Related papers: Optimal measures and Markov transition kernels
In this paper the turnpike property is established for a non-convex optimal control problem in discrete time. The functional is defined by the notion of the ideal convergence and can be considered as an analogue of the terminal functional…
Quantum information processing is limited, in practice, to efficiently implementable operations. This motivates the study of quantum divergences that preserve their operational meaning while faithfully capturing these computational…
This paper provides a unifying view of optimal kernel hypothesis testing across the MMD two-sample, HSIC independence, and KSD goodness-of-fit frameworks. Minimax optimal separation rates in the kernel and $L^2$ metrics are presented, with…
An optimal transport problem on finite spaces is a linear program. Recently, a relaxation of the optimal transport problem via strictly convex functions, especially via the Kullback--Leibler divergence, sheds new light on data sciences.…
The ergodic decomposition theorem is a cornerstone result of dynamical systems and ergodic theory. It states that every invariant measure on a dynamical system is a mixture of ergodic ones. Here we formulate and prove the theorem in terms…
Predicting the outcomes of quantum measurements is a cornerstone of quantum information theory and a key resource for quantum technologies. Here, we introduce a comprehensive framework for quantifying the predictability of measurements on a…
There are many applications that benefit from computing the exact divergence between 2 discrete probability measures, including machine learning. Unfortunately, in the absence of any assumptions on the structure or independencies within…
We consider a finite-state, continuous-time Markov process, represented in the "linear framework" by a directed graph with labelled edges which specifies the infinitesimal generator of the process. If the graph is strongly connected, the…
Many problems in machine learning can be formulated as optimizing a convex functional over a vector space of measures. This paper studies the convergence of the mirror descent algorithm in this infinite-dimensional setting. Defining Bregman…
Optimal designs minimize the number of experimental runs (samples) needed to accurately estimate model parameters, resulting in algorithms that, for instance, efficiently minimize parameter estimate variance. Governed by knowledge of past…
An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…
This paper describes the structure of optimal policies for infinite-state Markov Decision Processes with setwise continuous transition probabilities. The action sets may be noncompact. The objective criteria are either the expected total…
Under general multivariate regular variation conditions, the extreme Value-at-Risk of a portfolio can be expressed as an integral of a known kernel with respect to a generally unknown spectral measure supported on the unit simplex. The…
This article considers the average optimality for a continuous-time Markov decision process with Borel state and action spaces and an arbitrarily unbounded nonnegative cost rate. The existence of a deterministic stationary optimal policy is…
This paper deals with maximization of classical $f$-divergence between the distributions of a measurement outputs of a given pair of quantum states. $f$-divergence $D_{f}$ between the probability density functions $p_{1}$ and $p_{2}$ over a…
Decision-making under uncertainty is a critical aspect of many practical autonomous systems due to incomplete information. Partially Observable Markov Decision Processes (POMDPs) offer a mathematically principled framework for formulating…
This paper describes sufficient conditions for the existence of optimal policies for Partially Observable Markov Decision Processes (POMDPs) with Borel state, observation, and action sets and with the expected total costs. Action sets may…
This article introduces a framework for evaluating statistical decisions under both prior ambiguity and likelihood misspecification. We begin with an ambiguity set - a frequentist model that pairs a possibly misspecified likelihood with…
A key concept of quantum information theory is that accessing information encoded in a quantum system requires us to discriminate between several possible states the system could be in. A natural generalization of this problem, namely,…
We introduce a method to numerically compute equilibrium measures for problems with attractive-repulsive power law kernels of the form $K(x-y) = \frac{|x-y|^\alpha}{\alpha}-\frac{|x-y|^\beta}{\beta}$ using recursively generated banded and…