criticized the New Deal from all sides. Senator Huy P. Long claimed to “show our wealth.” nullification from conservative supreme court, FDR threatened to restructure + hurts his coalition.

• FDR ordered cuts in spending
• 1938 midterms: Republicans can block programs — gained control of congress + created ability to gain control

Cross Entropy Method is a “conditional MLE” objective; whereby we try to maximize:

• the log prob
• of the true y labels in the training data
• given the observations

Derivation

Recall the Bernoulli distribution, and specifically:

\begin{equation} P(Y=y) = p^{y} (1-p)^{1-y} \end{equation}

Meaning, we want to maximize:

\begin{equation} \log P(y=y) = y \log p + (1-y)\log (1-y) \end{equation}

specifically, we’d like to minimize:

\begin{equation} -[y \log p + (1-y)\log (1-y)] \end{equation}

Intuition

This function should be

This method introduces a search distribution instead of discrete points:

\begin{equation} p(\theta | \psi) \end{equation}

We want to know how parameters \(\theta\) are distributed, given some input parameters \(\psi\) (for instance, we assume parameters are gaussian distributed such as the mean/variance).

1. Given this distribution, we sample \(m\) samples of \(\theta\) from the distribution. Those are our starting candidate points.
2. We then check its policy for its utility via the Roll-out utility
3. We want to take top \(k\) of our best performers, called “elite samples” \(m_{elite}\)
4. Use the set of \(m_{elite}\) points, we fit a new distribution parameter \(\psi\) that describes those sample

This allows us to bound how many Roll-out utilities we are doing.