From ccf3cbba55b30241a32f06edead25f4a99973c3c Mon Sep 17 00:00:00 2001
From: Thibaut Horel <thibaut.horel@gmail.com>
Date: Tue, 28 Jun 2022 14:09:05 -0400
Subject: AOAS 2103-005, second revision

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+\documentclass[11pt]{article}
+\usepackage[T1]{fontenc}
+\usepackage[utf8]{inputenc}
+\usepackage[hmargin=1.2in, vmargin=1.2in]{geometry}
+\usepackage{amsmath,amsfonts}
+
+
+\title{\vspace{-2em}\large Review of \emph{A Multi-Agent Reinforcement Learning
+		Framework\\ for Off-Policy Evaluation in Two-Sided Markets}}
+		\author{Submission \textsf{2103--005} to the \emph{Annals of Applied Statistics},
+1\textsuperscript{st} revision}
+
+\begin{document}
+
+\maketitle
+
+I would like to thank the authors for carefully addressing all my comments in
+their response and revision. In particular, I noted significant improvements
+regarding the framing and contributions of the paper in Section 1, and
+clarifications regarding the setup and assumptions in Section 2. I also
+appreciate the improved discussion on the mean-field approximation and how to
+test it empirically using a conditional independence test. I only have two
+minor comments:
+\begin{itemize}
+	\item  I believe there a few inaccuracies in the derivation in Appendix C:
+		\begin{itemize}
+			\item in the first displayed expression for $Q_i^{\bf\pi}({\bf a},{\bf
+				s})$, the parenthesis after $m_i^a({\bf A_t})$ should instead be
+				placed after $\tilde S_{i,t}$. Same remark about the inlined
+				expression on the next line.
+			\item the sequence of equalities on page 25 should be stated for an
+				arbitrary square-integrable function $h$ instead of $\bar r_i$
+				to be consistent with the induction hypothesis.
+			\item in the same sequence of equalities, the last equality should
+				have $m_i^a(\pi({\bf S}_{j}))$ instead of $m_i^a(\pi({\bf
+				S}_{j+1}))$ in the “conditioning” part (after the ‘$|$’
+				character).
+		\end{itemize}
+	\item In Appendix E in the supplementary material, I suggest adding plots
+		similar to the ones in Fig. 4 of the main file, but only showing the
+		two curves corresponding to the proposed method and the QV baseline.
+		This is because these two curves are so close together in the current
+		Fig.\ 4 that it is hard to tell them apart due to the scale imposed by the
+		  other curves. My hope is that restricting to these two curves only in
+		  the appendix will allow for a better scale on the $y$-axis that will
+		  make them easier to distinguish and provide visual support for the
+		  $t$-test reported in Table 1 and 2.
+\end{itemize}
+I recommend acceptance after the above minor points are addressed.
+
+\vspace{1em}
+
+\paragraph{Additional typos.}
+\begin{itemize}
+	\item page 4, second paragraph: \emph{Event through} $\to$ \emph{Even though}
+	\item the running title at the top of each page does not match the new
+		paper title.
+\end{itemize}
+%\bibliographystyle{plain}
+%\bibliography{main}
+
+\end{document}
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