counter-Adversarial Autonomous Systems

We consider fixed-interval smoothing problems for counter-adversarial autonomous systems. An adversary deploys an autonomous filtering and control system that i) measures our current state via a noisy sensor, ii) computes a posterior estimate (belief) and iii) takes an action that we can observe. Based on such observed actions and our knowledge of our state sequence, we aim to estimate the adversary's past and current beliefs -- this forms a foundation for predicting, and counteracting against, future actions. We derive the optimal smoother for the adversary's beliefs (we treat the problem in a Bayesian framework). Moreover, we demonstrate how the smoother can be computed for discrete systems even though the corresponding backward variables do not admit a finite-dimensional characterization. Finally, we illustrate our results in numerical simulations.

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arXiv2019

What Do Your Friends Think? Efficient Polling Methods for Networks Using Friendship Paradox

This paper deals with randomized polling of a social network. In the case of forecasting the outcome of an election between two candidates A and B, classical intent polling asks randomly sampled individuals: who will you vote for? Expectation polling asks: who do you think will win? In this paper, we propose a novel neighborhood expectation polling (NEP) strategy that asks randomly sampled individuals: what is your estimate of the fraction of votes for A? Therefore, in NEP, sampled individuals will naturally look at their neighbors (defined by the underlying social network graph) when answering this question. Hence, the mean squared error (MSE) of NEP methods rely on selecting the optimal set of samples from the network. To this end, we propose three NEP algorithms for the following cases: (i) the social network graph is not known but, random walks (sequential exploration) can be performed on the graph (ii) the social network graph is unknown. For case (i) and (ii), two algorithms based on a graph theoretic consequence called friendship paradox are proposed. Theoretical results on the dependence of the MSE of the algorithms on the properties of the network are established. Numerical results on real and synthetic data sets are provided to illustrate the performance of the algorithms.

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arXiv2019

How to Calibrate your Adversary's Capabilities? Inverse Filtering for Counter-Autonomous Systems

We consider an adversarial Bayesian signal processing problem involving "us" and an "adversary". The adversary observes our state in noise; updates its posterior distribution of the state and then chooses an action based on this posterior. Given knowledge of "our" state and sequence of adversary's actions observed in noise, we consider three problems: (i) How can the adversary's posterior distribution be estimated? Estimating the posterior is an inverse filtering problem involving a random measure - we formulate and solve several versions of this problem in a Bayesian setting. (ii) How can the adversary's observation likelihood be estimated? This tells us how accurate the adversary's sensors are. We compute the maximum likelihood estimator for the adversary's observation likelihood given our measurements of the adversary's actions where the adversary's actions are in response to estimating our state. (iii) How can the state be chosen by us to minimize the covariance of the estimate of the adversary's observation likelihood? "Our" state can be viewed as a probe signal which causes the adversary to act; so choosing the optimal state sequence is an input design problem. The above questions are motivated by the design of counter-autonomous systems: given measurements of the actions of a sophisticated autonomous adversary, how can our counter-autonomous system estimate the underlying belief of the adversary, predict future actions and therefore guard against these actions.

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arXiv2019

Friendship Paradox Biases Perceptions in Directed Networks

How popular a topic or an opinion appears to be in a network can be very different from its actual popularity. For example, in an online network of a social media platform, the number of people who mention a topic in their posts---i.e., its global popularity---can be dramatically different from how people see it in their social feeds---i.e., its perceived popularity---where the feeds aggregate their friends' posts. We trace the origin of this discrepancy to the friendship paradox in directed networks, which states that people are less popular than their friends (or followers) are, on average. We identify conditions on network structure that give rise to this perception bias, and validate the findings empirically using data from Twitter. Within messages posted by Twitter users in our sample, we identify topics that appear more frequently within the users' social feeds, than they do globally, i.e., among all posts. In addition, we present a polling algorithm that leverages the friendship paradox to obtain a statistically efficient estimate of a topic's global prevalence from biased perceptions of individuals. We characterize the bias of the polling estimate, provide an upper bound for its variance, and validate the algorithm's efficiency through synthetic polling experiments on our Twitter data. Our paper elucidates the non-intuitive ways in which the structure of directed networks can distort social perceptions and resulting behaviors.

