相关论文: Is Witsenhausen's counterexample a relevant toy?
A linear stochastic transport equation with non-regular coefficients is considered. Under the same assumption of the deterministic theory, all weak $L^\infty$-solutions are renormalized. But then, if the noise is nondegenerate, uniqueness…
In the recent years self-testing has grown into a rich and active area of study with applications ranging from practical verification of quantum devices to deep complexity theoretic results. Self-testing allows a classical verifier to…
When designing a distributed control system, the system designer has a choice in how to connect the different units through communication channels. In practice, noiseless and noisy channels may coexist. Using the standard toy example of…
This paper revisits a classical scenario in communication theory: a waveform sampled at regular intervals is to be encoded so as to minimize distortion in its reconstruction, despite noise. This transformation must be online (causal), to…
We consider communications through a Gaussian noise channel between an encoder and a decoder which have subjective probabilistic models on the source distribution. Although they consider the same cost function, the induced expected costs…
We consider a Bayesian persuasion problem where the persuader and the decision maker communicate through an imperfect channel that has a fixed and limited number of messages and is subject to exogenous noise. We provide an upper bound on…
It is well known that the extension of Watkins' algorithm to general function approximation settings is challenging: does the projected Bellman equation have a solution? If so, is the solution useful in the sense of generating a good…
A previous paper analyzed in detail the difficulties associated with the application of numerical methods to Hallen's integral equation with the approximate kernel for the case of a lossless surrounding medium. The present paper extends to…
This paper considers the comparison of noisy channels from the viewpoint of statistical decision theory. Various orderings are discussed, all formalizing the idea that one channel is "better" than another for information transmission. The…
In this paper, we identify sufficient conditions under which static teams and a class of sequential dynamic teams admit team-optimal solutions. We first investigate the existence of optimal solutions in static teams where the observations…
Considering what the world would be like if backwards causation were possible is usually mind-bending. Here I discuss something that is easier to study: a toy model that incorporates a very restricted sort of backwards causation. It defines…
In the paper arXiv:1802.03250, a criterion for exponential mixing is established for a class of random dynamical systems. In that paper, the criterion is applied to PDEs perturbed by a noise localised in the Fourier space. In the present…
The linear quadratic Gaussian (LQG) control problem for the linear wave equation on the unit circle with fully distributed actuation and partial state measurements is considered. An analytical solution to a spatial discretization of the…
Consider the regression problem where the response $Y\in\mathbb{R}$ and the covariate $X\in\mathbb{R}^d$ for $d\geq 1$ are \textit{unmatched}. Under this scenario, we do not have access to pairs of observations from the distribution of $(X,…
A new paradigm is proposed for the robustification of the LQG controller against distributional uncertainties on the noise process. Our controller optimizes the closed-loop performances in the worst possible scenario under the constraint…
We study multitask learning for stochastic and partially observed control systems, focusing on the linear quadratic Gaussian (LQG) problem. Our goal is to learn a common stabilizing controller that generalizes across a distribution of…
A local, deterministic toy model for quantum mechanics is introduced and discussed. It is demonstrated that, when averaged over the hidden variables, the model produces the same predictions as quantum mechanics. In the model considered…
We pursue the investigations initiated in [Aur{\'e}lien Deya: A non-linear wave equation with fractional perturbation (2017)] about a wave-equation model with quadratic perturbation and stochastic forcing given by a space-time fractional…
Motivated by recent experiments with Josephson-junction circuits we reconsider decoherence effects in quantum two-level systems (TLS). On one hand, the experiments demonstrate the importance of 1/f noise, on the other hand, by operating at…
It is currently unknown whether the laws of physics permit time travel into the past. While general relativity indicates the theoretical possibility of causality violation, it is now widely accepted that a theory of quantum gravity must…