# Forecasting for Swap Regret for All Downstream Agents

arXiv: https://arxiv.org/abs/2402.08753 · HTML: https://mlsanity.com/paper/2402.08753/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 26 references that are in the map.
- First posted on arXiv 13 Feb 2024.

## Builds on (most cited first, 9 of 9)

- [Calibrating Predictions to Decisions: A Novel Approach to Multi-Class Calibration](https://mlsanity.com/paper/2107.05719/) (2021)
- [Omnipredictors](https://mlsanity.com/paper/2109.05389/) (2021)
- [Loss Minimization through the Lens of Outcome Indistinguishability](https://mlsanity.com/paper/2210.08649/) (2022)
- [U-Calibration: Forecasting for an Unknown Agent](https://mlsanity.com/paper/2307.00168/) (2023)
- [Stronger Calibration Lower Bounds via Sidestepping](https://mlsanity.com/paper/2012.03454/) (2020)
- [Calibrated Stackelberg Games: Learning Optimal Commitments Against Calibrated Agents](https://mlsanity.com/paper/2306.02704/) (2023)
- [Smooth Calibration, Leaky Forecasts, Finite Recall, and Nash Dynamics](https://mlsanity.com/paper/2210.07152/) (2022)
- [Multicalibrated Regression for Downstream Fairness](https://mlsanity.com/paper/2209.07312/) (2022)
- [Faster Recalibration of an Online Predictor via Approachability](https://mlsanity.com/paper/2310.17002/) (2023)

## Built on by (most cited first, 25 of 25)

- [Decision Theoretic Foundations for Conformal Prediction: Optimal Uncertainty Quantification for Risk-Averse Agents](https://mlsanity.com/paper/2502.02561/) (2025)
- [Full Swap Regret and Discretized Calibration](https://mlsanity.com/paper/2502.09332/) (2025)
- [Calibration Error for Decision Making](https://mlsanity.com/paper/2404.13503/) (2024)
- [High dimensional online calibration in polynomial time](https://mlsanity.com/paper/2504.09096/) (2025)
- [High-Dimensional Calibration from Swap Regret](https://mlsanity.com/paper/2505.21460/) (2025)
- [Can a calibration metric be both testable and actionable?](https://mlsanity.com/paper/2502.19851/) (2025)
- [Truthfulness of Calibration Measures](https://mlsanity.com/paper/2407.13979/) (2024)
- [Explaining and Improving Information Complementarities in Multi-Agent Decision-making](https://mlsanity.com/paper/2502.06152/) (2025)
- [Three Types of Calibration with Properties and their Semantic and Formal Relationships](https://mlsanity.com/paper/2504.18395/) (2025)
- [Learning and Computation of Phi-Equilibria at the Frontier of Tractability](https://mlsanity.com/paper/2502.18582/) (2025)
- [Improved Bounds for Swap Multicalibration and Swap Omniprediction](https://mlsanity.com/paper/2505.20885/) (2025)
- [Robust Decision Making with Partially Calibrated Forecasts](https://mlsanity.com/paper/2510.23471/) (2025)
- [Dimension-Free Decision Calibration for Nonlinear Loss Functions](https://mlsanity.com/paper/2504.15615/) (2025)
- [Online Omniprediction with Long-Term Constraints](https://mlsanity.com/paper/2509.11357/) (2025)
- [Testable and Actionable Calibration for Full Swap Regret](https://mlsanity.com/paper/2605.17749/) (2026)
- [Conformal Risk-Averse Decision Making with Action Conditional Guarantee](https://mlsanity.com/paper/2606.05551/) (2026)
- [Optimal Deterministic Multicalibration and Omniprediction](https://mlsanity.com/paper/2606.20557/) (2026)
- [Scalable Utility-Aware Multiclass Calibration](https://mlsanity.com/paper/2510.25458/) (2025)
- [Computational and Statistical Hardness of Calibration Distance](https://mlsanity.com/paper/2603.18391/) (2026)
- [Toward Simultaneously Optimal Regret in U-Calibration](https://mlsanity.com/paper/2606.18527/) (2026)
- [Dynamic Regret Bounds for Online Omniprediction with Long Term Constraints](https://mlsanity.com/paper/2510.07266/) (2025)
- [Prior-Agnostic Incentive-Compatible Exploration](https://mlsanity.com/paper/2602.20465/) (2026)
- [Improved Multi-Dimensional Forecasting for Swap Regret](https://mlsanity.com/paper/2606.29533/) (2026)
- [Dirichlet Follow-the-Leader Closes the Gap in Simultaneous Multiclass U-Calibration](https://mlsanity.com/paper/2608.06656/) (2026)
- [High-dimensional online calibration from harmonic weights](https://mlsanity.com/paper/2610.07740/) (2026)

## Abstract (arXiv)

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(√T) rate. In the high dimensional setting we show how to make forecasts that guarantee regret scaling at a rate of O(T2/3) (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.