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arXiv2018

Estimating Rationally Inattentive Utility Functions with Deep Clustering for Framing - Applications in YouTube Engagement Dynamics

We consider a framework involving behavioral economics and machine learning. Rationally inattentive Bayesian agents make decisions based on their posterior distribution, utility function and information acquisition cost Renyi divergence which generalizes Shannon mutual information). By observing these decisions, how can an observer estimate the utility function and information acquisition cost? Using deep learning, we estimate framing information (essential extrinsic features) that determines the agent's attention strategy. Then we present a preference based inverse reinforcement learning algorithm to test for rational inattention: is the agent an utility maximizer, attention maximizer, and does an information cost function exist that rationalizes the data? The test imposes a Renyi mutual information constraint which impacts how the agent can select attention strategies to maximize their expected utility. The test provides constructive estimates of the utility function and information acquisition cost of the agent. We illustrate these methods on a massive YouTube dataset for characterizing the commenting behavior of users.

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arXiv2018

Real-Time Reinforcement Learning of Constrained Markov Decision Processes with Weak Derivatives

We present on-line policy gradient algorithms for computing the locally optimal policy of a constrained, average cost, finite state Markov Decision Process. The stochastic approximation algorithms require estimation of the gradient of the cost function with respect to the parameter that characterizes the randomized policy. We propose a spherical coordinate parametrization and present a novel simulation based gradient estimation scheme involving weak derivatives (measure-valued differentiation). Such methods have substantially reduced variance compared to the widely used score function method. Similar to neuro-dynamic programming algorithms (e.g. Q-learning or Temporal Difference methods), the algorithms proposed in this paper are simulation based and do not require explicit knowledge of the underlying parameters such as transition probabilities. However, unlike neuro-dynamic programming methods, the algorithms proposed here can handle constraints and time varying parameters. Numerical examples are given to illustrate the performance of the algorithms. This paper was originally written in 2004. One reason we are putting this on arxiv now is that the score function gradient estimator continues to be used in the online reinforcement learning literature even though its variance grows as $O(n)$ given $n$ data points (for a Markov process). In comparison the weak derivative estimator has significantly smaller variance of $O(1)$ as reported in this paper (and elsewhere).

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arXiv2018

Information Diffusion in Social Networks: Friendship Paradox based Models and Statistical Inference

Dynamic models and statistical inference for the diffusion of information in social networks is an area which has witnessed remarkable progress in the last decade due to the proliferation of social networks. Modeling and inference of diffusion of information has applications in targeted advertising and marketing, forecasting elections, predicting investor sentiment and identifying epidemic outbreaks. This chapter discusses three important aspects related to information diffusion in social networks: (i) How does observation bias named friendship paradox (a graph theoretic consequence) and monophilic contagion (influence of friends of friends) affect information diffusion dynamics. (ii) How can social networks adapt their structural connectivity depending on the state of information diffusion. (iii) How one can estimate the state of the network induced by information diffusion. The motivation for all three topics considered in this chapter stems from recent findings in network science and social sensing. Further, several directions for future research that arise from these topics are also discussed.

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arXiv2018

New Sufficient Conditions for Lower Bounding the Optimal Policy of a POMDP using Lehmann Precision

This paper provides new sufficient conditions so that the optimal policy of a partially observed Markov decision process (POMDP) can be lower bounded by a myopic policy. The two new proposed conditions, namely, Lehmann precision and copositive dominance, completely fix the problems with two crucial assumptions in the well known papers of Lovejoy 1987 and Rieder 1991. For controlled sensing POMDPs, Lehmann precision exploits both convexity and monotonicity of the value function, whereas the classical Blackwell dominance only exploits convexity. Numerical examples are presented where Lehmann precision holds but Blackwell dominance does not hold, thereby illustrating the usefulness of the main result in controlled sensing applications.

