Pre-final read over: major progress all around

MSCS-TODO.txt

@@ -0,0 +1,36 @@
+TODO:
+[x] combine references.bib
+[x] See Dorsa notes
+[ ] See Mykel notes
+[x] Subsections for tooling: CrossEntropyVariants.jl and FailureRepresentation.jl
+[x] Combine Acknowledgments
+[x] "dissertation" wording in the signatures page
+[x] Remove "graduate studies" committee?
+
+
+Mykel notes:
+[x] Concatenate research papers from MS (if they're related work / extensions)
+[x] Add introduction
+[ ] Flow together body chapters
+[ ] Remove redundancies between them
+[x] Change conclusions/future work into discussion
+- Two big things:
+    [x] 1) intro chapter
+        [x] shortest intro chapter possible (concise)
+        [x] "freshman undergrad could understand contributions"
+    [x] 2) final chapter
+        [x] one section "Summary" high level, no jargon, no non-sense
+        [x] second section "Contributions", summarize how you've supported your claims (back references, specialized terminology)
+        [x] third: future work
+[x] https://www2.eecs.berkeley.edu/Pubs/Theses/
+[x] Fix \texttt to use old monofont
+[x] Move JuliaMono font files.
+[x] Page header to be small caps
+[x] POMDPStressTesting.jl Acknowledgments moved to main Acknowledgments (TRPO/PPO)
+[x] Check for duplicate references
+[x] Comb through references (you know Mykel will)
+[x] Appendix reformatting (figures/fix overflow)
+[ ] Clean everything up
+[ ] Publically release __after__ approved by Stanford.
+[x] Algorithm size \small:
+   https://tex.stackexchange.com/questions/435649/algorithm-caption-size-reduction

algorithms/ce-surrogate.tex

@@ -0,0 +1,13 @@
+\begin{lstlisting}[language=JuliaLocal]
+function ce_surrogate(S, 𝐌; m, m_elite, k_max)
+    for k in 1:k_max
+        mₑ, m_elite = evaluation_schedule(k, k_max) # number of evaluations from a schedule
+        𝐗 = rand(𝐌, mₑ) # draw mₑ samples from 𝐌
+        𝐘 = map(S, eachcol(𝐗)) # evaluate samples 𝐗 using true objective S
+        𝐞 = 𝐗[:, sortperm(𝐘)[1:m_elite]] # select elite samples output from true objective
+        𝐄 = model_elite_set!(𝐗, 𝐘, 𝐌, 𝐞, m, m_elite) # find model-elites using a surrogate
+        𝐌 = fit(𝐌, 𝐄) # re-fit distribution 𝐌 using model-elite samples
+    end
+    return 𝐌
+end
+\end{lstlisting}

algorithms/cem-variants-functions.tex

@@ -0,0 +1,5 @@
+\begin{lstlisting}[language=JuliaLocal]
+𝐌′ = cross_entropy_method(S, 𝐌) # standard CEM
+𝐌′ = ce_surrogate(S, 𝐌) # surrogate-based CEM
+𝐌′ = ce_mixture(S, 𝐌) # surrogate-based CEM using mixture models
+\end{lstlisting}

algorithms/cem-variants-usage-basis.tex

@@ -0,0 +1,6 @@
+\begin{lstlisting}[language=JuliaLocal]
+S = paraboloid # objective function
+𝐌 = MvNormal([0, 0], [200 0; 0 200]) # proposal distribution
+
+(𝐌, bestₓ, bestᵥ) = ce_surrogate(S, 𝐌; basis=:squared)
+\end{lstlisting}

algorithms/cem-variants-usage.tex

@@ -0,0 +1,11 @@
+\begin{lstlisting}[language=JuliaLocal]
+using CrossEntropyVariants
+using Distributions
+
+S = sierra # objective function
+𝛍 = [0, 0] # initial mean
+𝚺 = [200 0; 0 200] # initial covariance
+𝐌 = MvNormal(𝛍, 𝚺) # proposal distribution
+
+(𝐌, bestₓ, bestᵥ) = ce_surrogate(S, 𝐌)
+\end{lstlisting}

