New Algorithm for Contextual Combinatorial Semi-bandits

A new research paper introduces SquareCB.Comb, an innovative algorithm designed to tackle the complex problem of contextual combinatorial semi-bandits. This algorithm is particularly efficient for scenarios involving a large number of potential choices, referred to as 'arms,' and where the reward function can be approximated generally. At each step, the system observes a context, selects a combination of basic arms, and receives individual rewards for each chosen arm. The primary objective is to maximize the total reward over time. SquareCB.Comb distinguishes itself by solving a convex optimization problem in each round, effectively balancing the need for exploration (trying new combinations) with exploitation (choosing known good combinations). A key advantage is its scalability to extensive arm sets and its flexibility, as it does not impose restrictive structural assumptions on the action set beyond a simple cardinality limit. The paper rigorously proves that SquareCB.Comb achieves a minimax optimal regret bound, matching state-of-the-art guarantees seen in more constrained settings like slate recommendation, while offering broader applicability to various combinatorial action structures and general reward function approximations.