a b s t r a c tAdding noise to inputs of some suboptimal detectors or estimators can improve their performance under certain conditions. In the literature, noise benefits have been studied for detection and estimation systems separately. In this study, noise benefits are investigated for joint detection and estimation systems. The analysis is performed under the Neyman-Pearson (NP) and Bayesian detection frameworks and according to the Bayesian estimation criterion. The maximization of the system performance is formulated as an optimization problem. The optimal additive noise is shown to have a specific form, which is derived under both NP and Bayesian detection frameworks. In addition, the proposed optimization problem is approximated as a linear programming (LP) problem, and conditions under which the performance of the system can or cannot be improved via additive noise are obtained. With an illustrative numerical example, performance comparison between the noise enhanced system and the original system is presented to support the theoretical analysis.
We study a model where a data collector obtains data from users through a payment mechanism, aiming to learn the underlying state from the elicited data. The private signal of each user represents her knowledge about the state; and through social interactions each user can also learn noisy versions of her social friends' signals, which is called 'learned group signals'. Thanks to social learning, users have richer information about the state beyond their private signals. Based on both her private signal and learned group signals, each user makes strategic decisions to report a privacy-preserved version of her data to the data collector. We develop a Bayesian game theoretic framework to study the impact of social learning on users' data reporting strategies and devise the payment mechanism for the data collector accordingly. Our findings reveal that, in general, the desired data reporting strategy at the Bayesian-Nash equilibrium can be in the form of either a symmetric randomized response (SR) strategy or an informative non-disclosive (ND) strategy. Specifically, a generalized majority voting rule is applied by each user to her noisy group signals to determine which strategy to follow. Further, when a user plays the ND strategy, she reports privacy-preserving data completely based on her group signals, independent of her private signal, which indicates that her privacy cost is zero. We emphasize that the reported data when a user plays the ND strategy is still informative about the underlying state because it is based on her learned group signals. As a result, both the data collector and the users can benefit from social learning which drives down the privacy costs and helps to improve the state estimation at a given payment budget. We further derive bounds on the minimum total payment required to achieve a given level of state estimation accuracy.
We consider a distributed learning setting where strategic users are incentivized by a fusion center, to train a learning model based on local data. The users are not obliged to provide their true gradient updates and the fusion center is not capable of validating the authenticity of reported updates. Thus motivated, we formulate the interactions between the fusion center and the users as repeated games, manifesting an under-explored interplay between machine learning and game theory. We then develop an incentive mechanism for the fusion center based on a joint gradient estimation and user action classification scheme, and study its impact on the convergence performance of distributed learning. Further, we devise adaptive zero-determinant (ZD) strategies, thereby generalizing the classical ZD strategies to the repeated games with time-varying stochastic errors. Theoretical and empirical analysis show that the fusion center can incentivize the strategic users to cooperate and report informative gradient updates, thus ensuring the convergence.
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