algorithms/mcts-pw-algorithm-part2.tex

@@ -1,6 +1,7 @@
-% \vspace{-2.5mm}
 \begin{algorithm}[!ht]
-  \caption{Monte Carlo tree search simulation.} 
+  \captionsetup{font=small}
+  \small
+  \caption{Monte Carlo tree search simulation.}
   \label{alg:mcts-pw-simulate}
   \begin{algorithmic}
   \Function{Simulate$(s, d)$}{}
@@ -23,23 +24,21 @@
   \end{algorithmic}
 \end{algorithm}
 %
-% \vspace{-2.5mm}
 \begin{algorithm}[!ht]
+  \captionsetup{font=small}
+  \small
   \caption{Modified rollout with end-of-depth evaluation.}
   \label{alg:mcts-pw-rollout}
   \begin{algorithmic}
   \Function{Rollout$(s,d)$}{}
   \If {$d = 0$}
     \State $(p, e, d) \leftarrow \textproc{Evaluate}(s)$
     \State $\tau \leftarrow \textproc{IsTerminal}(s)$
-    % \State $(\bar{a},s^\prime) \leftarrow \textproc{Evaluate}(s)$
     \State $\bar{a}^* \leftarrow \textproc{UpdateBestAction}(s,Q)$
     \State \Return $R(p,e,d,\tau)$
-    % \State \Return $R(s,\bar{a},s^\prime)$
   \ElsIf {$d = \floor{d_\text{max}/2}$}
     \State $\bar{a} \leftarrow \bar{a}^*$ \algorithmiccomment{feed best action}
   \Else
-    % \State $\bar{a} \sim \mathbb{U}$ \algorithmiccomment{sample seed uniformly}
       \State $\bar{a} \leftarrow \textproc{SampleAction}(s,Q)$
   \EndIf
   \State $(s^\prime, r) \sim G(s,\bar{a})$
@@ -49,13 +48,14 @@
 \end{algorithm}
 %
 \begin{algorithm}[!ht]
+  \captionsetup{font=small}
+  \small
   \caption{Action selection with progressive widening.}
   \label{alg:mcts-pw-action-widen}
   \begin{algorithmic}
   \Function{SelectAction$(s)$}{}
   \If {$| A(s) | \le kN(s)^\alpha$}
     \State $\bar{a} \leftarrow \textproc{SampleAction}(s,Q)$
-    % \State $\bar{a} \sim \mathbb{U}$ \algorithmiccomment{sample seed uniformly}
     \State $(N(s,\bar{a}), Q(s,\bar{a})) \leftarrow (N_0(s,\bar{a}), Q_0(s,\bar{a}))$
     \State $A(s) \leftarrow A(s) \cup \{\bar{a}\}$
   \EndIf
@@ -65,25 +65,21 @@
 \end{algorithm}
 %
 \begin{algorithm}[!ht]
-  \caption{Single deterministic next state.} 
+  \captionsetup{font=small}
+  \small
+  \caption{Single deterministic next state.}
   \label{alg:mcts-pw-deterministic-state}
   \begin{algorithmic}
   \Function{DeterministicStep$(s,\bar{a})$}{}
   \If {$N(s,\bar{a},\cdot) = \emptyset$}
     \State $(s^\prime, r) \sim G(s,\bar{a})$
-    % \State $R(s,\bar{a},s^\prime) \leftarrow r$
     \State $\textproc{SetCache}(s, \bar{a}, s^\prime, r)$
     \State $N(s,\bar{a},s^\prime) \leftarrow N_0(s,\bar{a},s^\prime)$
   \Else
-    % \State $s^\prime \leftarrow \arg_{s^\prime} N(s,\bar{a},\cdot)$
-    % \State $(s^\prime, r) \leftarrow (\textproc{CachedNextState}(s,\bar{a}), R(s,\bar{a},s^\prime))$
-    % \State $(s^\prime, r) \leftarrow \textproc{CachedNextState}(s,\bar{a})$
     \State $(s^\prime, r) \leftarrow \textproc{GetCache}(s,\bar{a})$
-    % \State $s^\prime \leftarrow (\cdot)$
-    % \State $r \leftarrow R(s,\bar{a},s^\prime)$
     \State $N(s,\bar{a},s^\prime) \leftarrow N(s,\bar{a},s^\prime)+1$
   \EndIf
   \State \Return $(s^\prime,r)$
   \EndFunction
   \end{algorithmic}
-\end{algorithm}
+\end{algorithm}

algorithms/mcts-pw-algorithm.tex

@@ -1,5 +1,6 @@
-% 
 \begin{algorithm}[!ht]
+  \captionsetup{font=small}
+  \small
   \caption{Top-level Monte Carlo tree search algorithm.} 
   \label{alg:mcts-pw}
   \begin{algorithmic}

