We study a generalization of the online binary prediction with expert advice
framework where at each round, the learner is allowed to pick $m\geq 1$ experts
from a pool of $K$ experts and the overall utility is a modular or submodular
function of the chosen experts. We focus on the setting in which experts act
strategically and aim to maximize their influence on the algorithm's
predictions by potentially misreporting their beliefs about the events. Among
others, this setting finds applications in forecasting competitions where the
learner seeks not only to make predictions by aggregating different forecasters
but also to rank them according to their relative performance. Our goal is to
design algorithms that satisfy the following two requirements: 1)
$\textit{Incentive-compatible}$: Incentivize the experts to report their
beliefs truthfully, and 2) $\textit{No-regret}$: Achieve sublinear regret with
respect to the true beliefs of the best fixed set of $m$ experts in hindsight.
Prior works have studied this framework when $m=1$ and provided
incentive-compatible no-regret algorithms for the problem. We first show that a
simple reduction of our problem to the $m=1$ setting is neither efficient nor
effective. Then, we provide algorithms that utilize the specific structure of
the utility functions to achieve the two desired goals.

本文研究了一种在线学习算法，该算法将多个专家的预测结果融合为一个预测结果以提高准确性，并利用特定结构的效用函数设计了激励兼容性和无悔策略两个要求的算法，以应对专家可能误导算法的情况。

具有战略专家的无悔在线预测

No-Regret Online Prediction with Strategic Experts

We initiate the study of incentive-compatible forecasting competitions in
which multiple forecasters make predictions about one or more events and
compete for a single prize. We have two objectives: (1) to incentivize
forecasters to report truthfully and (2) to award the prize to the most
accurate forecaster. Proper scoring rules incentivize truthful reporting if all
forecasters are paid according to their scores. However, incentives become
distorted if only the best-scoring forecaster wins a prize, since forecasters
can often increase their probability of having the highest score by reporting
more extreme beliefs. In this paper, we introduce two novel forecasting
competition mechanisms. Our first mechanism is incentive compatible and
guaranteed to select the most accurate forecaster with probability higher than
any other forecaster. Moreover, we show that in the standard single-event,
two-forecaster setting and under mild technical conditions, no other
incentive-compatible mechanism selects the most accurate forecaster with higher
probability. Our second mechanism is incentive compatible when forecasters'
beliefs are such that information about one event does not lead to belief
updates on other events, and it selects the best forecaster with probability
approaching 1 as the number of events grows. Our notion of incentive
compatibility is more general than previous definitions of dominant strategy
incentive compatibility in that it allows for reports to be correlated with the
event outcomes. Moreover, our mechanisms are easy to implement and can be
generalized to the related problems of outputting a ranking over forecasters
and hiring a forecaster with high accuracy on future events.

本研究旨在通过引入两种新的预测竞赛机制，提高预测者的准确性，避免预测者为赢得比赛而夸大预测结果，并使预测者的报告与事件结果相对应。