Blackwell's Approachability for Sequential Conformal Inference

The main problem this paper addresses is the challenge of maintaining both coverage and efficiency in sequential conformal inference, particularly in non-exchangeable environments. In traditional conformal inference, the data are assumed to be exchangeable, but this assumption often fails in real-world settings, such as time series forecasting, where the distribution of observations may shift over time.

The paper presents a novel approach to sequential conformal inference using Blackwell's theory of approachability. The key innovation is to recast adaptive conformal inference (ACI) as a repeated two-player vector-valued finite game and to design a calibration-based approachability strategy to achieve coverage and efficiency objectives.

This research has the potential to improve the performance of time series forecasting models and other sequential prediction tasks. By providing a framework for balancing coverage and efficiency in non-exchangeable environments, this work can help to develop more accurate and efficient prediction sets. This, in turn, can lead to better decision-making in various fields, such as finance, healthcare, and energy.

Imagine you're trying to predict the stock market's performance over the next few days. You want to make sure your predictions are accurate (coverage) and also want to minimize the uncertainty around your predictions (efficiency). In traditional conformal inference, you'd assume the market's behavior is consistent, but in reality, the market can be unpredictable and change over time. This paper's approach is like having a game plan that adapts to the market's behavior, ensuring you balance accuracy and efficiency while navigating the unpredictable market. --- This paper's key contributions are to formulate sequential conformal inference as a repeated two-player vector-valued finite game and to design a calibration-based approachability strategy that achieves coverage and efficiency objectives. By leveraging Blackwell's approachability theory, the authors provide a framework for balancing coverage and efficiency in non-exchangeable environments. This work has the potential to improve the performance of time series forecasting models and other sequential prediction tasks.