algorithms/monte-carlo-algorithm.tex

@@ -1,8 +1,6 @@
-\algtext*{EndLoop}% Remove "end _X_" text
-\algtext*{EndIf}
-\algtext*{EndFor}
-\algtext*{EndFunction}
 \begin{algorithm}[th!]
+  \captionsetup{font=small}
+  \small
   \caption{Direct Monte Carlo simulation.}
   \label{alg:mc}
   \begin{algorithmic}
@@ -13,4 +11,4 @@
   \EndFor
   \EndFunction
   \end{algorithmic}
-\end{algorithm}
+\end{algorithm}

algorithms/pomdp-stress-testing-interface.tex

@@ -0,0 +1,13 @@
+\begin{lstlisting}[language=JuliaLocal]
+# GrayBox simulator and environment
+abstract type GrayBox.Simulation end
+function GrayBox.environment(sim::Simulation)::GrayBox.Environment end
+function GrayBox.transition!(sim::Simulation)::Real end
+
+# BlackBox.interface(input::InputType)::OutputType
+function BlackBox.initialize!(sim::Simulation)::Nothing end
+function BlackBox.evaluate!(sim::Simulation)::Tuple{Real, Real, Bool} end
+function BlackBox.distance(sim::Simulation)::Real end
+function BlackBox.isevent(sim::Simulation)::Bool end
+function BlackBox.isterminal(sim::Simulation)::Bool end
+\end{lstlisting}

appendices/episodic_ast_appendix.tex

@@ -1,43 +1,24 @@
-% "and Miss Distances"
 \chapter{Alternative FMS Failure Events}\label{sec:application_events}
-This section details alternative failure events investigated and their associated miss distance calculations.
+This section details alternative failure events investigated and their associated miss distance calculations when stress testing the trajectory predictions in a flight management system (FMS).
 Ultimately, analysis of these failure events showed their inadequacy and arc length failures were selected as the primary event.
 
 \section{Tangency Kinks}
 Tangency kinks arise when a small angle threshold is exceeded between the inbound straight segment and the tangent of the turn segment at a given waypoint. The failure event occurs when this angle difference $\theta$ is above the threshold $\tau_k = 0.001$ \si{\radian}.
 
 \begin{figure}[!ht]
 \centering
-\resizebox{0.6\columnwidth}{!}{\input{diagrams/tangent-angle.tex}}
+\resizebox{0.5\columnwidth}{!}{\input{diagrams/tangent-angle.tex}}
 \caption{Tangency kink failure event and miss distance.}
 \label{fig:tangency_kink}
 \end{figure}
 
-Miss distance for the tangency kinks is calculated by first determining the azimuth angle $z$ between the start point of the arc $s$ and the center point $c$. The azimuth is calculated using a WGS84 Earth flattening leveraging the Geodesic.jl\footnote{\url{https://github.com/anowacki/Geodesics.jl}} package which implements Vincenty's formula  \cite{vincenty}. The tangency angle $\theta$ is then calculated for each $\ell \in L$ where $L$ is the set of lateral packets that each have a straight segment and a turn arc with radius $r$. The sign of the radius $r$ indicates the direction of turn, where left is negative and right is positive. The course-in angle of the straight segment $\ell$ is denoted $\angle \ell$,
-% \begin{align*}
-%   U(\phi) &= \arctan((1 - f) \tan \phi))\\
-%   (U_s, U_c) &= (U(\phi_s),\, U(\phi_c))
-% \end{align*}
-%
-% \begin{align*}
-%   \lambda = \Lambda(L, f)
-% \end{align*}
-% https://github.com/anowacki/Geodesics.jl
-% 
-% \begin{align*}
-%   % https://en.wikipedia.org/wiki/Vincenty%27s_formulae#Inverse_problem
-%   % Inverse problem
-%   % 1. Vincenty, T. (1975). "Direct and Inverse Solutions of Geodesics on the Ellipsoid with application of nested equations" (PDF). Survey Review. XXIII (176): 88–93. doi:10.1179/sre.1975.23.176.88
-%   z = \arctan(\cos U_c \sin \lambda,\, \cos U_s \sin U_c - \sin U_s \cos U_c \cos \lambda)
-%   % \alpha_c = \arctan(\cos U_s \sin \lambda,\, -\sin U_s \cos U_c + \cos U_s \sin U_c \cos \lambda)
-% \end{align*}
-%
+Miss distance for the tangency kinks is calculated by first determining the azimuth angle $z$ between the start point of the arc $s$ and the center point $c$. The azimuth is calculated using a WGS84 Earth flattening leveraging the Geodesic.jl\footnote{\url{https://github.com/anowacki/Geodesics.jl}} package which implements Vincenty's formula  \cite{vincenty}. The tangency angle $\theta$ is then calculated for each $\ell \in L$ where $L$ is the set of lateral packets that each have a straight segment and a turn arc with radius $r$. The sign of the radius $r$ indicates the direction of turn, where left is negative and right is positive. The course-in angle of the straight segment $\ell$ is denoted $\angle \ell$, which we then get a distance metric of:
 \begin{equation*}
-  % d = \tau_k - \max\left\{ \abs{z - \angle \ell + \sign(r)\frac{\pi}{2}} : (\ell,r) \in L \right\}.
-  d = \tau_k - \max\limits_{(\ell,r) \in L} \abs{z - \angle \ell + \sign(r)\frac{\pi}{2}}.
+    d = \tau_k - \max\limits_{(\ell,r) \in L} \abs{z - \angle \ell + \sign(r)\frac{\pi}{2}}
 \end{equation*}
+\phantom{}
 
