		\begin{algorithm}[H] 
			\centering
			\caption{Top-two Thompson sampling (TTTS) with cost-aware selection rule}\label{alg:ttts}
			\begin{algorithmic}[1]
				\State {\bf Input:} History $\mathcal{H}_t$
				\State Sample $I_t^{(1)} \sim \mathrm{TS}(\mathcal{H}_t)$ using Algorithm \ref{alg:ts}
				\Repeat 
				\State Sample $I_t^{(2)} \sim \mathrm{TS}(\mathcal{H}_t)$ using Algorithm \ref{alg:ts}
				\Until{$I_t^{(2)} \neq I_t^{(1)}$}
				\State Determine coin bias $h_t$ via~\eqref{eq:cost-aware-IDS}.
				\State \Return $I_t^{(1)}$ w/ prob $h_t$, $I_{t}^{(2)}$ otherwise. 
			\end{algorithmic}
		\end{algorithm}

\begin{algorithm}[H]
\centering
\caption{Top-two Thompson sampling (TTTS) with cost-aware selection rule}   \begin{algorithmic}
[1]
\State {\bf Input:} History $\mathcal{H}_t$
\State Sample $I_t^{(1)} \sim \mathrm{TS}(\mathcal{H}_t)$ using Algorithm \ref{alg:ts}
\Repeat
\State Sample $I_t^{(2)} \sim \mathrm{TS}(\mathcal{H}_t)$ using Algorithm \ref{alg:ts}
\Until{$I_t^{(2)} \neq I_t^{(1)}$}
\State Determine coin bias $h_t$ via~\eqref{eq:cost-aware-IDS}.
\State \Return $I_t^{(1)}$ w/ prob $h_t$, $I_{t}^{(2)}$ otherwise.
\end{algorithmic}
\end{algorithm}
{
    "title": "optimizing adaptive experiments: a unified approach to regret   minimization and best-arm identification",
    "id": "2402.10592",
    "abstract": "practitioners conducting adaptive experiments often encounter two competing priorities: reducing the cost of experimentation by effectively assigning treatments during the experiment itself, and gathering information swiftly to conclude the experiment and implement a treatment across the population. currently, the literature is divided, with studies on regret minimization addressing the former priority in isolation, and research on best-arm identification focusing solely on the latter. this paper proposes a unified model that accounts for both within-experiment performance and post-experiment outcomes. we then provide a sharp theory of optimal performance in large populations that unifies canonical results in the literature. this unification also uncovers novel insights. for example, the theory reveals that familiar algorithms, like the recently proposed top-two thompson sampling algorithm, can be adapted to optimize a broad class of objectives by simply adjusting a single scalar parameter. in addition, the theory reveals that enormous reductions in experiment duration can sometimes be achieved with minimal impact on both within-experiment and post-experiment regret.",
    "categories": "cs.lg econ.em stat.ml",
    "doi": "",
    "created": "2024-02-16",
    "updated": "",
    "authors": [
        "chao qin",
        "daniel russo"
    ],
    "affiliation": [],
    "url": "https://arxiv.org/abs/2402.10592"
}
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