2016/06/17 by Nicholas D. Johnson, V. Sivakumar, Johnson, Nicholas +3 · 2 citations
Computer Science · Decision Sciences · #Advanced Bandit Algorithms Research #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Optimization and Search Problems #Reinforcement Learning in Robotics
paper · pdf · doi:10.48550/arxiv.1606.05693
openalex publication_date 2016/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The stochastic linear bandit problem proceeds in rounds where at each round the algorithm selects a vector from a decision set after which it receives a noisy linear loss parameterized by an unknown vector. The goal in such a problem is to minimize the (pseudo) regret which is the difference between the total expected loss of the algorithm and the total expected loss of the best fixed vector in hindsight. In this paper, we consider settings where the unknown parameter has structure, e.g., sparse, group sparse, low-rank, which can be captured by a norm, e.g., L1, L(1,2), nuclear norm. We focus on constructing confidence ellipsoids which contain the unknown parameter across all rounds with high-probability. We show the radius of such ellipsoids depend on the Gaussian width of sets associated with the norm capturing the structure. Such characterization leads to tighter confidence ellipsoids and, therefore, sharper regret bounds compared to bounds in the existing literature which are based on the ambient dimensionality.