arXiv subjects

Mikael Skoglund

Publications and source records attributed to Mikael Skoglund.

At least 127 records · Page 7Linked to original sources

arXiv2023

Thompson Sampling Regret Bounds for Contextual Bandits with sub-Gaussian rewards

In this work, we study the performance of the Thompson Sampling algorithm for Contextual Bandit problems based on the framework introduced by Neu et al. and their concept of lifted information ratio. First, we prove a comprehensive bound on the Thompson Sampling expected cumulative regret that depends on the mutual information of the environment parameters and the history. Then, we introduce new bounds on the lifted information ratio that hold for sub-Gaussian rewards, thus generalizing the results from Neu et al. which analysis requires binary rewards. Finally, we provide explicit regret bounds for the special cases of unstructured bounded contextual bandits, structured bounded contextual bandits with Laplace likelihood, structured Bernoulli bandits, and bounded linear contextual bandits.

stat.ML↗

arXiv2023

Pointwise Maximal Leakage on General Alphabets

Pointwise maximal leakage (PML) is an operationally meaningful privacy measure that quantifies the amount of information leaking about a secret $X$ to a single outcome of a related random variable $Y$. In this paper, we extend the notion of PML to random variables on arbitrary probability spaces. We develop two new definitions: First, we extend PML to countably infinite random variables by considering adversaries who aim to guess the value of discrete (finite or countably infinite) functions of $X$. Then, we consider adversaries who construct estimates of $X$ that maximize the expected value of their corresponding gain functions. We use this latter setup to introduce a highly versatile form of PML that captures many scenarios of practical interest whose definition requires no assumptions about the underlying probability spaces.

cs.IT↗

arXiv2023

Bounds for Privacy-Utility Trade-off with Non-zero Leakage

The design of privacy mechanisms for two scenarios is studied where the private data is hidden or observable. In the first scenario, an agent observes useful data $Y$, which is correlated with private data $X$, and wants to disclose the useful information to a user. A privacy mechanism is employed to generate data $U$ that maximizes the revealed information about $Y$ while satisfying a privacy criterion. In the second scenario, the agent has additionally access to the private data. To this end, the Functional Representation Lemma and Strong Functional Representation Lemma are extended relaxing the independence condition and thereby allowing a certain leakage. Lower bounds on privacy-utility trade-off are derived for the second scenario as well as upper bounds for both scenarios. In particular, for the case where no leakage is allowed, our upper and lower bounds improve previous bounds.

cs.IT↗

arXiv2022

On the Privacy-Utility Trade-off With and Without Direct Access to the Private Data

We study an information theoretic privacy mechanism design problem for two scenarios where the private data is either observable or hidden. In each scenario, we first consider bounded mutual information as privacy leakage criterion, then we use two different per-letter privacy constraints. In the first scenario, an agent observes useful data $Y$ that is correlated with private data $X$, and wishes to disclose the useful information to a user. A privacy mechanism is designed to generate disclosed data $U$ which maximizes the revealed information about $Y$ while satisfying a bounded privacy leakage constraint. In the second scenario, the agent has additionally access to the private data. To this end, we first extend the Functional Representation Lemma and Strong Functional Representation Lemma by relaxing the independence condition and thereby allowing a certain leakage to find lower bounds for the second scenario with different privacy leakage constraints. Furthermore, upper and lower bounds are derived in the first scenario considering different privacy constraints. In particular, for the case where no leakage is allowed, our upper and lower bounds improve previous bounds. Moreover, considering bounded mutual information as privacy constraint we show that if the common information and mutual information between $X$ and $Y$ are equal, then the attained upper bound in the second scenario is tight. Finally, the privacy-utility trade-off with prioritized private data is studied where part of $X$, i.e., $X_1$, is more private than the remaining part, i.e., $X_2$, and we provide lower and upper bounds.

cs.IT↗

arXiv2022

Multi-User Privacy Mechanism Design with Non-zero Leakage

A privacy mechanism design problem is studied through the lens of information theory. In this work, an agent observes useful data $Y=(Y_1,...,Y_N)$ that is correlated with private data $X=(X_1,...,X_N)$ which is assumed to be also accessible by the agent. Here, we consider $K$ users where user $i$ demands a sub-vector of $Y$, denoted by $C_{i}$. The agent wishes to disclose $C_{i}$ to user $i$. Since $C_{i}$ is correlated with $X$ it can not be disclosed directly. A privacy mechanism is designed to generate disclosed data $U$ which maximizes a linear combinations of the users utilities while satisfying a bounded privacy constraint in terms of mutual information. In a similar work it has been assumed that $X_i$ is a deterministic function of $Y_i$, however in this work we let $X_i$ and $Y_i$ be arbitrarily correlated. First, an upper bound on the privacy-utility trade-off is obtained by using a specific transformation, Functional Representation Lemma and Strong Functional Representaion Lemma, then we show that the upper bound can be decomposed into $N$ parallel problems. Next, lower bounds on privacy-utility trade-off are derived using Functional Representation Lemma and Strong Functional Representaion Lemma. The upper bound is tight within a constant and the lower bounds assert that the disclosed data is independent of all $\{X_j\}_{i=1}^N$ except one which we allocate the maximum allowed leakage to it. Finally, the obtained bounds are studied in special cases.

