10 papers
Generalizing Markowitz Portfolio Optimization by a Quadratic Risk Measure
Ignas Gasparavičius, Andrius Grigutis
We show that the key optimization results of the classical Markowitz portfolio selection theory, originally formulated for variance as the risk measure, remain available in explici…
Self-normalised Bennett inequalities for Hilbert-valued martingales
David Janz
We prove time-uniform self-normalised Bennett inequalities for a martingale in a separable Hilbert space, with and increments bounded in norm by one. Writi…
Variance-sensitive Thompson sampling for generalised linear bandits, revisited
Tom Perneczky, Marc Abeille, David Janz
We prove a variance-sensitive regret bound for Thompson sampling in stochastic generalised linear bandits. The argument assumes a warm-up, after which the regret is controlled thro…
Sharp analysis of linear ensemble sampling
David Janz, Arya Akhavan, Csaba Szepesvári
We analyse linear ensemble sampling (ES) with standard Gaussian perturbations in stochastic linear bandits. We show that for ensemble size , ES attains $\tilde O(d^{3…
Eluder dimension: localise it!
Alireza Bakhtiari, Alex Ayoub, Samuel Robertson +2
We establish a lower bound on the eluder dimension of generalised linear model classes, showing that standard eluder dimension-based analysis cannot lead to first-order regret boun…
High-probability zeroth-order online convex optimisation beyond Euclidean geometry
David Janz, El-Mahdi El-Mhamdi, Arya Akhavan
We study online convex optimisation with -Lipschitz losses, -regularised FTRL, and randomised two-point finite-difference gradient estimators based on cone-measure…
Bernstein-type dimension-free concentration for self-normalised martingales
Arya Akhavan, Amitis Shidani, Alex Ayoub +1
We introduce a dimension-free Bernstein-type tail inequality for self-normalised martingales, where the normalisation uses the predictable quadratic variation and the radius depend…
When and why randomised exploration works (in linear bandits)
Marc Abeille, David Janz, Ciara Pike-Burke
We provide an approach for the analysis of randomised exploration algorithms like Thompson sampling that does not rely on forced optimism or posterior inflation. With this, we demo…
Ensemble sampling for linear bandits: small ensembles suffice
David Janz, Alexander E. Litvak, Csaba Szepesvári
We provide the first useful and rigorous analysis of ensemble sampling for the stochastic linear bandit setting. In particular, we show that, under standard assumptions, for a -…
Exploration via linearly perturbed loss minimisation
David Janz, Shuai Liu, Alex Ayoub +1
We introduce exploration via linear loss perturbations (EVILL), a randomised exploration method for structured stochastic bandit problems that works by solving for the minimiser of…