Structured Stochastic Linear Bandits

Understand

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., $L_1$, $L_{(1,2)}$, nuclear norm.
• We focus on constructing confidence ellipsoids which contain the unknown parameter across all rounds with high-probability.