New THV-UCB algorithm slates Pareto-optimal arms with proven regret bounds
Selecting k arms to jointly approximate Pareto frontier with sub-linear regret...
Deep Dive
Researchers Nicolas Gutowski, Fabien Chhel, Alexandre Letard, and Sylvain Lamprier introduced THV-UCB, an algorithm for multi-objective bandit problems where an agent selects a slate of k arms each round. The algorithm uses optimistic estimates of marginal hypervolume contributions to greedily pick arms that approximate the Pareto frontier. They prove a gap-free regret bound of O~(d√(nkT)) and a gap-dependent bound of O~(nk²·⁵/Δ_min), providing theoretical support for using small subsets to
Key Points
- THV-UCB selects k arms per round to approximate the Pareto frontier using marginal hypervolume contributions and UCB optimism.
- Gap-free regret bound of Õ(d√(nkT)) holds for all instances; gap-dependent bound Õ(nk²·⁵/Δ_min) is polylogarithmic in T with well-separated arms.
- Proof uses submodularity of hypervolume and an α = 1-1/e approximation guarantee for greedy maximization.
Why It Matters
First rigorous regret analysis for multi-objective slate selection, enabling efficient Pareto-front approximation in recommendation and optimization systems.