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Drop \! spacing command from the KL formula #3

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Merged
Le-Brown merged 1 commit into from
Aug 5, 2026
Merged

Drop \! spacing command from the KL formula #3

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2 changes: 1 addition & 1 deletion _posts/2026-08-04-rombrl-post.md
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Expand Up @@ -44,7 +44,7 @@ $$\max_\theta J(\theta, \phi') \quad \text{s.t.} \quad \phi' \in \arg\min_{\phi

where $\Phi$ is an uncertainty set of world models $\phi \in \mathcal{M}$ anchored to the maximum-likelihood estimate $\hat\phi$ — a KL trust region around what the offline data actually supports:

$$\mathbb{E}_{(s,a)\sim\mathcal{D}}\left[ \mathrm{KL}\!\left(P_{\hat\phi}(\cdot|s,a) \,\|\, P_\phi(\cdot|s,a)\right) \right] \le \epsilon$$
$$\mathbb{E}_{(s,a)\sim\mathcal{D}}\left[ \mathrm{KL}\left(P_{\hat\phi}(\cdot|s,a) \,\|\, P_\phi(\cdot|s,a)\right) \right] \le \epsilon$$

(conservatism still matters offline, we're not letting the model run wild). The policy maximizes its return against the *worst* model in that set; the model adversarially minimizes it.

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