We study the problem of making predictions so that downstream agents who best respond to them will be guaranteed diminishing swap regret, no matter what their utility functions are. It has been known since Foster and Vohra (1997) that agents who best-respond to calibrated forecasts have no swap regret. Unfortunately, the best known algorithms for guaranteeing calibrated forecasts in sequential adversarial environments do so at rates that degrade exponentially with the dimension of the prediction space. In this work, we show that by making predictions that are not calibrated, but are unbiased subject to a carefully selected collection of events, we can guarantee arbitrary downstream agents diminishing swap regret at rates that substantially improve over the rates that result from calibrated forecasts -- while maintaining the appealing property that our forecasts give guarantees for any downstream agent, without our forecasting algorithm needing to know their utility function. We give separate results in the ``low'' (1 or 2) dimensional setting and the ``high'' ($> 2$) dimensional setting. In the low dimensional setting, we show how to make predictions such that all agents who best respond to our predictions have diminishing swap regret -- in 1 dimension, at the optimal $O(\sqrt{T})$ rate. In the high dimensional setting we show how to make forecasts that guarantee regret scaling at a rate of $O(T^{2/3})$ (crucially, a dimension independent exponent), under the assumption that downstream agents smoothly best respond. Our results stand in contrast to rates that derive from agents who best respond to calibrated forecasts, which have an exponential dependence on the dimension of the prediction space.

翻译：我们研究预测问题，使得最优响应这些预测的下游智能体，无论其效用函数如何，都能保证具有递减的交换遗憾。自Foster和Vohra（1997）以来，已知最优响应校准预测的智能体没有交换遗憾。遗憾的是，在顺序对抗环境中保证校准预测的最著名算法，其速率随预测空间维度呈指数级下降。在本工作中，我们表明，通过做出并非校准、但针对精心选择的事件集合无偏的预测，可以保证任意下游智能体具有递减的交换遗憾，其速率相较于校准预测结果显著提升——同时保持一个吸引人的性质：我们的预测为任意下游智能体提供保证，且预测算法无需知晓其效用函数。我们分别给出“低维度”（1或2维）和“高维度”（>2维）设置下的结果。在低维度设置中，我们展示了如何做出预测，使得所有最优响应这些预测的智能体具有递减的交换遗憾——在1维情况下，达到最优的O(√T)速率。在高维度设置中，我们展示了如何做出预测，保证遗憾以O(T^{2/3})速率增长（关键在于，指数与维度无关），假设下游智能体平滑地最优响应。我们的结果与那些最优响应校准预测的智能体所得的速率形成对比，后者与预测空间维度呈指数依赖关系。