-
+\vspace{-6mm}
 \section{Course Directions}
 In-bound and out-bound course directions may deviate from one another and can be classified as a failure event.
 Closely related to the \textit{disconnection} failure event, the course direction failures can arise when two sequential lateral packets are disconnected. This failure specifically looks for angle differences between the course-out $\theta_{\text{out}}$ and course-in $\theta_\text{in}$ directions of the sequential lateral packets. If this angle difference $\omega = \abs{\theta_\text{out} - \theta_\text{in}}$ is above the threshold $\tau_c = 1\si{\degree}$ then it is classified as a failure.
@@ -51,20 +32,9 @@ \section{Course Directions}
 
 Miss distance is calculated as how close to the threshold $\tau_c$ is the maximum wrapped angle difference between the course-out angle and course-in angle denoted by $\omega$, namely
 \begin{equation*}
-  % d = \tau_c - \max\left\{ \abs{\theta_\text{out} - \theta_\text{in}} : \theta_\text{out} \in L_i, \theta_\text{in} \in L_{i+1} \right\}.
-  % d = \tau_c - \max\limits_{\theta_\text{out} \in L_i, \theta_\text{in} \in L_{i+1}}\abs{\theta_\text{out} - \theta_\text{in}}.
-  d = \tau_c - \max\limits_{\substack{\theta_\text{out} \in L_i\\\theta_\text{in} \in L_{i+1}}}\abs{\theta_\text{out} - \theta_\text{in}}.
+    d = \tau_c - \max\limits_{\substack{\theta_\text{out} \in L_i\\\theta_\text{in} \in L_{i+1}}}\abs{\theta_\text{out} - \theta_\text{in}}.
 \end{equation*}
 
-% \begin{itemize}
-%   \item Explain how tangent angle is calculated
-%   \item Talk about WGS84 flattening
-%   \item Mention Vincenty's inverse formula, Karney's inverse formula, and cite comparison paper (get papers, \textit{GEODESIC ALGORITHMS: AN EXPERIMENTAL STUDY})
-%   \item Describe all variables used ($r = \text{radius}$, etc)
-%   \item Update how the angle is calculated based on Nick's adjustments
-% \end{itemize}
-
-
 \section{Disconnections}
 Disconnected lateral packets occur when two sequential lateral packets are not connected end-to-start, thus leaving a distance $\delta$ between them. If this geodesic distance $\delta = \lVert e_i - p_{i+1} \rVert$ is above the threshold $\tau_d = 10$ \si{ft} then a failure occurred.
 
@@ -77,12 +47,5 @@ \section{Disconnections}
 
 Miss distance is calculated as the threshold $\tau_d$ minus the maximum distance between the end points $e_i$ (or $s_i$ if no arc is provided) and the initial point $p_{i+1}$ of the next lateral packet:
 \begin{equation*}
-  % d = \tau_d - \max\left\{ \lVert e_i - p_{i+1} \rVert : (e_i,p_{i+1}) \in L \right\}.
-  % d = \tau_d - \max\limits_{(e_i,p_{i+1}) \in L}\lVert e_i - p_{i+1} \rVert.
-  % d = \tau_d - \max\limits_{e_i \in L_i, p_{i+1} \in L_{i+1}}\lVert e_i - p_{i+1} \rVert.
-  d = \tau_d - \max\limits_{\substack{e_i \in L_i\\p_{i+1} \in L_{i+1}}}\lVert e_i - p_{i+1} \rVert
+    d = \tau_d - \max\limits_{\substack{e_i \in L_i\\p_{i+1} \in L_{i+1}}}\lVert e_i - p_{i+1} \rVert
 \end{equation*}
-
-
-% We use the modified reward function that incorporates severity based on the miss distance at the time of an event.
-% For our four miss distances described above, we want to reward egregious miss distances, thus finding events that are more severe.