Transformer-based Model Predictive Control: Trajectory Optimization via Sequence Modeling

Transformer architecture and parameters

The transformer architecture proposed in this work is inspired by the DecisionTransformer architecture implemented in the HuggingFace library [1]. Our implementation can be found in the $\texttt{art.py}$ file in the $\texttt{decision transformer}$ folder of each specific scenario.

Parameter description	Value
Embedding dimension	$384$
Maximum context length	$100$
Number of layers	$6$
Number of attention heads	$6$
Batch size	$4$
Non-linearity	$\textrm{ReLU}$
Dropout	$0.1$
Learning rate	$3e^{-5}$
Learning rate decay	$\textrm{None}$
Gradient norm clip	$1.0$
Gradient accumulation iters	$8$

_{[1] “Huggingface’s Tranformers Library”, https://huggingface.co/docs/transformers/index.}

Open-loop training hyperparameters

Parameter description	Symbol	Value
Number of samples in the dataset	$N_d$	$400,000$
Number of REL solutions in the dataset	$N_{d_{REL}}$	$200,000$
Number of SCP solutions in the dataset	$N_{d_{SCP}}$	$200,000$
Train split (%)	-	$90$
Test split (%)	-	$10$

Closed-loop training hyperparameters

Parameter description	Symbol	Value
Interaction with the environment collected at each $\text{DA\small{GGER}}$ iteration	$\texttt{num trajectories}$	$4,000$
Possible values for the planning horizon for each interaction	$H$	$[10, 20, 30, 40, 50, 60, 70, 80, 90, 100]$
Initial open-loop to closed-loop ratio in the aggregated dataset	-	$9:1$
Train split (%)	-	$90$
Test split (%)	-	$10$