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<h1 id="communication-scheme-message-passing">Communication scheme (Message Passing)</h1>
<p>Remember our research question:</p>
<blockquote>
<p>"What is the impact of different levels of controller modularity on learning speed, coordination, and fault tolerance
(e.g. amputations) in brittle-star-like robots trained with Reinforcement Learning?"</p>
</blockquote>
<p>To test decentralized modularity (such as arm-level or segment-level controllers), the various modules <em>must</em> be able to
communicate with each other to achieve coordinated locomotion. This is accomplished through <em>message passing</em> in a Graph
Neural Network (GNN)-like architecture. Two prominent communication styles from the literature are N-step NerveNet (Wang
et al., 2018) and bottom-up top-down Shared Modular Policies (Huang et al., 2020).</p>
<p>We have chosen to apply <strong>one uniform communication style</strong> across all modular architectures, specifically opting for
<strong>N-step NerveNet</strong>.</p>
<h2 id="rationale">Rationale</h2>
<p>Initially, our idea was to equip arm-level controllers with NerveNet message passing and segment-level controllers with
SMP. However, we evaluated that this introduces a threat to the validity of our research question. If we observe
differences in performance, it would be impossible to determine whether the variance is caused by the <em>level of
modularity</em>, or by the difference in the message passing scheme. To purely compare modularity, the communication scheme
style must remain constant.</p>
<p>Second, we decided that NerveNet is a better fit for our research. The morphology of our brittle star contains cycles at
the decentralized level (e.g., a ring of segments or arms around the body). NerveNet has proven to be robust for
arbitrary structures, including graphs with cycles. SMP inherently expects a tree structure for its bottom-up and
top-down pass. Applying SMP to a ring structure requires a workaround to break that cycle.</p>
<h2 id="limitations-and-alternatives">Limitations and alternatives</h2>
<p>Choosing NerveNet introduces a scalability issue as the morphology grows. In NerveNet, a message advances only one
segment or node per propagation step. When dealing with long arms (e.g., &gt; 5 segments), this requires a large number of
propagation steps to transmit information from one tip of an arm to another.</p>
<p>If we were to use SMP instead - which is possible - the inner states of nodes are shared across the entire graph in just
two passes. For very large or long morphologies, this would be much more scalable.</p>
<p>By rejecting SMP, we accept that our model might learn slower or require more computational power for highly segmented,
extended morphologies.</p>
<p><strong>References</strong></p>
<ul>
<li>Wang, Tingwu, Renjie Liao, Jimmy Ba, and S. Fidler. ‘NerveNet: Learning Structured Policy with Graph Neural Networks’. Conference paper presented at International Conference on Learning Representations. 15 February 2018. https://www.semanticscholar.org/paper/NerveNet:-Learning-Structured-Policy-with-Graph-Wang-Liao/249408527106d7595d45dd761dd53c83e5a02613.</li>
<li>Huang, Wenlong, Igor Mordatch, and Deepak Pathak. ‘One Policy to Control Them All: Shared Modular Policies for Agent-Agnostic Control’. arXiv:2007.04976. Preprint, arXiv, 9 July 2020. https://doi.org/10.48550/arXiv.2007.04976.</li>
</ul>
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