In this monograph, I introduce the basic concepts of Online Learning through a modern view
of Online Convex Optimization. Here, online learning refers to the framework of regret …

This work introduces the first small-loss and gradual-variation regret bounds for online
portfolio selection, marking the first instances of data-dependent bounds for online convex …

Online portfolio selection has been actively studied to maximise overall returns by selecting
the optimal portfolio weights using online algorithms. However, most work has focused on …

The Blahut-Arimoto algorithm is a well-known method to compute classical channel
capacities and rate-distortion functions. Recent works have extended this algorithm to …

Consider the problem of minimizing an expected logarithmic loss over either the probability
simplex or the set of quantum density matrices. This problem includes tasks such as solving …

We consider the problem of regret minimization in non-parametric stochastic bandits. When
the rewards are known to be bounded from above, there exists asymptotically optimal …

Online learning quantum states with the logarithmic loss (LL-OLQS) is a quantum
generalization of online portfolio selection, a classic open problem in the field of online …

In maximum-likelihood quantum state tomography, both the sample size and dimension
grow exponentially with the number of qubits. It is therefore desirable to develop a stochastic …

This paper introduces a novel family of generalized exponentiated gradient (EG) updates
derived from an Alpha-Beta divergence regularization function. Collectively referred to as …

This dissertation studies\textit {Data-Dependent} regret bounds for two online learning
problems. As opposed to worst-case regret bounds, data-dependent bounds are able to …