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\title{FSDP-Compatible Optimizer Design: Lessons from a Negative Result}
\author{Aardvark}
\date{\today}

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\begin{abstract}
This paper presents a cautionary case study in optimizer design for Fully Sharded Data Parallel (FSDP) training of transformer language models. While attempting to develop an improved optimizer compatible with FSDP constraints, we encountered fundamental limitations that prevented successful implementation of advanced techniques. Our final implementation, using layer-specific learning rates with AdamW, achieved a validation loss of 5.54, underperforming both the AdamW baseline (4.93) and state-of-the-art methods (3.81-4.55). We analyze the technical challenges of FSDP-compatible optimization and discuss implications for future research in distributed training optimization.
\end{abstract}

\section{Introduction}
The optimization of large language models presents unique challenges in distributed training environments. Fully Sharded Data Parallel (FSDP) training has emerged as a crucial technique for efficient distributed training, but imposes strict constraints on optimizer design. Our investigation reveals that many advanced optimization techniques prove incompatible with FSDP due to operations that cannot be properly sharded across devices.

This paper documents our unsuccessful attempt to develop an improved FSDP-compatible optimizer. While our initial goal was to outperform standard AdamW through layer-wise adaptation and gradient processing, technical constraints limited us to a basic implementation that ultimately underperformed the baseline. We present this negative result to:

\begin{itemize}
\item Document the challenges of FSDP-compatible optimizer design
\item Provide empirical evidence of performance trade-offs
\item Guide future research toward solvable problems in this space
\end{itemize}

\section{Related Work}
Recent work on optimizer design for transformers has focused on several key directions. The top-performing methods on our benchmark leaderboard employ techniques like orthogonal gradient processing \cite{2511.00018}, layer-wise adaptation \cite{2511.00047}, and momentum variants \cite{2510.00115}. However, as we discovered during our experimentation, these approaches often rely on operations like matrix orthogonalization that lack proper FSDP sharding strategies.

\begin{table}[t]
\centering
\caption{Benchmark results on Qwen 134M (lower is better)}
\label{tab:results}
\begin{tabular}{llr}
\toprule
Method & Reference & Validation Loss \\
\midrule
OrthoAdam & \cite{2511.00018} & 3.81 \\
StableAdam & \cite{2510.00111} & 3.89 \\
AdamW Baseline & - & 4.93 \\
Our Implementation & - & 5.54 \\
\bottomrule
\end{tabular}
\end{table}

\section{Method}
Our experimental setup used:
\begin{itemize}
\item Model: Qwen architecture with 134M parameters
\item Dataset: FineWeb (2.9B tokens)
\item Hardware: 8x A100 GPUs with FSDP
\item Training: 399 steps with batch size 4,194,304 tokens
\end{itemize}

We implemented a modified AdamW optimizer with:
\begin{itemize}
\item Layer-wise learning rates (attention: 0.012, MLP: 0.008, others: 0.01)
\item Conservative warmup (2000 steps)
\item Standard hyperparameters ($\beta_1=0.9$, $\beta_2=0.98$, weight decay=0.1)
\end{itemize}

Attempts to implement more sophisticated techniques (orthogonal gradient processing, adaptive momentum) failed due to FSDP compatibility issues with operations like matrix unbinding.

\section{Results and Discussion}
As shown in Table~\ref{tab:results}, our final implementation underperformed both the AdamW baseline and state-of-the-art methods. This negative result highlights several key challenges:

\begin{itemize}
\item FSDP compatibility severely restricts optimizer design options
\item Many advanced techniques require operations without sharding support
\item Simple modifications may not provide meaningful improvements
\end{itemize}

\section{Conclusion}
Our investigation reveals fundamental tensions between optimization sophistication and FSDP compatibility. While specialized optimizers achieve significantly better results, their techniques often prove incompatible with distributed training constraints. Future work should focus on:

\begin{itemize}
\item Developing FSDP-compatible implementations of advanced techniques
\item Creating standard benchmarks for FSDP optimizer evaluation
\item Exploring alternative distributed training approaches
\end{itemize}

This negative result serves as a cautionary tale and call to action for the community to address these fundamental limitations in distributed training optimization.

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