cs.IT↗

arXiv2022

Beam Tracking for Dynamic mmWave Channels: A New Training Beam Sequence Design Approach

In this paper, we develop an efficient training beam sequence design approach for millimeter wave MISO tracking systems. We impose a discrete state Markov process assumption on the evolution of the angle of departure and introduce the maximum a posteriori criterion to track it in each beam training period. Since it is infeasible to derive an explicit expression for the resultant tracking error probability, we turn to its upper bound, which possesses a closed-form expression and is therefore leveraged as the objective function to optimize the training beam sequence. Considering the complicated objective function and the unit modulus constraints imposed by analog phase shifters, we resort to the particle swarm algorithm to solve the formulated optimization problem. Numerical results validate the superiority of the proposed training beam sequence design approach.

cs.IT↗

arXiv2022

An Information-Theoretic Analysis of Bayesian Reinforcement Learning

Building on the framework introduced by Xu and Raginksy [1] for supervised learning problems, we study the best achievable performance for model-based Bayesian reinforcement learning problems. With this purpose, we define minimum Bayesian regret (MBR) as the difference between the maximum expected cumulative reward obtainable either by learning from the collected data or by knowing the environment and its dynamics. We specialize this definition to reinforcement learning problems modeled as Markov decision processes (MDPs) whose kernel parameters are unknown to the agent and whose uncertainty is expressed by a prior distribution. One method for deriving upper bounds on the MBR is presented and specific bounds based on the relative entropy and the Wasserstein distance are given. We then focus on two particular cases of MDPs, the multi-armed bandit problem (MAB) and the online optimization with partial feedback problem. For the latter problem, we show that our bounds can recover from below the current information-theoretic bounds by Russo and Van Roy [2].

cs.LG↗

arXiv2022

Goodput Maximization with Quantized Feedback in the Finite Blocklength Regime for Quasi-Static Channels

In this paper, we study a quantized feedback scheme to maximize the goodput of a finite blocklength communication scenario over a quasi-static fading channel. It is assumed that the receiver has perfect channel state information (CSI) and sends back the CSI to the transmitter over a resolution-limited error-free feedback channel. With this partial CSI, the transmitter is supposed to select the optimum transmission rate, such that it maximizes the overall goodput of the communication system. This problem has been studied for the asymptotic blocklength regime, however, no solution has so far been presented for finite blocklength. Here, we study this problem in two cases: with and without constraint on reliability. We first formulate the optimization problems and analytically solve them. Iterative algorithms that successfully exploit the system parameters for both cases are presented. It is shown that although the achievable maximum goodput decreases with shorter blocklengths and higher reliability requirements, significant improvement can be achieved even with coarsely quantized feedback schemes.

cs.IT↗

arXiv2022

Bounds for Privacy-Utility Trade-off with Per-letter Privacy Constraints and Non-zero Leakage

An information theoretic privacy mechanism design problem for two scenarios is studied where the private data is either hidden or observable. In each scenario, privacy leakage constraints are considered using two different measures. In these scenarios the private data is hidden or observable. In the first scenario, an agent observes useful data $Y$ that is correlated with private data $X$, and wishes to disclose the useful information to a user. A privacy mechanism is designed to generate disclosed data $U$ which maximizes the revealed information about $Y$ while satisfying a per-letter privacy constraint. In the second scenario, the agent has additionally access to the private data. First, the Functional Representation Lemma and Strong Functional Representation Lemma are extended by relaxing the independence condition to find a lower bound considering the second scenario. Next, lower bounds as well as upper bounds on privacy-utility trade-off are derived for both scenarios. In particular, for the case where $X$ is deterministic function of $Y$, we show that our upper and lower bounds are asymptotically optimal considering the first scenario.

