Accelerating Linear Bandits with Persistent Candidate Sets
PC-LinUCB keeps a small persistent action set so linear bandits avoid scoring every arm each round.
Persistent Candidate LinUCB maintains k active actions and samples q challengers from the remaining arms, reducing optimistic score evaluations from O(K) to O(k+q) per round. Its high-probability regret bounds combine a standard linear-bandit term with a discovery cost of order O((K-k) log(K-k)/q) that does not grow with the horizon. For fixed gaps and long horizons, an Omega((K-k)/q) lower bound shows uniform partial access has an unavoidable regret cost. Experiments report substantially faster LinUCB with comparable regret, and the mechanism can extend beyond LinUCB.
- Scores k persistent actions plus q uniformly sampled challengers.
- Cuts per-round evaluations from order K to order k plus q.
- Adds a horizon-independent discovery cost to standard regret bounds.
- Experiments speed up LinUCB while keeping comparable regret.
From the original article
1 min read at arxiv.orgExhaustive optimistic scoring can make action selection costly in linear bandits with a large fixed set of $K$ actions, requiring $\mathcal{O}(K)$ score evaluations per round. We introduce Persistent Candidate LinUCB (\textsc{PC-LinUCB}), which maintains $k$ active actions and samples $q$ challengers uniformly from the remaining $K-k$ actions at each round.
By Bingkui Tong · arxiv.org
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