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Merge pull request #6 from arthbohra/ab/agent-arena
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prettier on extended arena
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infwinston authored Oct 9, 2024
2 parents 640cf64 + 78505bf commit 89e0c14
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2 changes: 1 addition & 1 deletion _posts/2024-09-30-extended-arena.md
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The Extended Online Arena Score amounts to running online logistic regression on the same feature set.
The algorithm is as follows:

$$ \theta^{(t+1)} = \theta^{(t)} - \eta \nabla \ell(\sigma(X_t^\top \theta^{(t)}), Y_t) - \lambda \nabla \|\theta^{(t)}\|_p,$$
$$ \theta^{(t+1)} = \theta^{(t)} - \eta \nabla \ell(\sigma(X_t^\top \theta^{(t)}), Y_t) - \lambda \nabla \|\theta^{(t)}\|\_p,$$

where $$\eta > 0$$ is the learning rate, and $$\nabla \|\cdot\|_p$$ is any valid subgradient of the $$\ell_p$$ norm.
The benefit, and drawback, of the online score is that it never converges.
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