cs.IT↗

arXiv2022

Privacy signaling games with binary alphabets

In this paper, we consider a privacy signaling game problem for binary alphabets and single-bit transmission where a transmitter has a pair of messages, one of which is a casual message that needs to be conveyed, whereas the other message contains sensitive data and needs to be protected. The receiver wishes to estimate both messages to acquire as much information as possible. For this setup, we study the interactions between the transmitter and the receiver with non-aligned information-theoretic objectives (modeled by mutual information and hamming distance) due to the privacy concerns of the transmitter. We derive conditions under which Nash and/or Stackelberg equilibria exist and identify the optimal responses of the encoder and decoders strategies for each type of game. One particularly surprising result is that when both types of equilibria exist, they admit the same encoding and decoding strategies. We corroborate our analysis with simulation studies.

cs.IT↗

arXiv2022

Tighter expected generalization error bounds via Wasserstein distance

This work presents several expected generalization error bounds based on the Wasserstein distance. More specifically, it introduces full-dataset, single-letter, and random-subset bounds, and their analogues in the randomized subsample setting from Steinke and Zakynthinou [1]. Moreover, when the loss function is bounded and the geometry of the space is ignored by the choice of the metric in the Wasserstein distance, these bounds recover from below (and thus, are tighter than) current bounds based on the relative entropy. In particular, they generate new, non-vacuous bounds based on the relative entropy. Therefore, these results can be seen as a bridge between works that account for the geometry of the hypothesis space and those based on the relative entropy, which is agnostic to such geometry. Furthermore, it is shown how to produce various new bounds based on different information measures (e.g., the lautum information or several $f$-divergences) based on these bounds and how to derive similar bounds with respect to the backward channel using the presented proof techniques.

stat.ML↗

arXiv2022

Asynchronous Parallel Incremental Block-Coordinate Descent for Decentralized Machine Learning

Machine learning (ML) is a key technique for big-data-driven modelling and analysis of massive Internet of Things (IoT) based intelligent and ubiquitous computing. For fast-increasing applications and data amounts, distributed learning is a promising emerging paradigm since it is often impractical or inefficient to share/aggregate data to a centralized location from distinct ones. This paper studies the problem of training an ML model over decentralized systems, where data are distributed over many user devices and the learning algorithm run on-device, with the aim of relaxing the burden at a central entity/server. Although gossip-based approaches have been used for this purpose in different use cases, they suffer from high communication costs, especially when the number of devices is large. To mitigate this, incremental-based methods are proposed. We first introduce incremental block-coordinate descent (I-BCD) for the decentralized ML, which can reduce communication costs at the expense of running time. To accelerate the convergence speed, an asynchronous parallel incremental BCD (API-BCD) method is proposed, where multiple devices/agents are active in an asynchronous fashion. We derive convergence properties for the proposed methods. Simulation results also show that our API-BCD method outperforms state of the art in terms of running time and communication costs.

cs.LG↗

arXiv2022

Continuous-Time Channel Gain Control for Minimum-Information Kalman-Bucy Filtering

We consider the problem of estimating a continuous-time Gauss-Markov source process observed through a vector Gaussian channel with an adjustable channel gain matrix. For a given (generally time-varying) channel gain matrix, we provide formulas to compute (i) the mean-square estimation error attainable by the classical Kalman-Bucy filter, and (ii) the mutual information between the source process and its Kalman-Bucy estimate. We then formulate a novel "optimal channel gain control problem" where the objective is to control the channel gain matrix strategically to minimize the weighted sum of these two performance metrics. To develop insights into the optimal solution, we first consider the problem of controlling a time-varying channel gain over a finite time interval. A necessary optimality condition is derived based on Pontryagin's minimum principle. For a scalar system, we show that the optimal channel gain is a piece-wise constant signal with at most two switches. We also consider the problem of designing the optimal time-invariant gain to minimize the average cost over an infinite time horizon. A novel semidefinite programming (SDP) heuristic is proposed and the exactness of the solution is discussed.

cs.IT↗

arXiv2022

Secure Source Coding with Side-information at Decoder and Shared Key at Encoder and Decoder

We study the problem of rate-distortion-equivocation with side-information only available at the decoder when an independent private random key is shared between the sender and the receiver. The sender compresses the sequence, and the receiver reconstructs it such that the average distortion between the source and the output is limited. The equivocation is measured at an eavesdropper that intercepts the source encoded message, utilizing side-information correlated with the source and the side-information at the decoder. We have derived the entire achievable rate-distortion-equivocation region for this problem.

cs.IT↗

arXiv2021

Federated Learning over Wireless IoT Networks with Optimized Communication and Resources

