Big idea: keep branching/selecting until a tally hits an upper/lower bound

Ingredients:

• \(Ulo(s)\): lower bound function of value function
• \(Qhi(s,a)\): upper bound function of action-value function
• \(\mathcal{P}\) problem (states, transitions, etc.)
• \(d\) depth (how many next states to look into)—more is more accurate but slower

Its Forward Search, but with bounds instead of exponentially looking into every possible next state, we only check the actions in the order of their bounded value. We start with the actions with the highest bound (most possible value), and if its already better than the upper bound, we can be done because we know everything else will have lower value as their bounds are lower.

Way of performing action research developed by Victoria Clarke and Virginia Braun in 2006

Professor Brian MacWhinney is a professor of psychology, modern languages, and language technology at CMU.

Brown v. Board of Education is a landmark case in the US. This lead for schools to be integrated, and many children were taken out of school out of protest due to the subsequent integration movement between schools.

Brownian Motion is the pattern for measuring the convergence of random walk through continuous timing.

discrete random walk

discrete random walk is a tool used to construct Brownian Motion. It is a random walk which only takes on two discrete values at any given time: \(\Delta\) and its additive inverse \(-\Delta\). These two cases take place at probabilities \(\pi\) and \(1-\pi\).

Therefore, the expected return over each time \(k\) is:

\begin{equation} \epsilon_{k} = \begin{cases} \Delta, p(\pi) \\ -\Delta, p(1-\pi) \end{cases} \end{equation}