` 包裹。长文用 `
`/`
` 划分小节。（文本是一段引言/摘要，可能只需要 `
`，或者也许我应该把它看作是需要少量结构的“长文”？让我们仔细看看文本。它是一段连续的文本，没有明显的章节划分。我将只用 `
` 包裹整个段落，或者也许将第一句作为引言？实际上，规则说“每个自然段落用 `
` 包裹”。这里的文本只是一个自然段落。所以我将用一个 `
` 包裹整个文本。等等，有没有子部分？它从背景/动机过渡到先前的工作，再到本文的贡献，最后到算法机制。我可以将其拆分以获得更好的语义，但规则 4 说“保留原文所有信息，不得增删改内容”。拆分句子是可以的，但不应改变文本。为了安全且严格遵循“每个自然段落用 `
` 包裹”，我将仅使用一个 `
` 标签，或者如果我觉得需要标题，也许可以为“引言”使用一个 `
`，但提示词没有提供标题。我将坚持仅使用 `
` 来代表该段落。） * 规则 3： 列表内容用 `
- `，引用用 `
`，代码用 `
`，重要句子可用 ``。 * 规则 4： 保留原文所有信息，不得增删改内容。（这是一个严格的约束。我必须逐字复制文本，只添加 HTML 标签。数学公式 `$H$`、`$\widetilde{O}(K^{2/3})$` 等必须保留原样，因为提示词没有要求转换为 MathJax 或 HTML 实体，只是“保留原文所有信息”。等等，如果文本是纯文本，我将直接逐字复制它。） * 规则 5： 不要输出 ``、``、`` 等文档级标签。 3. 详细分析文本： * "We study online learning in two-player uninformed Markov games, where the opponent may follow an arbitrary, unknown policy in each episode and the learner does not observe the opponent's actions."（第 1 句：问题设定。） * "[TWYS21] showed that achieving sublinear external regret requires an exponential dependence on the episode length $H$."（第 2 句：[TWYS21] 的发现。） * "Motivated by this limitation, they studied the weaker notion of Nash-value regret and obtained an $\widetilde{O}(K^{2/3})$ regret bound, where $K$ is the number of episodes."（第 3 句：[TWYS21] 的贡献。） * "More recently, [LLZR26] introduced a stronger notion called empirical Nash-value regret and achieved an $\widetilde{O}(\sqrt{K})$ bound when the opponent's non-stationarity is moderate, including the case where the opponent follows a fixed policy."（第 4 句：[LLZR26] 的贡献。） * "However, whether the $\sqrt{K}$ rate is achievable in the worst case remained open."（第 5 句：开放问题。） * "In this paper, we resolve this open question by developing an algorithm that achieves $\widetilde{O}(H^{3/2}S\sqrt{AK})$ empirical Nash-value regret against arbitrary opponent policies, where $S$ is the number of states and $A$ is the number of learner's actions."（第 6 句：本文贡献/主要结果。这里很适合使用 ``。） * "Specifically, our algorithm combines global and local planning by maintaining a collection of candidate predictions of future losses, each associated with a policy."（第 7 句：算法机制。） * "Global planning learns which candidates to favor across episodes, while local planning combines their policies differently at each state to make decisions."（第 8 句：全局与局部规划。） * "A key ingredient is to coordinate these two components to control the discrepancy between local loss estimates and the total loss of the executed policy, using only the learner's observed trajectories."（第 9 句：关键成分。） 4. 起草 HTML： * 文本是一个连续的段落。我将用 `` 包裹整个段落。 * 我可以在某处使用 `` 吗？规则说“重要句子可用 ``”。第 6 句是主要贡献：“In this paper, we resolve this open question by developing an algorithm that achieves $\widetilde{O}(H^{3/2}S\sqrt{AK})$ empirical Nash-value regret against arbitrary opponent policies, where $S$ is the number of states and $A$ is the number of learner's actions.” 我将把这句包裹在 `` 中。 * 有引用吗？没有。 * 有列表吗？没有。 * 有代码吗？没有。 * 我需要 `
` 或 `
` 吗？提示词说“长文用 `
`/`
` 划分小节”。这段文本很短（一段）。如果我只使用 `
`，这是可以接受的。如果我想过度设计，我可以添加一个 `
`，比如“Introduction”，但这会“增”加内容，违反了规则 4（“不得增删改内容”）。所以严格来说，没有标题。 5. 优化 HTML 结构： * 让我们再次检查确切的文本，以确保逐字匹配。 * "We study online learning in two-player uninformed Markov games, where the opponent may follow an arbitrary, unknown policy in each episode and the learner does not observe the opponent's actions. [TWYS21] showed that achieving sublinear external regret requires an exponential dependence on the episode length $H$. Motivated by this limitation, they studied the weaker notion of Nash-value regret and obtained an $\widetilde{O}(K^{2/3})$ regret bound, where $K$ is the number of episodes. More recently, [LLZR26] introduced a stronger notion called empirical Nash-value regret and achieved an $\widetilde{O}(\sqrt{K})$ bound when the opponent's non-stationarity is moderate, including the case where the opponent follows a fixed policy. However, whether the $\sqrt{K}$ rate is achievable in the worst case remained open. " * "In this paper, we resolve this open question by developing an algorithm that achieves $\widetilde{O}(H^{3/2}S\sqrt{AK})$ empirical Nash-value regret against arbitrary opponent policies, where $S$ is the number of states and $A$ is the number of learner's actions." * "Specifically, our algorithm combines global and local planning by maintaining a collection of candidate predictions of future losses, each associated with a policy. Global planning learns which candidates to favor across episodes, while local planning combines their policies differently at each state to make decisions. A key ingredient is to coordinate these two components to control the discrepancy between local loss estimates and the total loss of the executed policy, using only the learner's observed trajectories." * 等等，如果我把第 6 句包裹在 `` 中，它会打断 `
` 标签吗？不会，`` 是一个行内元素。 * 让我们构建 `
` 标签。 `
We study online learning... remained open. In this paper, we resolve... learner's actions. Specifically, our algorithm... observed trajectories.
` * 让我重读一下规则 2：“每个自然段落用 `` 包裹，长文用 `
`/`
` 划分小节”。文本只有一个自然段落。所以用一个 `
` 包裹是正确的。 * 规则 3：“重要句子可用 ``”。第 6 句是摘要中最重要的句子（主要结果）。我将对它使用 ``。 6. 对照约束进行最终检查： * 仅输出 HTML 片段？是的。 * 无