Linear Bandits beyond Inner Product Spaces, the case of Bandit Optimal Transport
The paper shows that classical linear bandit methods, which require an inner product structure, can be adapted to solve Bandit Optimal Transport problems even when an inner product is not present. The proposed EntUCB algorithm achieves the same learning performance bounds as standard linear bandits in Hilbert spaces, proving that the inner product structure is not essential for efficient learning in this context.