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arXiv 2312.06641cs.LGcs.SYeess.SY
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具有历史平均依赖成本的在线决策(扩展版)

Online Decision Making with History-Average Dependent Costs (Extended)

University of Illinois at Urbana–Champaign(伊利诺伊大学厄巴纳-香槟分校)

Vijeth Hebbar, Cedric Langbort

AI总结:

针对成本依赖历史决策时间平均的在线决策问题,提出FTARL算法,通过自适应正则化满足阶段式约束并证明紧致遗憾界,同时分析历史跨度影响及全跨度不可能性。

摘要:

在许多在线序贯决策场景中,学习者的选择不仅影响其当前成本,还会影响未来成本。在本工作中,我们考察此类情形的一个特定案例,其中成本依赖于过去决策在一个历史跨度内的时间平均。我们首先将这一具有历史依赖成本的问题重新表述为阶段式约束下的决策问题。为解决该问题,我们随后提出新颖的 Follow-The-Adaptively-Regularized-Leader(FTARL,跟随自适应正则化领导者)算法。我们的创新算法纳入了显式依赖于过去决策的自适应正则化项,使我们能够强制执行阶段式约束,同时建立紧致的遗憾界。我们还讨论了历史跨度长度对本问题无遗憾算法设计的影响,并给出当其为整个学习跨度时的不可能性结果。

英文摘要:

In many online sequential decision-making scenarios, a learner's choices affect not just their current costs but also the future ones. In this work, we look at one particular case of such a situation where the costs depend on the time average of past decisions over a history horizon. We first recast this problem with history dependent costs as a problem of decision making under stage-wise constraints. To tackle this, we then propose the novel Follow-The-Adaptively-Regularized-Leader (FTARL) algorithm. Our innovative algorithm incorporates adaptive regularizers that depend explicitly on past decisions, allowing us to enforce stage-wise constraints while simultaneously enabling us to establish tight regret bounds. We also discuss the implications of the length of history horizon on design of no-regret algorithms for our problem and present impossibility results when it is the full learning horizon.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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