Expected Sample Complexity in Multi-Armed Bandits
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The paper introduces the expected sample complexity metric for stochastic multi‑armed bandits and analyzes it within a new framework called approximately correct in expectation (ACE). It demonstrates that ACE guarantees lead to almost sure convergence to the optimal expected reward, contrasts this with high‑probability guarantees, and shows how to translate ACE bounds into explicit expected regret bounds. The authors prove that deterministic algorithms cannot achieve favorable ACE bounds, propose an explore‑then‑ε‑greedy algorithm when ε is known, analyze Thompson sampling when ε is unknown, and provide nearly matching lower bounds that establish tightness and a performance separation between the two regimes.
arXiv:2402. 07391v3 Announce Type: replace-cross Abstract: We consider a replicable stochastic multi-armed bandit algorithm that ensures, with high probability, that the algorithm's sequence of actions is not affected by the randomness inherent in the dataset.
The paper presents the first high‑probability regret bounds for both cumulative and current‑step variants of Feel‑Good Thompson Sampling (FGTS) in contextual bandits with general realizable function approximation. The bounds rely on decoupling coefficients and prior mass near the true reward function, and in the linear setting they achieve ≠d√T log(2T)+√T log(1/δ) regret with probability at least 1‑δ. This matches the dimension and horizon dependence of upper‑confidence‑bound algorithms up to logarithmic factors, while the high‑probability cost adds only linear dependence on log(1/δ).
arXiv:2409. 18909v2 Announce Type: replace Abstract: Motivated by real-world applications that necessitate responsible experimentation, we introduce the problem of best arm identification (BAI) with minimal regret.
arXiv:2606. 04931v1 Announce Type: new Abstract: Mean-based algorithms are a class of online learning algorithms that assign low probability to actions with low average rewards.
arXiv:2610.01951v1 Announce Type: cross Abstract: Top-two algorithms are simple and effective for fixed-confidence best-arm identification, but their sharp non-asymptotic behavior is still not well u...