To leverage massive distributed data and computation resources, machine learning in the network edge is considered to be a promising technique especially for large-scale model training. Federated learning (FL), as a paradigm of collaborative learning techniques, has obtained increasing research attention with the benefits of communication efficiency and improved data privacy. Due to the lossy communication channels and limited communication resources (e.g., bandwidth and power), it is of interest to investigate fast responding and accurate FL schemes over wireless systems. Hence, we investigate the problem of jointly optimized communication efficiency and resources for FL over wireless Internet of things (IoT) networks. To reduce complexity, we divide the overall optimization problem into two sub-problems, i.e., the client scheduling problem and the resource allocation problem. To reduce the communication costs for FL in wireless IoT networks, a new client scheduling policy is proposed by reusing stale local model parameters. To maximize successful information exchange over networks, a Lagrange multiplier method is first leveraged by decoupling variables including power variables, bandwidth variables and transmission indicators. Then a linear-search based power and bandwidth allocation method is developed. Given appropriate hyper-parameters, we show that the proposed communication-efficient federated learning (CEFL) framework converges at a strong linear rate. Through extensive experiments, it is revealed that the proposed CEFL framework substantially boosts both the communication efficiency and learning performance of both training loss and test accuracy for FL over wireless IoT networks compared to a basic FL approach with uniform resource allocation.

cs.LG↗

arXiv2021

Indirect NRDF for Partially Observable Gauss-Markov Processes with MSE Distortion: Complete Characterizations and Optimal Solutions

In this paper we study the problem of characterizing and computing the nonanticipative rate distortion function (NRDF) for partially observable multivariate Gauss-Markov processes with hard mean squared error (MSE) distortion constraints. For the finite time horizon case, we first derive the complete characterization of this problem and its corresponding optimal realization which is shown to be a linear functional of the current time sufficient statistic of the past and current observations signals. We show that when the problem is strictly feasible, it can be computed via semidefinite programming (SDP) algorithm. For time-varying scalar processes with average total MSE distortion we derive an optimal closed form expression by means of a dynamic reverse-waterfilling solution that we also implement via an iterative scheme that convergences linearly in finite time, and a closed-form solution under pointwise MSE distortion constraint. For the infinite time horizon, we give necessary and sufficient conditions to ensure that asymptotically the sufficient statistic process of the observation signals achieves a steady-state solution for the corresponding covariance matrices and impose conditions that allow existence of a time-invariant solution. Then, we show that when a finite solution exists in the asymptotic limit, it can be computed via SDP algorithm. We also give strong structural properties on the characterization of the problem in the asymptotic limit that allow for an optimal solution via a reverse-waterfilling algorithm that we implement via an iterative scheme that converges linearly under a finite number of spatial components. Our results are corroborated with various simulation studies and are also compared with existing results in the literature.

cs.IT↗

arXiv2021

A Multi-Objective Optimization Framework for URLLC with Decoding Complexity Constraints

Stringent constraints on both reliability and latency must be guaranteed in ultra-reliable low-latency communication (URLLC). To fulfill these constraints with computationally constrained receivers, such as low-budget IoT receivers, optimal transmission parameters need to be studied in detail. In this paper, we introduce a multi-objective optimization framework for the optimal design of URLLC in the presence of decoding complexity constraints. We consider transmission of short-blocklength codewords that are encoded with linear block encoders, transmitted over a binary-input AWGN channel, and finally decoded with order-statistics (OS) decoder. We investigate the optimal selection of a transmission rate and power pair, while satisfying the constraints. For this purpose, a multi-objective optimization problem (MOOP) is formulated. Based on the empirical model that accurately quantifies the trade-off between the performance of an OS decoder and its computational complexity, the MOOP is solved and the Pareto boundary is derived. In order to assess the overall performance among several Pareto-optimal transmission pairs, two scalarization methods are investigated. To exemplify the importance of the MOOP, a case study on a battery-powered communication system is provided. It is shown that, compared to the classical fixed rate-power transmissions, the MOOP provides the optimum usage of the battery and increases the energy efficiency of the communication system while maintaining the constraints.

cs.IT↗

arXiv2021

Generalized Talagrand Inequality for Sinkhorn Distance using Entropy Power Inequality

In this paper, we study the connection between entropic optimal transport and entropy power inequality (EPI). First, we prove an HWI-type inequality making use of the infinitesimal displacement convexity of optimal transport map. Second, we derive two Talagrand-type inequalities using the saturation of EPI that corresponds to a numerical term in our expression. We evaluate for a wide variety of distributions this term whereas for Gaussian and i.i.d. Cauchy distributions this term is found in explicit form. We show that our results extend previous results of Gaussian Talagrand inequality for Sinkhorn distance to the strongly log-concave case.

cs.IT↗