Riemannian Dueling Optimization
Dueling optimization considers optimizing an objective with access to only a comparison oracle of the objective function. It finds important applications in emerging fields such as recommendation systems and robotics. Existing works on dueling optimization mainly focused on unconstrained problems in the Euclidean space. In this work, we study dueling optimization over Riemannian manifolds, which covers important applications that cannot be solved by existing dueling optimization algorithms. In particular, we propose a Riemannian Dueling Normalized Gradient Descent (RDNGD) method and establish its iteration complexity when the objective function is geodesically L-smooth or geodesically (strongly) convex. We also propose a projection-free algorithm, named Riemannian Dueling Frank-Wolfe (RDFW) method, to deal with the situation where projection is prohibited. We establish the iteration and oracle complexities for RDFW. We illustrate the effectiveness of the proposed algorithms through numerical experiments on both synthetic and real applications.
Code (0)
등록된 구현이 없습니다.
Tasks
Recommendation SystemsSimilar Papers 제목 키워드 기반
Regret Analysis for Continuous Dueling Bandit
The dueling bandit is a learning framework wherein the feedback information in the learning process is restricted to a noisy comparison between a pair of actions. In this research, we address a dueling bandit problem bas…
Bias-Robust Bayesian Optimization via Dueling Bandits
We consider Bayesian optimization in settings where observations can be adversarially biased, for example by an uncontrolled hidden confounder. Our first contribution is a reduction of the confounded setting to the dueli…
Bayesian OptimizationDueling Convex Optimization with General Preferences
We address the problem of \emph{convex optimization with dueling feedback}, where the goal is to minimize a convex function given a weaker form of \emph{dueling} feedback. Each query consists of two points and the duelin…
Dueling Bandits with Adversarial Sleeping
We introduce the problem of sleeping dueling bandits with stochastic preferences and adversarial availabilities (DB-SPAA). In almost all dueling bandit applications, the decision space often changes over time; eg, retail…
ManagementMulti-Armed BanditsLarge-Scale Riemannian Meta-Optimization via Subspace Adaptation
Riemannian meta-optimization provides a promising approach to solving non-linear constrained optimization problems, which trains neural networks as optimizers to perform optimization on Riemannian manifolds. However, exi…