5 papers
Regret Lower Bound for Online Learning of Quantum States with Logarithmic Loss, with Applications to Quantum State Tomography and Confidence Sequences for Matrix Means
Yen-Huan Li, Wei-Fu Tseng
We study the problem of online learning of quantum states with logarithmic loss, which is a quantum generalization of online portfolio selection and has applications to quantum sta…
Multiplicative Gradient Method for Log-Homogeneous Optimization: A Unified Mirror-Descent Framework
Chun-Neng Chu, Yen-Huan Li
Consider the problems of computing -Lewis weights, Kelly portfolios, D-optimal designs, general equilibria in Fisher markets, and optimal error exponents for channel coding…
Algorithms for Computing the Petz-Augustin Capacity
Chun-Neng Chu, Wei-Fu Tseng, Yen-Huan Li
We propose the first algorithms with non-asymptotic convergence guarantees for computing the Petz-Augustin capacity, which generalizes the channel capacity and characterizes the op…
A Linearly Convergent Algorithm for Petz-Augustin Means with Applications to Computing Petz-Augustin Capacity and Equilibrium Prices in Fisher Markets
Chun-Neng Chu, Wei-Fu Tseng, Yen-Huan Li
We study the computation of the Petz-Augustin mean of order , defined as the minimizer of a weighted sum of Petz-Rényi divergences of order over…
Online Learning Quantum States with the Logarithmic Loss via VB-FTRL
Wei-Fu Tseng, Kai-Chun Chen, Zi-Hong Xiao +1
Online learning of quantum states with the logarithmic loss (LL-OLQS) is a quantum generalization of online portfolio selection (OPS), a classic open problem in online learning for…