arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2302.06014cs.LGcs.GTcs.IR

具有折扣自适应偏好的智能体在线推荐

Online Recommendations for Agents with Discounted Adaptive Preferences

Arpit Agarwal, William Brown

AI总结:

本文研究具有折扣自适应偏好的智能体在线推荐问题,提出在长期和短期记忆机制下针对平滑或尺度有界偏好模型实现高效次线性遗憾的算法,并证明扩展目标的NP困难性及信息论障碍。

摘要:

我们考虑一个多臂老虎机推荐问题,其中智能体的偏好(表示对推荐物品的选择概率)根据未知的偏好模型,作为过去选择结果的函数而演化。在每一轮中,我们向智能体展示一个包含 $k$ 个物品(总共 $n$ 个)的菜单,智能体随后选择一个物品,我们的目标是在智能体选择的对抗性损失下,相对于某个目标集合(物品单纯形的一个子集)最小化遗憾。我们扩展了 Agarwal 和 Brown (2022) 的设置,该设置考虑均匀记忆的智能体,这里我们允许非均匀记忆,其中在每个后续轮次对智能体的记忆向量应用一个折扣因子。在“长期记忆”机制下(当有效记忆视界随 $T$ 次线性增长时),我们证明对于任何平滑偏好模型,相对于每个位置瞬时可实现分布集合(即先前工作中提出的“EIRD 集合”),可以获得高效的次线性遗憾。此外,对于偏好被记忆权重的线性函数上下界所限制(我们称之为“尺度有界”偏好)的情况,我们给出了一种算法,该算法相对于几乎整个物品单纯形获得高效的次线性遗憾。我们证明了在一般情况下将目标扩展到 EIRD 之外是 NP 困难的。在“短期记忆”机制下(当记忆视界为常数时),我们表明,如果损失变化不频繁,即使没有平滑性,尺度有界偏好也能对几乎整个单纯形实现高效的次线性遗憾;然而,我们证明了在任意平滑偏好模型下,即使损失是恒定的,与 EIRD 集合竞争也存在信息论障碍。

英文摘要:

We consider a bandit recommendations problem in which an agent's preferences (representing selection probabilities over recommended items) evolve as a function of past selections, according to an unknown $\textit{preference model}$. In each round, we show a menu of $k$ items (out of $n$ total) to the agent, who then chooses a single item, and we aim to minimize regret with respect to some $\textit{target set}$ (a subset of the item simplex) for adversarial losses over the agent's choices. Extending the setting from Agarwal and Brown (2022), where uniform-memory agents were considered, here we allow for non-uniform memory in which a discount factor is applied to the agent's memory vector at each subsequent round. In the "long-term memory" regime (when the effective memory horizon scales with $T$ sublinearly), we show that efficient sublinear regret is obtainable with respect to the set of $\textit{everywhere instantaneously realizable distributions}$ (the "EIRD set", as formulated in prior work) for any $\textit{smooth}$ preference model. Further, for preferences which are bounded above and below by linear functions of memory weight (we call these "scale-bounded" preferences) we give an algorithm which obtains efficient sublinear regret with respect to nearly the $\textit{entire}$ item simplex. We show an NP-hardness result for expanding to targets beyond EIRD in general. In the "short-term memory" regime (when the memory horizon is constant), we show that scale-bounded preferences again enable efficient sublinear regret for nearly the entire simplex even without smoothness if losses do not change too frequently, yet we show an information-theoretic barrier for competing against the EIRD set under arbitrary smooth preference models even when losses are constant.

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。

↑