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In this paper we present global and person-by-person (PbP) optimality conditions for general decentralized stochastic dynamic optimal control problems, using a discrete-time version of Girsanov's change of measure. The PbP optimality…
This paper focuses on multi-block optimization problems over transport polytopes, which underlie various applications including strongly correlated quantum physics and machine learning. Conventional block coordinate descent-type methods for…
In Bayesian inverse problems sampling the posterior distribution is often a challenging task when the underlying models are computationally intensive. To this end, surrogates or reduced models are often used to accelerate the computation.…
Annealing algorithms such as simulated annealing and population annealing are widely used both for sampling the Gibbs distribution and solving optimization problems (i.e. finding ground states). For both statistical mechanics and…
This chapter describes techniques for the numerical resolution of optimal transport problems. We will consider several discretizations of these problems, and we will put a strong focus on the mathematical analysis of the algorithms to solve…
Here and in a follow-on paper, we consider a simple control problem in which the underlying dynamics depend on a parameter $a$ that is unknown and must be learned. In this paper, we assume that $a$ is bounded, i.e., that $|a| \le…
This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…
We study the decentralized consensus and stochastic optimization problems with compressed communications over static directed graphs. We propose an iterative gradient-based algorithm that compresses messages according to a desired…
We propose an {\em implementable} numerical scheme for the discretization of linear-quadratic optimal control problems involving SDEs in higher dimensions with {\em control constraint}. For time discretization, we employ the implicit Euler…
The paper proves convergence to global optima for a class of distributed algorithms for nonconvex optimization in network-based multi-agent settings. Agents are permitted to communicate over a time-varying undirected graph. Each agent is…
Denoising diffusion models have recently emerged as the predominant paradigm for generative modelling on image domains. In addition, their extension to Riemannian manifolds has facilitated a range of applications across the natural…
Classical deterministic optimal control problems assume full information about the controlled process. The theory of control for general partially-observable processes is powerful, but the methods are computationally expensive and typically…
We consider the problem of information embedding where the encoder modifies a white Gaussian host signal in a power-constrained manner to encode a message, and the decoder recovers both the embedded message and the modified host signal.…
This paper develops a method to learn optimal controls from data for bilinear systems without a priori knowledge of the system dynamics. Given an unknown bilinear system, we first characterize when the available data is suitable to solve…
It is known in the context of decentralised control that there exist control strategies consistent with the requirements of a given information structure, yet physically unimplementable through any amount of passive common randomness. This…
This paper considers the problem of determining an optimal control action based on observed data. We formulate the problem assuming that the system can be modelled by a nonlinear state-space model, but where the model parameters, state and…
Diffusion models are vastly used in generative AI, leveraging their capability to capture complex data distributions. However, their potential remains largely unexplored in the field of resource allocation in wireless networks. This paper…
In this paper, we propose a minimax linear-quadratic control method to address the issue of inaccurate distribution information in practical stochastic systems. To construct a control policy that is robust against errors in an empirical…
A method is developed to numerically solve chance constrained optimal control problems. The chance constraints are reformulated as nonlinear constraints that retain the probability properties of the original constraint. The reformulation…
We study the problem of distributed information bottleneck, in which multiple encoders separately compress their observations in a manner such that, collectively, the compressed signals preserve as much information as possible about another…