We study a problem of designing replication-proof bandit mechanisms when
agents strategically register or replicate their own arms to maximize their
payoff. We consider Bayesian agents who are unaware of ex-post realization of
their own arms' mean rewards, which is the first to study Bayesian extension of
Shin et al. (2022). This extension presents significant challenges in analyzing
equilibrium, in contrast to the fully-informed setting by Shin et al. (2022)
under which the problem simply reduces to a case where each agent only has a
single arm. With Bayesian agents, even in a single-agent setting, analyzing the
replication-proofness of an algorithm becomes complicated. Remarkably, we first
show that the algorithm proposed by Shin et al. (2022), defined H-UCB, is no
longer replication-proof for any exploration parameters. Then, we provide
sufficient and necessary conditions for an algorithm to be replication-proof in
the single-agent setting. These results centers around several analytical
results in comparing the expected regret of multiple bandit instances, which
might be of independent interest. We further prove that exploration-then-commit
(ETC) algorithm satisfies these properties, whereas UCB does not, which in fact
leads to the failure of being replication-proof. We expand this result to
multi-agent setting, and provide a replication-proof algorithm for any problem
instance. The proof mainly relies on the single-agent result, as well as some
structural properties of ETC and the novel introduction of a restarting round,
which largely simplifies the analysis while maintaining the regret unchanged
(up to polylogarithmic factor). We finalize our result by proving its sublinear
regret upper bound, which matches that of H-UCB.

设计复制验证的赌博机制，分析 Bayesian 代理参与下的均值奖励，提供单个代理和多个代理情况下的复制验证算法及后悔上界。

可复制的赌徒机制设计

Replication-proof Bandit Mechanism Design

Pimentel et al. (2020) recently analysed probing from an
information-theoretic perspective. They argue that probing should be seen as
approximating a mutual information. This led to the rather unintuitive
conclusion that representations encode exactly the same information about a
target task as the original sentences. The mutual information, however, assumes
the true probability distribution of a pair of random variables is known,
leading to unintuitive results in settings where it is not. This paper proposes
a new framework to measure what we term Bayesian mutual information, which
analyses information from the perspective of Bayesian agents -- allowing for
more intuitive findings in scenarios with finite data. For instance, under
Bayesian MI we have that data can add information, processing can help, and
information can hurt, which makes it more intuitive for machine learning
applications. Finally, we apply our framework to probing where we believe
Bayesian mutual information naturally operationalises ease of extraction by
explicitly limiting the available background knowledge to solve a task.

该论文提出了一种名为贝叶斯互信息的新框架，它从贝叶斯代理的角度分析信息，使得在有限数据情况下处理可以帮助增加信息的同时也有可能削减信息，更加符合机器学习应用的直觉，最终将该框架运用到探针任务中，通过限制可用背景知识来实现抽取的易于性。

信息熵探测的贝叶斯框架

A Bayesian Framework for Information-Theoretic Probing

Cooperation is often implicitly assumed when learning from other agents.
Cooperation implies that the agent selecting the data, and the agent learning
from the data, have the same goal, that the learner infer the intended
hypothesis. Recent models in human and machine learning have demonstrated the
possibility of cooperation. We seek foundational theoretical results for
cooperative inference by Bayesian agents through sequential data. We develop
novel approaches analyzing consistency, rate of convergence and stability of
Sequential Cooperative Bayesian Inference (SCBI). Our analysis of the
effectiveness, sample efficiency and robustness show that cooperation is not
only possible in specific instances but theoretically well-founded in general.
We discuss implications for human-human and human-machine cooperation.

研究了合作推理的基础理论，提出了一种新方法 SCBI 来分析一致性，收敛率和稳定性，并表明合作对于特定情况不仅是可能的，而且从理论上讲在一般情况下也是可行的，以及探讨了人类之间和人机之间合作的意义。

顺序协作贝叶斯推理

Sequential Cooperative Bayesian Inference

We study the problem of eliciting and aggregating probabilistic information
from multiple agents. In order to successfully aggregate the predictions of
agents, the principal needs to elicit some notion of confidence from agents,
capturing how much experience or knowledge led to their predictions. To
formalize this, we consider a principal who wishes to elicit predictions about
a random variable from a group of Bayesian agents, each of whom have privately
observed some independent samples of the random variable, and hopes to
aggregate the predictions as if she had directly observed the samples of all
agents. Leveraging techniques from Bayesian statistics, we represent confidence
as the number of samples an agent has observed, which is quantified by a
hyperparameter from a conjugate family of prior distributions. This then allows
us to show that if the principal has access to a few samples, she can achieve
her aggregation goal by eliciting predictions from agents using proper scoring
rules. In particular, if she has access to one sample, she can successfully
aggregate the agents' predictions if and only if every posterior predictive
distribution corresponds to a unique value of the hyperparameter. Furthermore,
this uniqueness holds for many common distributions of interest. When this
uniqueness property does not hold, we construct a novel and intuitive mechanism
where a principal with two samples can elicit and optimally aggregate the
agents' predictions.

该研究探讨了从多个代理中收集和聚合概率信息的问题，通过使用贝叶斯统计学的技术，将信心表示为代理观察到的样本数量，进而使用适当的评分规则收集代理的预测，实现了基于少量样本的聚合。