arXiv subjects

Wouter M Koolen

Publications and source records attributed to Wouter M Koolen.

3 recordsLinked to original sources

arXiv2025

Sequential Learning of the Pareto Front for Multi-objective Bandits

We study the problem of sequential learning of the Pareto front in multi-objective multi-armed bandits. An agent is faced with K possible arms to pull. At each turn she picks one, and receives a vector-valued reward. When she thinks she has enough information to identify the Pareto front of the different arm means, she stops the game and gives an answer. We are interested in designing algorithms such that the answer given is correct with probability at least 1-$\delta$. Our main contribution is an efficient implementation of an algorithm achieving the optimal sample complexity when the risk $\delta$ is small. With K arms in d dimensions p of which are in the Pareto set, the algorithm runs in time O(Kp^d) per round.

stat.ML↗

arXiv2024

Accelerated Mirror Descent for Non-Euclidean Star-convex Functions

Acceleration for non-convex functions is a fundamental challenge in optimisation. We revisit star-convex functions, which are strictly unimodal on all lines through a minimizer. [1] accelerate unconstrained star-convex minimization of functions that are smooth with respect to the Euclidean norm. To do so, they add a certain binary search step to gradient descent. In this paper, we accelerate unconstrained star-convex minimization of functions that are weakly smooth with respect to an arbitrary norm. We add a binary search step to mirror descent, generalize the approach and refine its complexity analysis. We prove that our algorithms have sharp convergence rates for star-convex functions with $\alpha$-Holder continuous gradients and demonstrate that our rates are nearly optimal for $p$-norms. [1] Near-Optimal Methods for Minimizing Star-Convex Functions and Beyond, Hinder Oliver and Sidford Aaron and Sohoni Nimit

math.OC↗

arXiv2023

Hebbian learning inspired estimation of the linear regression parameters from queries

Local learning rules in biological neural networks (BNNs) are commonly referred to as Hebbian learning. [26] links a biologically motivated Hebbian learning rule to a specific zeroth-order optimization method. In this work, we study a variation of this Hebbian learning rule to recover the regression vector in the linear regression model. Zeroth-order optimization methods are known to converge with suboptimal rate for large parameter dimension compared to first-order methods like gradient descent, and are therefore thought to be in general inferior. By establishing upper and lower bounds, we show, however, that such methods achieve near-optimal rates if only queries of the linear regression loss are available. Moreover, we prove that this Hebbian learning rule can achieve considerably faster rates than any non-adaptive method that selects the queries independently of the data.

math.ST↗