From b54a7c8218869acdd32545f4004847d8a1221fb5 Mon Sep 17 00:00:00 2001 From: Le-Brown Date: Wed, 5 Aug 2026 11:19:59 +0800 Subject: [PATCH 1/3] Fix pipe characters breaking display-math into a table MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Lines containing raw | inside a $$...$$ block (the KL conditioning bar "(cdot|s,a)", the "||" divergence notation, and "|Phi|" for the covering number) were being picked up by kramdown's table-row detection since they sat alone on their own line between blank lines. That split the formula's text across cells, so MathJax could no longer find a matching $$...$$ pair and the raw LaTeX source rendered as literal text in a broken table instead of a formula. Replaced literal | with \vert and || with \Vert (pure LaTeX commands, no raw pipe character in the source) — same visual output once MathJax renders it, but nothing left for kramdown's table detector to latch onto. Co-Authored-By: Claude Sonnet 5 --- _posts/2026-08-04-rombrl-post.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/_posts/2026-08-04-rombrl-post.md b/_posts/2026-08-04-rombrl-post.md index 090fdd5364..e4b6f7f8d7 100644 --- a/_posts/2026-08-04-rombrl-post.md +++ b/_posts/2026-08-04-rombrl-post.md @@ -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 \vert s,a) \,\Vert\, P_\phi(\cdot \vert s,a)\right) \right] \le \epsilon$$ (conservatism still matters offline, we're not letting the model run wild). The policy maximizes its return against the *worst* model in that set; the model adversarially minimizes it. @@ -60,9 +60,9 @@ The full algorithm, **ROMBRL**, is summarized in Appendix J of the paper. Theorem 3.1 gives a formal bound on the resulting policy's suboptimality gap, assuming the true environment lies in the uncertainty set $\Phi$ with probability at least $1 - \delta/2$: -$$J(\theta^{\ast}, \phi^{\ast}) - J(\hat\theta, \phi^{\ast}) \;\le\; \frac{\sqrt{C}}{(1-\gamma)^2} \sqrt{4\epsilon + c\left(\sqrt{\frac{\log(2|\Phi|/\delta)}{N}} + \frac{\log(2|\Phi|/\delta)}{N}\right)}$$ +$$J(\theta^{\ast}, \phi^{\ast}) - J(\hat\theta, \phi^{\ast}) \;\le\; \frac{\sqrt{C}}{(1-\gamma)^2} \sqrt{4\epsilon + c\left(\sqrt{\frac{\log(2\vert\Phi\vert/\delta)}{N}} + \frac{\log(2\vert\Phi\vert/\delta)}{N}\right)}$$ -where $N$ is the offline dataset size, $|\Phi|$ the covering number of the uncertainty set, $C$ a concentrability coefficient, and $\epsilon$ the uncertainty-set radius — so the gap shrinks as the dataset grows, giving a formal robustness guarantee rather than a purely heuristic one. Theorems 3.2 and 3.3 instantiate this bound for tabular MDPs and for continuous MDPs with Gaussian world models respectively, characterizing how $\epsilon$ should scale with dataset size and dimensionality. +where $N$ is the offline dataset size, $\vert\Phi\vert$ the covering number of the uncertainty set, $C$ a concentrability coefficient, and $\epsilon$ the uncertainty-set radius — so the gap shrinks as the dataset grows, giving a formal robustness guarantee rather than a purely heuristic one. Theorems 3.2 and 3.3 instantiate this bound for tabular MDPs and for continuous MDPs with Gaussian world models respectively, characterizing how $\epsilon$ should scale with dataset size and dimensionality. ## From MuJoCo to a Real Fusion Reactor From 0107e956f8d5e7eda40fe9c0f8f7a453369c13f7 Mon Sep 17 00:00:00 2001 From: Le-Brown Date: Wed, 5 Aug 2026 11:33:05 +0800 Subject: [PATCH 2/3] Add a portrait cover image for the ROMBRL blog post 2:3 abstract illustration (two glowing orbs in orbit, on a dark navy gradient) standing in for the paper's Stackelberg policy/world-model dynamic, without relying on literal diagram labels or paper figures (none of which are portrait-oriented). Set as the post's `image` frontmatter field, replacing the poster thumbnail. Co-Authored-By: Claude Sonnet 5 --- _posts/2026-08-04-rombrl-post.md | 2 +- images/rombrl-cover.png | Bin 0 -> 438879 bytes 2 files changed, 1 insertion(+), 1 deletion(-) create mode 100644 images/rombrl-cover.png diff --git a/_posts/2026-08-04-rombrl-post.md b/_posts/2026-08-04-rombrl-post.md index e4b6f7f8d7..ee0a654290 100644 --- a/_posts/2026-08-04-rombrl-post.md +++ b/_posts/2026-08-04-rombrl-post.md @@ -1,6 +1,6 @@ --- title: ROMBRL — Policy-Driven World Model Adaptation for Robust Offline Model-based RL (ICML 2026) -image: images/rombrl-poster.png +image: images/rombrl-cover.png author: Le Xu tags: publication offline-rl robustness model-based-rl redirect_from: diff --git a/images/rombrl-cover.png b/images/rombrl-cover.png new file mode 100644 index 0000000000000000000000000000000000000000..6b6e87512a860ce33c24b720521225c1792d7537 GIT binary patch literal 438879 zcmc$_cUV(h*C!lMEFi+I0)hf6BAQSX4816d2ndLnM(-%Smr#NQkS2oCn~H#>00BY? 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zWNXdsDIgYWZ19sCs3so5DL=VAN)Dcv*#oRq$s++%M*Jp{U7k*<6vzB-6T|1 Date: Wed, 5 Aug 2026 14:18:32 +0800 Subject: [PATCH 3/3] Replace cover image with final version Swap in the user-provided cover: a full Stackelberg maximin game diagram (offline dataset -> Policy/Leader <-> World Model/Follower under adversarial perturbation -> robust policy), replacing the earlier abstract two-orb illustration. 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