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arXiv2018

Contagions in Social Networks: Effects of Monophilic Contagion, Friendship Paradox and Reactive Networks

We consider SIS contagion processes over networks where, a classical assumption is that individuals' decisions to adopt a contagion are based on their immediate neighbors. However, recent literature shows that some attributes are more correlated between two-hop neighbors, a concept referred to as monophily. This motivates us to explore monophilic contagion, the case where a contagion (e.g. a product, disease) is adopted by considering two-hop neighbors instead of immediate neighbors (e.g. you ask your friend about the new iPhone and she recommends you the opinion of one of her friends). We show that the phenomenon called friendship paradox makes it easier for the monophilic contagion to spread widely. We also consider the case where the underlying network stochastically evolves in response to the state of the contagion (e.g. depending on the severity of a flu virus, people restrict their interactions with others to avoid getting infected) and show that the dynamics of such a process can be approximated by a differential equation whose trajectory satisfies an algebraic constraint restricting it to a manifold. Our results shed light on how graph theoretic consequences affect contagions and, provide simple deterministic models to approximate the collective dynamics of contagions over stochastic graph processes.

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arXiv2018

Adaptive Polling in Hierarchical Social Networks using Blackwell Dominance

Consider a population of individuals that observe an underlying state of nature that evolves over time. The population is classified into different levels depending on the hierarchical influence that dictates how the individuals at each level form an opinion on the state. The population is sampled sequentially by a pollster and the nodes (or individuals) respond to the questions asked by the pollster. This paper considers the following problem: How should the pollster poll the hierarchical social network to estimate the state while minimizing the polling cost (measurement cost and uncertainty in the Bayesian state estimate)? This paper proposes adaptive versions of the following polling methods: Intent Polling, Expectation Polling, and the recently proposed Neighbourhood Expectation Polling to account for the time varying state of nature and the hierarchical influence in social networks. The adaptive polling problem in a hierarchical social network is formulated as a partially observed Markov decision process (POMDP). Our main results exploit the structure of the polling problem, and determine novel conditions for Blackwell dominance to construct myopic policies that provably upper bound the optimal policy of the adaptive polling POMDP. The LeCam deficiency is used to determine approximate Blackwell dominance for general polling problems. These Blackwell dominance conditions also facilitate the comparison of Renyi Divergence and Shannon capacity of more general channel structures that arise in hierarchical social networks. Numerical examples are provided to illustrate the adaptive polling policies with parameters estimated from YouTube data.

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arXiv2018

Dynamics of Information Diffusion and Social Sensing

Statistical inference using social sensors is an area that has witnessed remarkable progress and is relevant in applications including localizing events for targeted advertising, marketing, localization of natural disasters and predicting sentiment of investors in financial markets. This chapter presents a tutorial description of four important aspects of sensing-based information diffusion in social networks from a communications/signal processing perspective. First, diffusion models for information exchange in large scale social networks together with social sensing via social media networks such as Twitter is considered. Second, Bayesian social learning models and risk averse social learning is considered with applications in finance and online reputation systems. Third, the principle of revealed preferences arising in micro-economics theory is used to parse datasets to determine if social sensors are utility maximizers and then determine their utility functions. Finally, the interaction of social sensors with YouTube channel owners is studied using time series analysis methods. All four topics are explained in the context of actual experimental datasets from health networks, social media and psychological experiments. Also, algorithms are given that exploit the above models to infer underlying events based on social sensing. The overview, insights, models and algorithms presented in this chapter stem from recent developments in network science, economics and signal processing. At a deeper level, this chapter considers mean field dynamics of networks, risk averse Bayesian social learning filtering and quickest change detection, data incest in decision making over a directed acyclic graph of social sensors, inverse optimization problems for utility function estimation (revealed preferences) and statistical modeling of interacting social sensors in YouTube social networks.

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