Suggest edit — Directed Exploration

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title: "Directed Exploration"
source: https://www.jemoka.com/posts/kbhdirected_exploration/
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Softmax Method Pull arm \(a\) with probability \(\propto \exp (\lambda \rho_{a})\), where \(\lambda \geq 0\) is the &ldquo;precision parameter&rdquo;.
When \(\lambda \to 0\), this system uses the same rate for each of the actions, so you are essentially randomly sampling; when \(\lambda \to \infty\), the system will use only the greedy action because only the element with the biggest \(\rho_{a}\) gets selected.
For a multi-state case:
\begin{equation} \propto \exp (\lambda Q(s,a)) \end{equation}
Quantile Exploration Choose the arm with the largest \(\theta\) at the highest \(\alpha\) percentile of its beta distribution, pull that arm, update priors
&ldquo;choose the arm with the highest \(\theta\) for the \(90\%\) percentile, then update the distribution&rdquo;
UCB 1 Inspired by monte-carlo exploration
take action \(a\) such that
\begin{equation} \max_{a} \rho_{a} + c \sqrt{ \frac{\log N}{N(a)}} \end{equation}
where, \(c\) is the exploration factor, \(N\) is the total number of trials, \(N(a)\) is the number of trials for \(a\) we have done.
This value is considered the &ldquo;upper confidence bound&rdquo;; hence &ldquo;UCB&rdquo;
Posterior Sampling Same one point from each Beta Distribution for each of your slot machines; then you pick the result that is the highest.
Does not require any parameter.
This is proven to do some over-exploration. But that&rsquo;s (mostly) just fine.
R-Max See R-Max